Remember the order of operations
\nB Brackets
\nO pOwers
\nD Division
\nM Multiplication
\nA Addition
\nS Subtraction
\na)
\nFirst do the calculations $\\displaystyle \\simplify[all,!simplifyFractions]{{a4}/{a5}={a4/a5}}$ and $\\simplify[all,!collectNumbers]{{a2}*{a3}={a2*a3}}$.
\nand then we get
\n\\[\\begin{align} \\simplify[all,!collectNumbers,!simplifyFractions]{{a1}+ {a2}{a3}+{a4}/{a5}}&=\\simplify[all,!collectNumbers,!simplifyFractions]{{a1}+ {a2*a3}+{a4/a5}}\\\\&=\\var{ans1}\\end{align}\\]
\nb)
\nFirst do the calculations $\\displaystyle \\simplify[all,!collectNumbers,!simplifyFractions]{{b1}/{b2}={b1/b2}} \\text{ and } \\simplify[all,!collectNumbers]{{b3}({b4}+{b5})={b3}{b4+b5}={b3*(b4+b5)}}$
\nand then we get
\n\\[\\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}\\]
\nc)
\nFirst do the calculations $\\displaystyle \\simplify[all,!collectNumbers,!simplifyFractions]{({c4}+{c5})/{c6}={c4+c5}/{c6}={(c4+c5)/c6}} \\text{ and } \\simplify[all,!collectNumbers]{{c1}({c2}+{c3})={c1}{c2+c3}={c1*(c2+c3)}}$
\nand then we get
\n\\[\\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}\\]
\n", "rulesets": {}, "parts": [{"prompt": "$\\displaystyle \\simplify[all,!collectNumbers,!simplifyFractions]{{a1}+ {a2}{a3}+{a4}/{a5}}=\\;$[[0]]
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", "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": "$\\displaystyle \\simplify[all,!collectNumbers,!simplifyFractions]{{c1}({c2}+{c3})+({c4}+{c5})/{c6}}=\\;$[[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"}], "statement": "Use the correct order of operations to calculate the following
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a1": {"definition": "random(-50..50 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "ans1": {"definition": "a1+a2*a3+a4/a5", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "b1/b2+b3*(b4+b5)*b6+b7", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "c1*(c2+c3)+(c4+c5)/c6", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "b1": {"definition": "random(10,20,30,40,50)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "a3": {"definition": "random(1..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "b4": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b5": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b5", "description": ""}, "b6": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "b6", "description": ""}, "a2": {"definition": "random(-4..4 except [-1,0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "b7": {"definition": "random(-50..50 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b7", "description": ""}, "a4": {"definition": "random(6,12,18,24,30)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "b2": {"definition": "random(2,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(-4..4 except [-1,0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "c3": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c2": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "random(-4..4 except [-1,0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "a5": {"definition": "random(2,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "c6": {"definition": "random(2,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c6", "description": ""}, "c5": {"definition": "c6*random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c5", "description": ""}, "c4": {"definition": "c6*random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}}, "metadata": {"description": "Order of Operations
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Decimal places", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["mes", "ans3", "r1", "r2", "r3", "ans1", "ans2", "grorle", "a3", "incorleave", "a1", "grorle1", "grorle2", "a2", "incorleave2", "incorleave1", "mes2", "n1", "n2", "n3", "mes1"], "tags": ["arithmetic", "Arithmetic", "decimal places", "decimals", "rounding", "strict rounding", "vet"], "advice": "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.
\n{mes}
\n \n2. 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.
\n{mes1}
\n3. 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.
\n{mes2}
", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "$\\var{a1}$ to $\\var{n1}$ decimal place = [[0]]
\n$\\var{a2}$ to $\\var{n2}$ decimal places = [[1]]
\n$\\var{a3}$ to $\\var{n3}$ decimal places = [[2]]
\n \n ", "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.
\nA 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.
\nIt 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.
\nThe way to do this is as follows:
\nTake 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.
\nBut we are not finished as we have to look at the next decimal place in $2.1372$.
\nIf 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.
\nSo 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 $4$.
\nHowever to three decimal places $2.1372 = 2.137$ as the $2$ in the fourth place tells us not to change the third place.
\nSo, 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:
\n$\\displaystyle 12\\% \\text{ of weight } = \\frac{12}{100} \\times 21.4=2.568$kg of weight to reduce by.
\nNow it is rather silly to require that degree of accuracy and so we may say in this case that one decimal place is sufficient.
\n$2.568 = 2.6$kgs to one decimal place as the $6$ in the second place tells us to increase the $5$ to $6$.
\nOther examples:
\n$1.375=1.38$ to $2$ decimal places (the $5$ in the third place tells us to increase the $7$ to $8$ in the second place)
\n$27.2789= 27.279$ to $3$ decimal places.
\n$134.975 = 135.0$ 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 $135$).
\n$0.8998 = 0.900$ to $3$ decimal places (why?)
\nIMPORTANT
\nNote that in the last two examples, we have included $0$ in $135.0$ and two $0$s for $0.900$.
\nThis 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.
\nAnother example:
\n$1.357983$ to $4$ decimal places is input as $1.3580$ and not as $1.358$.
\n \n ", "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": "You can get help on rounding by clicking on Show steps.
\nOr look at the BBC Bitesize Page on decimal places.
\nAnswer the following questions.
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\nrebelmaths
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\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Evaluate the following to the nearest cent:
", "advice": "First we need to find $\\var{VAT}$% of $€\\var{a}$. To do this we need to multiply $€\\var{a}$ by $\\var{VAT}$ and divide by 100. The easiest way is to multiply $€\\var{a}$ by $\\frac{\\var{VAT}}{100}$. This is the amount of VAT that must be paid. Add this on to the original cost priceto find the total selling price including VAT.
\n$€\\var{a} \\times \\var{newVAT1} = €\\var{ans}$
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\n€[[0]]
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\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Evaluate the following to the nearest cent:
", "advice": "The selling price of an item before VAT is equal to 100%, and the selling price including VAT of $\\var{VAT}$% has to equal $\\var{newVAT}$%.
\nTherefore to get the selling price including VAT, divide by 100 and multiply by $\\var{newVAT}$, or simply multiply by $\\var{newVAT1}$ as seen below:
\n$€\\var{a} \\times \\var{newVAT1} = €\\var{ans}$
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\n€[[0]]
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Please remember to submit your answers. Answers that have not been submitted will not be graded.
After you have completed the exam, save a PDF of your results. To do this, follow these steps:
\n1) Select the 'print results' option at the bottom of the Results Summary page.
\n2) Under Destination, select 'Save as PDF'.
\n3) Save your results with the following title: 'student name_Sample Numbas Results'
\n4) Email your results to patricia.cogan@cit.ie
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