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Your time is up. Thank you for doing this online test.

Remember the Academic Learning Centre provides free maths support. Check out room D259.

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You have 5 minutes remaining.

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Integer Multiplication, Order of operations, working with fractions, decimal places, significant figures

rebel

rebelmaths

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Part 1:

i) $\\var{numberlow[0]} \\times \\var{numberlow[1]} + \\var{numberlow[2]} = \\var{ans1}$

ii) $\\var{numberlow[0]} \\times (\\var{numberlow[1]} + \\var{numberlow[2]}) = \\var{ans2}$

iii) $\\var{num3b} - \\var{num3a} \\div \\var{numberlow[5]} = \\var{ans3}$

iv) $\\var{numberlow[8]} + \\var{numberlow[4]} \\times (\\var{numberlow[3]} + \\var{numsq[0]}) = \\var{ans4}$

v) $(\\var{numberlow[1]} + \\var{numberlow[7]}) \\times \\var{numberlow[8]} + \\var{numsq[1]} = \\var{ans5}$

vi) $\\var{numberlow[6]} + \\var{numberlow[0]}^2 \\times \\var{numsq[0]} = \\var{ans6}$

vii) $\\var{numberlow[4]} \\times \\var{numberlow[9]} - \\var{numsq1} \\div \\var{numberlow[2]} = \\var{ans7}$

viii) $(\\var{numsq2[1]} - \\var{numsq[1]})^2 = \\var{ans8}$

ix) $(\\var{numsq2[0]} - \\var{numsq[0]})^2 * \\var{numsq3} \\div \\var{numberlow[6]} = \\var{ans9}$

x) $\\var{numsq2[1]} \\times \\var{numsq[0]}^2 - \\var{numsq4} \\div \\var{numberlow[3]} = \\var{ans10}$

", "rulesets": {}, "parts": [{"prompt": "

$\\var{numberlow[0]} \\times \\var{numberlow[1]} + \\var{numberlow[2]}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{numberlow[7]} \\times (\\var{numberlow[3]} + \\var{numberlow[6]})$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{num3b} - \\var{num3a} \\div \\var{numberlow[5]}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{numberlow[8]} + \\var{numberlow[4]} \\times (\\var{numberlow[3]} + \\var{numsq[0]})$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$(\\var{numberlow[1]} + \\var{numberlow[7]}) \\times \\var{numberlow[8]} + \\var{numsq[1]}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans5}", "minValue": "{ans5}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{numberlow[6]} + \\var{numberlow[0]}^2 \\times \\var{numsq[0]}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans6}", "minValue": "{ans6}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{numberlow[4]} \\times \\var{numberlow[9]} - \\var{numsq1} \\div \\var{numberlow[2]}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans7}", "minValue": "{ans7}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$(\\var{numsq2[1]} - \\var{numsq[1]})^2$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans8}", "minValue": "{ans8}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$(\\var{numsq2[0]} - \\var{numsq[0]})^2 \\times \\var{numsq3} \\div \\var{numberlow[6]}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans9}", "minValue": "{ans9}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{numsq2[1]} \\times \\var{numsq[0]}^2 - \\var{numsq4} \\div \\var{numberlow[3]}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans10}", "minValue": "{ans10}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "

Evaluate each of the following, without using a calculator, to 2 decimal places:

Remember the BODMAS rule

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"ans8": {"definition": "(numsq2[1] - numsq[1])^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans8", "description": ""}, "ans9": {"definition": "(numsq2[0] - numsq[0])^2 * {numsq3} / numberlow[6]\n ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans9", "description": ""}, "numberlow": {"definition": "shuffle(1..12)[0..12]", "templateType": "anything", "group": "Ungrouped variables", "name": "numberlow", "description": ""}, "ans1": {"definition": "numberlow[0] * numberlow[1] + numberlow[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "numberlow[7] * (numberlow[3] + numberlow[6])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "{num3b} - {num3a} / numberlow[5]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "numberlow[8] + numberlow[4] * (numberlow[3] + {numsq[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "num3a": {"definition": "numberlow[5] * numberlow[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "num3a", "description": ""}, "num3b": {"definition": "{num3a} + {numberhigh}", "templateType": "anything", "group": "Ungrouped variables", "name": "num3b", "description": ""}, "ans5": {"definition": "(numberlow[1] + numberlow[7]) * numberlow[8] + numsq[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5", "description": ""}, "numberhigh": {"definition": "random(18..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberhigh", "description": ""}, "ans10": {"definition": "numsq2[1] * numsq[0]^2 - {numsq4} / numberlow[3]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans10", "description": ""}, "ans6": {"definition": "numberlow[6] + numberlow[0]^2 * numsq[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6", "description": ""}, "numsq": {"definition": "shuffle(2..3)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "numsq", "description": ""}, "numsq4": {"definition": "numberlow[3] * numsq[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "numsq4", "description": ""}, "ans7": {"definition": "numberlow[4] * numberlow[9] - {numsq1} / numberlow[2]\n", "templateType": "anything", "group": "Ungrouped variables", "name": "ans7", "description": ""}, "numsq2": {"definition": "shuffle(4..6)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "numsq2", "description": ""}, "numsq3": {"definition": "numberlow[6] * numsq[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "numsq3", "description": ""}, "numsq1": {"definition": "numberlow[2] * numsq[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "numsq1", "description": ""}}, "metadata": {"description": "

rebelmaths

N.B. Rules

$(+) \\times (+) = (+)$

$(+) \\times (-) = (-)$

$(-) \\times (+) = (-)$

$(-) \\times (-) = (+)$

(-(-a)) = (a) e.g $(-(-5)) = 5$

(+(-a)) or (-(+a)) = (-a) e.g $(+(-5)) = 5$ or $(-(+5)) = 5$

If both numbers are negative, keep the minus sign and add the numbers e.g

$\\var{g2} - \\var{g1} = \\var{ans7}$

If the numbers have different signs, keep the sign of the bigger number abd subtract the smaller number from it e.g

$-15 + 20 = 5$ or $20 - 15 = 5$

", "rulesets": {}, "parts": [{"prompt": "

$(\\var{a1}) \\times (\\var{a2})$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{b1} \\times (\\var{b2})$

[[0]]

$\\var{c1} \\times \\var{c2}$

[[0]]

$(\\var{d1}) \\times (\\var{d2})$

[[0]]

$\\var{e1} \\div \\var{e2}$

[[0]]

$\\var{f1} \\div (\\var{f2})$

[[0]]

$\\var{g2} - \\var{g1}$

[[0]]

$\\var{h1} - (\\var{h2})$

[[0]]

$\\var{i1} + (\\var{i2}) - \\var{i3}$

[[0]]

$\\var{j1} - (\\var{j2}) - (\\var{j3})$

[[0]]

Evaluate each of the following, without using a calculator, to 2 decimal places:

N.B. Rules

$(+) \\times (+) = (+)$

$(+) \\times (-) = (-)$

$(-) \\times (+) = (-)$

$(-) \\times (-) = (+)$

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"Ans3": {"definition": "{c1}*{c2}", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans3", "description": ""}, "Ans5": {"definition": "random(-8..-3)", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans5", "description": ""}, "b1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "Ans7": {"definition": "g2-g1", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans7", "description": ""}, "G2": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "G2", "description": ""}, "G1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "G1", "description": ""}, "I1": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "I1", "description": ""}, "I3": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "I3", "description": ""}, "I2": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "I2", "description": ""}, "A1": {"definition": "(neg())", "templateType": "anything", "group": "Ungrouped variables", "name": "A1", "description": ""}, "Ans10": {"definition": "{j1} - {j2} - {j3}", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans10", "description": ""}, "C2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "C2", "description": ""}, "C1": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "C1", "description": ""}, "E1": {"definition": "ans5*e2", "templateType": "anything", "group": "Ungrouped variables", "name": "E1", "description": ""}, "E2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "E2", "description": ""}, "F1": {"definition": "ans6*f2", "templateType": "anything", "group": "Ungrouped variables", "name": "F1", "description": ""}, "a2": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "Ans6": {"definition": "random(4..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans6", "description": ""}, "Ans8": {"definition": "{h1} - {h2}", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans8", "description": ""}, "Ans9": {"definition": "{i1} + {i2} - {i3}", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans9", "description": ""}, "F2": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "F2", "description": ""}, "H2": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "H2", "description": ""}, "Ans1": {"definition": "{a1}*{a2}", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans1", "description": ""}, "Ans2": {"definition": "{b1}*{b2}", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans2", "description": ""}, "H1": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "H1", "description": ""}, "Ans4": {"definition": "{d1}*{d2}", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans4", "description": ""}, "J1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "J1", "description": ""}, "J2": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "J2", "description": ""}, "J3": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "J3", "description": ""}, "B2": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "B2", "description": ""}, "D2": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "D2", "description": ""}, "D1": {"definition": "neg()", "templateType": "anything", "group": "Ungrouped variables", "name": "D1", "description": ""}}, "metadata": {"description": "

rebelmaths

N.B. Rules

$(+) \\times (+) = (+)$

$(+) \\times (-) = (-)$

$(-) \\times (+) = (-)$

$(-) \\times (-) = (+)$

(-(-a)) = (a) e.g $(-(-5)) = 5$

(+(-a)) or (-(+a)) = (-a) e.g $(+(-5)) = 5$ or $(-(+5)) = 5$

If both numbers are negative, keep the minus sign and add the numbers e.g

$(-9) + (-4)= -13$

If the numbers have different signs, keep the sign of the bigger number abd subtract the smaller number from it e.g

$-15 + 20 = 5$ or $20 - 15 = 5$

", "rulesets": {}, "parts": [{"prompt": "

$\\var{a1} \\times \\var{a2} - \\var{a3} \\times \\var{a4}$

[[0]]

$\\var{b1} + \\var{b2} \\div (\\var{b3}) + \\var{b4} \\times \\var{b5}$

[[0]]

$(\\var{c1} - \\var{c2}) \\times \\var{c3} - (\\var{c4} - \\var{c5})^2$

[[0]]

$(\\var{d1})^3 - (\\var{d2})^2 + (\\var{d3})^2$

[[0]]

$(\\var{e1})^2 - (\\var{e2})^3 - (\\var{e3})^3$

[[0]]

Evaluate the following to the nearest whole number, without using a calculator:

N.B. Rules

$(+) \\times (+) = (+)$

$(+) \\times (-) = (-)$

$(-) \\times (+) = (-)$

$(-) \\times (-) = (+)$

Remember the BODMAS rule

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rebelmaths

What's $\\frac {\\var{num}} {\\var{denom} }$ in its simplest form (please enter your answer in the form a/b)? Answer: [[0]]

\n ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "\n

You need to find a number that divides exactly into $\\var{num}$ and $\\var{denom}$ (a \"common factor\").

When you've found one, you can simplify the fraction $\\frac {\\var{num}} {\\var{denom}}$ by dividing $\\var{num}$ and $\\var{denom}$ by the common factor.

Carry on until there aren't any more common factors..

\n ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{simplenum}/{simpledenom}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "

You shouldn't need a calculator for these...

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"perc": {"definition": "simplenum*100/simpledenom", "templateType": "anything", "group": "Ungrouped variables", "name": "perc", "description": ""}, "num1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "simplenum": {"definition": "num/gcd(num,denom)", "templateType": "anything", "group": "Ungrouped variables", "name": "simplenum", "description": ""}, "num": {"definition": "if(num2rebelmaths

Remember the order of operations

B Brackets

O pOwers

D Division

M Multiplication

A Addition

S Subtraction

First do the calculations $\\displaystyle \\simplify[all,!simplifyFractions]{{a4}/{a5}={a4/a5}}$ and $\\simplify[all,!collectNumbers]{{a2}*{a3}={a2*a3}}$.

and then we get

\\[\\begin{align} \\simplify[all,!collectNumbers,!simplifyFractions]{{a1}+ {a2}{a3}+{a4}/{a5}}&=\\simplify[all,!collectNumbers,!simplifyFractions]{{a1}+ {a2*a3}+{a4/a5}}\\\\&=\\var{ans1}\\end{align}\\]

First do the calculations $\\displaystyle \\simplify[all,!collectNumbers,!simplifyFractions]{{b1}/{b2}={b1/b2}} \\text{ and } \\simplify[all,!collectNumbers]{{b3}({b4}+{b5})={b3}{b4+b5}={b3*(b4+b5)}}$

and then we get

\\[\\begin{align} \\simplify[all,!collectNumbers,!simplifyFractions]{{b1}/{b2}+{b3}*({b4}+{b5}){b6}+{b7}}&=\\simplify[all,!collectNumbers]{{b1/b2}+{b3*(b4+b5)}+{b7}}\\\\&=\\var{ans2}\\end{align}\\]

First do the calculations $\\displaystyle \\simplify[all,!collectNumbers,!simplifyFractions]{({c4}+{c5})/{c6}={c4+c5}/{c6}={(c4+c5)/c6}} \\text{ and } \\simplify[all,!collectNumbers]{{c1}({c2}+{c3})={c1}{c2+c3}={c1*(c2+c3)}}$

and then we get

\\[\\begin{align} \\simplify[all,!collectNumbers,!simplifyFractions]{{c1}*({c2}+{c3})+({c4}+{c5})/{c6}}&=\\simplify[all,!collectNumbers]{{c1*(c2+c3)}+{(c4+c5)/c6}}\\\\&=\\var{ans3}\\end{align}\\]

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$\\displaystyle \\simplify[all,!collectNumbers,!simplifyFractions]{{a1}+ {a2}{a3}+{a4}/{a5}}=\\;$[[0]]

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$\\displaystyle \\simplify[all,!simplifyFractions,!collectNumbers]{{b1}/{b2}+{b3}({b4}+{b5}){b6}+{b7}}=\\;$[[0]]

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$\\displaystyle \\simplify[all,!collectNumbers,!simplifyFractions]{{c1}({c2}+{c3})+({c4}+{c5})/{c6}}=\\;$[[0]]

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Use the correct order of operations to calculate the following

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Order of Operations

rebelmaths

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When adding and/or subtracting fractions, do the following;

First make sure the number is a fraction, including an improper fraction i.e. $1\\frac{2}{3} = \\frac{5}{3}$

Find the lowest common multiply of the denominator i.e. $\\frac{5}{3} + \\frac{1}{2} = \\frac{}{6}$

Next, transform each number into the form of the LCM i.e. $\\frac{5}{3} + \\frac{1}{2} = \\frac{10}{6} + \\frac{3}{6}$

Add/subtract the numbers above the denominator i.e. $\\frac{10}{6} + \\frac{3}{6} = \\frac{10 + 3}{6} = \\frac{13}{6} = 2\\frac{1}{6}$

When multipling fractions, multipy the numbers above the line by each other and then the numbers below the line by each other i.e.

$\\frac{5}{3} \\times \\frac{1}{4} = \\frac{5}{12}$

If possible simplify the answer i.e.

$\\frac{5}{3} \\times \\frac{1}{5} = \\frac{5}{15} = \\frac{1}{3}$

If no than 2 fractions follow the same rules:

i.e. $\\frac{5}{3} \\times \\frac{1}{4} \\times \\frac{2}{5} \\times \\frac{3}{2} = \\frac{30}{120} = \\frac{1}{4}$

When dividing fractions, invert the divisor and then follow the rules for multiplying fractions (multipy the numbers above the line by each other and then the numbers below the line by each other) i.e.

$\\frac{5}{3} \\div \\frac{3}{4} = \\frac{5}{3} \\times \\frac{4}{3} = \\frac{20}{9}$

If possible simplify the answer i.e.

$\\frac{5}{3} \\div \\frac{4}{21} = \\frac{5}{3} \\times \\frac{21}{4} = \\frac{105}{12} = \\frac{35}{4} = 8\\frac{3}{4}$

If no than 2 fractions follow the same rules:

i.e. $\\frac{5}{3} \\div \\frac{1}{4} \\div \\frac{2}{5} \\div \\frac{3}{2} = \\frac{5}{3} \\times \\frac{4}{1} \\times \\frac{5}{2} \\times \\frac{2}{3} = \\frac{200}{18} = \\frac{100}{9} = 11\\frac{1}{9}$

$\\frac{5}{3} \\div \\frac{1}{4} \\times \\frac{2}{7} = \\frac{5}{3} \\times \\frac{4}{1} \\times \\frac{2}{7} = \\frac{40}{21} = 1\\frac{19}{20}$

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$\\simplify{{a2}/{a1}} + \\simplify{{a4}/{a3}} - \\simplify{{a6}/{a5}}$

[[0]][[1]]

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$\\var{b1}\\simplify{{b3}/{b2}} + \\var{b4}\\simplify{{b6}/{b5}} - \\var{b7}\\simplify{{b9}/{b8}} $

[[0]][[1]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans22}/{ans2b}", "minValue": "{ans22}/{ans2b}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{c1}\\simplify{{c3}/{c2}} \\times \\var{c4}\\simplify{{c6}/{c5}} - \\var{c7}\\simplify{{c9}/{c8}} $

[[0]][[1]]

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$\\var{d1}\\simplify{{d3}/{d2}} \\div (\\var{d4}\\simplify{{d6}/{d5}} \\times \\var{d7}\\simplify{{d9}/{d8}}) $

[[0]][[1]]

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$\\frac{\\var{e1}\\simplify{{e3}/{e2}} \\times \\var{e4}\\simplify{{e6}/{e5}}}{\\var{e7}\\simplify{{e9}/{e8}} \\times \\var{e10}\\simplify{{e12}/{e11}}}$

[[0]][[1]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans555}", "minValue": "{ans555}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "{ans55}/{ans5e}", "minValue": "{ans55}/{ans5e}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{f1}\\simplify{{f3}/{f2}} \\div \\var{f4}\\simplify{{f6}/{f5}}$

[[0]][[1]]

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Evaluate the following without using a calculator:

Answer in whole number and/or fraction!!

Remember the BODMAS rule

N.B.

First box is for whole number and second box is for fraction.

If no whole number place 0 in the first box.

E.g. $\\frac{3}{2} => $first box $ =1 $ second box$ =\\frac{1}{2}$

E.g. $\\frac{1}{2} => $first box $ =0 $ second box$ =\\frac{1}{2}$

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"group": "Ungrouped variables", "name": "d7", "description": ""}, "d4": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "d4", "description": ""}, "d5": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "d5", "description": ""}, "b8": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "b8", "description": ""}, "d3": {"definition": "random(1..{d2}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "ans4a": {"definition": "((d4*d5)+d6)*((d7*d8)+d9)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4a", "description": ""}, "e6": {"definition": "random(1..{e5}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e6", "description": ""}, "e11": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e11", "description": ""}, "e10": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e10", "description": ""}, "c8": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "c8", "description": ""}, "e12": {"definition": "random(1..{e11}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e12", "description": ""}, "e5": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e5", "description": ""}, "Ans2b": {"definition": "lcm([b2,b5,b8])", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans2b", "description": ""}, "b9": {"definition": "random(1..{b8}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b9", "description": ""}, "A1": {"definition": "(pos())", "templateType": "anything", "group": "Ungrouped variables", "name": "A1", "description": ""}, "e3": {"definition": "random(1..{e2}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "ans1": {"definition": "floor(ans1a/ans1b)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "c7": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "c7", "description": ""}, "C2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "C2", "description": ""}, "C1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "C1", "description": ""}, "ans5e": {"definition": "ans5a * ans5b", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5e", "description": ""}, "ans5b": {"definition": "((e7*e8)+e9) * ((e10*e11)+e12)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5b", "description": ""}, "ans5c": {"definition": "e8 * e11", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5c", "description": ""}, "E2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "E2", "description": ""}, "ans4d": {"definition": "ans4a*d2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4d", "description": ""}, "ans3c": {"definition": "lcm([ans3b,c8])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3c", "description": ""}, "ans666": {"definition": "floor(ans6/ans6a)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans666", "description": ""}, "ans4": {"definition": "floor(ans4c/ans4d)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "ans3": {"definition": "floor(ans3d/ans3c)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans2a": {"definition": "((ans2b/b2)*((b2*b1)+b3))+((ans2b/b5)*((b4*b5)+b6))-((ans2b/b8)*((b7*b8)+b9))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2a", "description": ""}, "a3": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "ans11": {"definition": "ans1a-(ans1b*ans1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "e9": {"definition": "random(1..{e8}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e9", "description": ""}, "e8": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e8", "description": ""}, "a6": {"definition": "random(1..{a5}-3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a6", "description": ""}, "c3": {"definition": "random(1..{c2}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "e4": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e4", "description": ""}, "e7": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "e7", "description": ""}, "ans33": {"definition": "abs(ans3d)-(ans3c*abs(ans3))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ans22": {"definition": "abs(ans2a)-(ans2b*abs(ans2))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "c6": {"definition": "random(1..{c5}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c6", "description": ""}, "c5": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "c5", "description": ""}, "c4": {"definition": "random(2..5)+c7", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "a4": {"definition": "random(2..{a3}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "Ans4b": {"definition": "d5*d8", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans4b", "description": ""}, "Ans1a": {"definition": "((ans1b/a1)*a2)+((ans1b/a3)*a4)-((ans1b/a5)*a6)", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans1a", "description": ""}, "ans5d": {"definition": "ans5 * ans5c", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5d", "description": ""}, "E1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "E1", "description": ""}, "Ans3b": {"definition": "c2*c5", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans3b", "description": ""}, "ans55": {"definition": "abs(ans5d)-(ans5e*abs(ans555))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans55", "description": ""}, "c9": {"definition": "random(1..{c8}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c9", "description": ""}, "Ans5": {"definition": "((e1*e2)+e3) * ((e4*e5)+e6)", "templateType": "anything", "group": "Ungrouped variables", "name": "Ans5", "description": ""}, "a5": {"definition": "random(2..5)+a1", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a2": {"definition": "random(2..{a1}-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "B2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "B2", "description": ""}, "ans44": {"definition": "abs(ans4c)-(ans4d*abs(ans4))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans44", "description": ""}, "ans555": {"definition": "floor(ans5d/ans5e)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans555", "description": ""}, "ans6a": {"definition": "((f4*f5)+f6)*f2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6a", "description": ""}, "ans5a": {"definition": "e2 * e5", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5a", "description": ""}, "D2": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "D2", "description": ""}, "ans4c": {"definition": "(((d2*d1)+d3))* ans4b", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4c", "description": ""}, "D1": {"definition": "pos()", "templateType": "anything", "group": "Ungrouped variables", "name": "D1", "description": ""}}, "metadata": {"description": "

Arithmetic

rebelmaths

1. As the second decimal place for {a1} is {grorle} we {incorleave} the first decimal place and the answer is {dpformat(ans1,1)} to 1 decimal place.

{mes}

2. The third decimal place of {a2} is {grorle1} and so we {incorleave1} the second decimal place and the answer is {dpformat(ans2,2)} to 2 decimal places.

{mes1}

3. The fourth decimal place of {a3} is {grorle2} and so we {incorleave2} the third decimal place and the answer is {dpformat(ans3,3)} to 3 decimal places.

{mes2}

", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "

$\\var{a1}$ to $\\var{n1}$ decimal place = [[0]]

$\\var{a2}$ to $\\var{n2}$ decimal places = [[1]]

$\\var{a3}$ to $\\var{n3}$ decimal places = [[2]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": 1, "maxValue": "ans1", "minValue": "ans1", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": 2, "maxValue": "ans2", "minValue": "ans2", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": 3, "maxValue": "ans3", "minValue": "ans3", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "

Rounding a number to a given number of decimal places.

A decimal has a number of places after the decimal point e.g. $1.023$ has $3$ places, $10$ has none, $23.35689234$ has $8$ places.

It is often the case that we want to present the result of a calculation to a specified number of places, the implication being that this is accurate enough for our purposes.

The way to do this is as follows:

Take the decimal and count along the number of places we want e.g. suppose we want $2.1372$ to $2$ decimal places. We have $2.13$ on counting along $2$ places.

But we are not finished as we have to look at the next decimal place in $2.1372$.

If this is $4$ or below we keep $2.13$, but if it is $5$ or above we change the $3$ to $4$ i.e. increase the second place.

So to $2$ decimal places $2.1372=2.14$ as the $7$ in the third place tells us that we have to increase $3$ in the second place to $4$.

However to three decimal places $2.1372 = 2.137$ as the $2$ in the fourth place tells us not to change the third place.

So, for example, suppose we want to reduce the weight of a dog by $12\\%$ and the original weight we want to reduce is $21.4$kgs then our calculations give:

$\\displaystyle 12\\% \\text{ of weight } = \\frac{12}{100} \\times 21.4=2.568$kg of weight to reduce by.

Now it is rather silly to require that degree of accuracy and so we may say in this case that one decimal place is sufficient.

$2.568 = 2.6$kgs to one decimal place as the $6$ in the second place tells us to increase the $5$ to $6$.

Other examples:

$1.375=1.38$ to $2$ decimal places (the $5$ in the third place tells us to increase the $7$ to $8$ in the second place)

$27.2789= 27.279$ to $3$ decimal places.

$134.975 = 135.0$ to one decimal place (the $7$ in the second place tells us to increase the $9$ by $1$, but it then becomes $0$ with $1$ left over to add to the $134$ to give $135$).

$0.8998 = 0.900$ to $3$ decimal places (why?)

IMPORTANT

Note that in the last two examples, we have included $0$ in $135.0$ and two $0$s for $0.900$.

This is because we have asked for a certain number of decimal places and it is correct to include $0$s to make sure that the answer has the right number of entries in the decimal places. If you miss out the $0$s then it will be marked as incorrect.

Another example:

$1.357983$ to $4$ decimal places is input as $1.3580$ and not as $1.358$.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"precisionType": "dp", "prompt": "

0.28923 to 3 decimal places

", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": 3, "maxValue": "0.290+0.001", "minValue": "0.290-0.001", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "

Rounding decimals to a given number of decimal places.

You can get help on rounding by clicking on Show steps.

Or look at the BBC Bitesize Page on decimal places.

Answer the following questions.

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"grorle": {"definition": "if(ans1>a1,\"greater than 4\", \"less than 5\")", "templateType": "anything", "group": "Ungrouped variables", "name": "grorle", "description": ""}, "incorleave1": {"definition": "if(ans2>a2,\"increase\", \"do not increase\")", "templateType": "anything", "group": "Ungrouped variables", "name": "incorleave1", "description": ""}, "r1": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "r1", "description": ""}, "r2": {"definition": "random(3,4)", "templateType": "anything", "group": "Ungrouped variables", "name": "r2", "description": ""}, "r3": {"definition": "random(4,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "r3", "description": ""}, "ans1": {"definition": "precround(a1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "precround(a2,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "precround(a3,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "grorle2": {"definition": "if(ans3>a3,\"greater than 4\", \"less than 5\")", "templateType": "anything", "group": "Ungrouped variables", "name": "grorle2", "description": ""}, "incorleave": {"definition": "if(ans1>a1,\"increase\", \"do not increase\")", "templateType": "anything", "group": "Ungrouped variables", "name": "incorleave", "description": ""}, "a1": {"definition": "random(11111..111111#2)/10^r1", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "grorle1": {"definition": "if(ans2>a2,\"greater than 4\", \"less than 5\")", "templateType": "anything", "group": "Ungrouped variables", "name": "grorle1", "description": ""}, "a3": {"definition": "random(1111111..11111111#2)/10^r3", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(11111..111111#2)/10^r2", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "incorleave2": {"definition": "if(ans3>a3,\"increase\", \"do not increase\")", "templateType": "anything", "group": "Ungrouped variables", "name": "incorleave2", "description": ""}, "mes": {"definition": "if(isint(10^(n1-1)*ans1),'Note that we have 0 in the first decimal place. You have to include this.',' ')", "templateType": "anything", "group": "Ungrouped variables", "name": "mes", "description": ""}, "mes2": {"definition": "if(isint(10^(n3-1)*ans3),'Note that we have had to include one or more 0s in order to get the correct number of decimal places' ,' ')", "templateType": "anything", "group": "Ungrouped variables", "name": "mes2", "description": ""}, "n1": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "2", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "n3": {"definition": "3", "templateType": "anything", "group": "Ungrouped variables", "name": "n3", "description": ""}, "mes1": {"definition": "if(isint(10^(n2-1)*ans2),'Note that we have had to include one or more 0s in order to get the correct number of decimal places' ,' ')", "templateType": "anything", "group": "Ungrouped variables", "name": "mes1", "description": ""}}, "metadata": {"description": "

Rounding decimals.

rebelmaths

When multipling using decimals

When multipling using decimals, count how many decimal places you need to move the number to make it a whole number e.g

0.000054 to get to 54, we moved 6 decimal places and 0.004 to get to 4, we moved 3 decimal places

So if we want to do $0.000054 \\times 0.004$ => we move the first number 6 decimal places and the second number 3 decimal places

=> $54 \\times 4 = 216$

Now since we moved 9 decimal places, altogether to the right, we move the answer 9 decimals places back to the left i.e.

216 becomes 0.000000216

When rounding to a given number of decimal places

When rounding to a given number of decimal places, do the following

Look at the next number after the last number of the decimal places you need to round to

If the number is 5 or greater, round up, if it is than 5, leave as is; i.e.

round to 3 decimal places the following

$0.0055 = 0.006$

$0.0071 = 0.007$

When rounding to a given number of significant figures

When rounding to a given number of significant figures, do the following

Look at the next number after the last number of the significant figuresyou need to round to

If the number is 5 or greater, round up, if it is than 5, leave as is; i.e.

N.B. Remember to keep the number you rounded to the significant number of places in the same unit e.g. 10's, 100's etc

round to 3 significant figures the following

$2573 = 2570$

$7828 = 7830$

round to 1 significant figures the following

$15 = 20$

$38851 = 40000$

", "rulesets": {}, "parts": [{"prompt": "

$\\var{numa1} \\times \\var{numa2}$

[[0]]

$\\var{numb1} \\times \\var{numb2}$

[[0]]

$\\var{numc1} \\times \\var{numc2}$

[[0]]

$\\var{d3} \\div \\var{d1}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{d2}", "minValue": "{d2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{e3} \\div \\var{e1}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{e2}", "minValue": "{e2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{f3} \\div \\var{f1}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{f2}", "minValue": "{f2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{g3} \\div \\var{g1}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{g2}", "minValue": "{g2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$\\var{h3} \\div \\var{h1}$

[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{h2}", "minValue": "{h2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "

Evaluate each of the following without using a calculator:

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"f1": {"definition": "random(0.0022..0.0049#0.0001) ", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "random(50000..100000#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "f1*f2", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "numa2": {"definition": "random(0.11..0.19#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "numa2", "description": ""}, "numa1": {"definition": "random(0.0011..0.0035)", "templateType": "anything", "group": "Ungrouped variables", "name": "numa1", "description": ""}, "h2": {"definition": "random(1.225..1.975#0.05) ", "templateType": "anything", "group": "Ungrouped variables", "name": "h2", "description": ""}, "ans1": {"definition": "numa1*numa2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "numb1*numb2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "numc1*numc2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "numd1*numd2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "numc1": {"definition": "random(1.2..1.4#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "numc1", "description": ""}, "numc2": {"definition": "random(0.0011..0.0059#0.0001)", "templateType": "anything", "group": "Ungrouped variables", "name": "numc2", "description": ""}, "d2": {"definition": "random(50.5..69.5#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "d1*d2", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "d1": {"definition": "random(0.2..0.8#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "sig": {"definition": "random(800..2000#0.0001) ", "templateType": "anything", "group": "Ungrouped variables", "name": "sig", "description": ""}, "h3": {"definition": "h1*h2", "templateType": "anything", "group": "Ungrouped variables", "name": "h3", "description": ""}, "numb2": {"definition": "random(0.002..0.009#0.001)", "templateType": "anything", "group": "Ungrouped variables", "name": "numb2", "description": ""}, "numb1": {"definition": "random(0.000033..0.000079#0.000001)", "templateType": "anything", "group": "Ungrouped variables", "name": "numb1", "description": ""}, "h1": {"definition": "random(0.0022..0.0055#0.000001) ", "templateType": "anything", "group": "Ungrouped variables", "name": "h1", "description": ""}, "g3": {"definition": "g1*g2", "templateType": "anything", "group": "Ungrouped variables", "name": "g3", "description": ""}, "g2": {"definition": "random(0.0022..0.0049#0.0001) ", "templateType": "anything", "group": "Ungrouped variables", "name": "g2", "description": ""}, "g1": {"definition": "random(21.1..31.1#0.2) ", "templateType": "anything", "group": "Ungrouped variables", "name": "g1", "description": ""}, "numd1": {"definition": "random(20.1..91.1#0.2)", "templateType": "anything", "group": "Ungrouped variables", "name": "numd1", "description": ""}, "numd2": {"definition": "random(0.0201..0.0299#0.0002)", "templateType": "anything", "group": "Ungrouped variables", "name": "numd2", "description": ""}, "e1": {"definition": "random(0.0002..0.0009)", "templateType": "anything", "group": "Ungrouped variables", "name": "e1", "description": ""}, "e3": {"definition": "e1*e2", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "e2": {"definition": "random(50000..100000#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "e2", "description": ""}, "rand1": {"definition": "rand()", "templateType": "anything", "group": "Ungrouped variables", "name": "rand1", "description": ""}, "rand2": {"definition": "random(1..4 except {rand1})", "templateType": "anything", "group": "Ungrouped variables", "name": "rand2", "description": ""}, "rand3": {"definition": "rand()", "templateType": "anything", "group": "Ungrouped variables", "name": "rand3", "description": ""}, "dec": {"definition": "random(0.0001..0.0009#0.0000001) ", "templateType": "anything", "group": "Ungrouped variables", "name": "dec", "description": ""}, "rand4": {"definition": "random(1..4 except{rand3})", "templateType": "anything", "group": "Ungrouped variables", "name": "rand4", "description": ""}, "rand5": {"definition": "random(1..4 except {rand4} except{rand3})", "templateType": "anything", "group": "Ungrouped variables", "name": "rand5", "description": ""}}, "metadata": {"description": "

Multiplying and dividing decimals

rebelmaths

Decimal Places and Significant Figures

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Evaluate each of the following:

", "advice": "

When rounding to a given number of decimal places

When rounding to a given number of decimal places, do the following

Look at the next number after the last number of the decimal places you need to round to

If the number is 5 or greater, round up, if it is than 5, leave as is; i.e.

round to 3 decimal places the following

$0.0055 = 0.006$

$0.0071 = 0.007$

When rounding to a given number of significant figures

When rounding to a given number of significant figures, do the following

Look at the next number after the last number of the significant figuresyou need to round to

If the number is 5 or greater, round up, if it is than 5, leave as is; i.e.

N.B. Remember to keep the number you rounded to the significant number of places in the same unit e.g. 10's, 100's etc

round to 3 significant figures the following

$2573 = 2570$

$7828 = 7830$

round to 1 significant figures the following

$15 = 20$

$38851 = 40000$

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Round off $\\var{sig}$ to:

i) 2 decimal places [[0]]

ii) 1 decimal place [[1]]

iii) 3 significant figures [[2]]

iv) 2 significant figures [[3]]

v) 1 significant figure [[4]]

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Round off $\\var{dec}$ to:

i) 4 decimal places [[0]]

ii) 5 decimal places [[1]]

iii) 3 significant figures [[2]]

iv) 2 significant figures [[3]]

v) 1 significant figure [[4]]

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