A quick practice set of problems for education students to take in preparation for their numeracy test.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], []], "questions": [{"name": "Fractions: reducing, simplifying, cancelling (basic)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": [], "metadata": {"description": "Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)
\nThe greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Write the following question down on paper and evaluate it without using a calculator.
\nIf you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.
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\n$\\displaystyle\\frac{\\var{num}}{\\var{den}}=$ [[0]]
\nNote: Use the / to signify the fraction bar. For example, $\\frac{1}{2}$ is entered as $1/2$.
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "To reduce/simplify a fraction we need to find common factors in the numerator and denominator, that is we need to find numbers that divide into both the top number and the bottom number.
\nDivide the top and bottom by the highest common factor, or divide the top and bottom by common factors as they are found (until the only common factor is $1$).
\nNotice that $\\var{num}$ and $\\var{den}$ are both divisible by $\\var{c}$. So we will divide both numbers by this common factor $\\var{c}$:
\n\\begin{align}\\frac{\\var{num}}{\\var{den}}&=\\frac{\\var{num}\\div\\var{c}}{\\var{den}\\div \\var{c}}\\\\&=\\simplify{{anum}/{aden}}\\end{align}
\nIn this case, our common factor was equal to the original denominator so simplifying was actually just the same as evaluating the fraction by doing the division!
\nNow $\\var{anum}$ and $\\var{aden}$ have no common factors (other than $1$) and so $\\frac{\\var{anum}}{\\var{aden}}$ is reduced.
\nTo summarise, simplifying/reducing/cancelling fractions requires you to know divisibility tests and be able to do divisions. You need to practice these skills to get better at simplifying fractions.
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Simplify the following fraction into its lowest form:
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\nTo reduce/simplify a fraction we need to find common factors in the numerator and denominator, that is we need to find numbers that divide into both the top number and the bottom number.
\nDivide the top and bottom by the highest common factor, or divide the top and bottom by common factors as they are found (until the only common factor is $1$).
\n\nNotice that $\\var{num}$ and $\\var{den}$ are both divisible by $\\var{c}$. So we will divide both numbers by this common factor $\\var{c}$:
\n\\begin{align}\\frac{\\var{num}}{\\var{den}}&=\\frac{\\var{num}\\div\\var{c}}{\\var{den}\\div \\var{c}}\\\\&=\\simplify{{anum}/{aden}}\\end{align}
\nIn this case, our common factor was equal to the original denominator so simplifying was actually just the same as evaluating the fraction by doing the division!
\nNow $\\var{anum}$ and $\\var{aden}$ have no common factors (other than $1$) and so $\\frac{\\var{anum}}{\\var{aden}}$ is reduced.
\nTo summarise, simplifying/reducing/cancelling fractions requires you to know divisibility tests and be able to do divisions. You need to practice these skills to get better at simplifying fractions.
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\na) Multiply numerical fractions. Simplifying is discussed in the advice but not required to get full marks.
\nb) Multiply a negative fraction by a whole number. Simplifying is discussed in the advice but not required to get full marks.
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\n\n\n", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Multiply the tops and the bottoms and look for common factors to cancel.
\n\n\\begin{align}\\displaystyle\\frac{\\var{a}}{\\var{b}}\\times \\frac{\\var{c}}{\\var{d}}&=\\frac{\\var{a}\\times\\var{c}}{\\var{b}\\times\\var{d}}\\\\[3pt]&=\\frac{\\var{ac}}{\\var{bd}}\\end{align}
\nWe can write this fraction on the computer using the slash, that is, $\\var{ac}/\\var{bd}$.
\n\nThis answer is correct but it is not reduced or simplified. We could write this fraction using smaller numbers on the top and bottom because $\\var{ac}$ and $\\var{bd}$ have a common divisor of $\\var{gcda}$. So we divide the top and bottom numbers by $\\var{gcda}$ to write our fraction in a simpler way.
\n\n
\\begin{align}\\displaystyle\\frac{\\var{ac}}{\\var{bd}}&=\\frac{\\var{ac}\\div\\var{gcda}}{\\var{bd}\\div\\var{gcda}}\\\\[3pt]&=\\frac{\\var{rednuma}}{\\var{reddena}}\\end{align}
\n\nTherefore a better answer to give would be $\\displaystyle\\frac{\\var{rednuma}}{\\var{reddena}}$, which we can enter as $\\var{rednuma}/\\var{reddena}$ .
\nActually, ideally we would write our answer as $\\var{rednuma}$.
\n\nWe actually recommend you look for common factors before multiplying, that way you can cancel them (divide out by them) before multiplying. See if you can find where the common factor of $\\var{gcda}$ comes from in the original question.
\nRecall that whole numbers can be written as fractions by putting them over $1$. Multiply the tops and the bottoms and look for common factors to cancel.
\n\n\\begin{align}\\displaystyle-\\frac{\\var{f}}{\\var{g}}\\times \\var{h}&=-\\frac{\\var{f}}{\\var{g}}\\times \\frac{\\var{h}}{1}\\\\[3pt]&=-\\frac{\\var{f}\\times\\var{h}}{\\var{g}\\times 1}\\\\[3pt]&=-\\frac{\\var{fh}}{\\var{g}}\\end{align}
\nWe can write this fraction on the computer using the slash, that is, $-\\var{fh}/\\var{g}$.
\n\nThis answer is correct but it is not reduced or simplified. We could write this fraction using smaller numbers on the top and bottom because $\\var{fh}$ and $\\var{g}$ have a common divisor of $\\var{gcdb}$. So we divide the top and bottom numbers by $\\var{gcdb}$ to write our fraction in a simpler way.
\n\n
\\begin{align}\\displaystyle-\\frac{\\var{fh}}{\\var{g}}&=-\\frac{\\var{fh}\\div\\var{gcdb}}{\\var{g}\\div\\var{gcdb}}\\\\[3pt]&=-\\frac{\\var{rednumb}}{\\var{reddenb}}\\end{align}
\n\nTherefore a better answer to give would be $\\displaystyle-\\frac{\\var{rednumb}}{\\var{reddenb}}$, which we can enter as $-\\var{rednumb}/\\var{reddenb}$ .
\nActually, ideally we would write our answer as $-\\var{rednumb}$.
\n\nWe actually recommend you look for common factors before multiplying, that way you can cancel them (divide out by them) before multiplying. See if you can find where the common factor of $\\var{gcdb}$ comes from in the original question.
\nFraction of an amount, some whole number answers, some need to be rounded.
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\n[[0]]
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\nThis question requires you to know how to multiply fractions. It is often useful to simplify fractions as well.
\n\n{percent2} of $\\var{amount2} = \\var[fractionNumbers]{percent2}\\times \\var{amount2}$
\nwhich is the same as
\n$\\dfrac{\\var{percent2*factorsofhun[0][1]}}{\\var{factorsofhun[0][1]}}\\times \\dfrac{\\var{amount2}}{1}$ and $\\dfrac{\\var{percent2*factorsofhun[0][1]}\\times \\var{amount2}}{\\var{factorsofhun[0][1]}}$
\nbefore multiplying, notice there is a common factor of $\\var{factorsofhun[0][1]}$ that can be cancelled to leave
\n$\\var{percent2*factorsofhun[0][1]}\\times \\var{amount2/factorsofhun[0][1]} = \\var{ans2}$.
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\n$\\simplify[fractionNumbers]{{fraction}}$ of $\\var{total}$ is [[0]]
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\nThis question requires you to know how to multiply fractions. It is often useful to simplify fractions as well.
\n\n$\\simplify[fractionNumbers]{{fraction}} \\text{ of }\\var{total} =\\simplify[fractionNumbers]{{fraction}}\\times\\var{total}$
\nwhich is the same as
\n$\\simplify[fractionNumbers]{{fraction}}\\times\\frac{\\var{total}}{1}$
\nif any common factors can be found they should be cancelled, otherwise multiply the numerators and divide by the denominator.
\nYou might use a calculator or just the division algorithm to determine the result which comes to $\\var{round}$$\\var{precround(round,3)}$ (to 3 decimal places).
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\nRandomly chooses one of the following
\na) Multiply numerical fractions. Simplifying is discussed in the advice but not required to get full marks.
\nb) Multiply a negative fraction by a whole number. Simplifying is discussed in the advice but not required to get full marks.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Write the following question down on paper and evaluate it without using a calculator. Write your answer as a fraction or whole number (not a decimal). Use / to signify a fraction or division, for example $\\frac{2}{3}$ is written 2/3.
\n", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b": {"name": "b", "group": "numerical fractions", "definition": "random(2..12 except a)", "description": "", "templateType": "anything", "can_override": false}, "ac": {"name": "ac", "group": "numerical fractions", "definition": "a*c", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "numerical fractions", "definition": "random(2..12 except f)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "numerical fractions", "definition": "random(2..12 except [a,b])", "description": "", "templateType": "anything", "can_override": false}, "reddena": {"name": "reddena", "group": "numerical fractions", "definition": "bd/gcda", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "numerical fractions", "definition": "random(2..12 except[a,b,c,10])", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "numerical fractions", "definition": "random(2..12 except [f,g])", "description": "", "templateType": "anything", "can_override": false}, "bd": {"name": "bd", "group": "numerical fractions", "definition": "b*d", "description": "", "templateType": "anything", "can_override": false}, "gcda": {"name": "gcda", "group": "numerical fractions", "definition": "gcd(ac,bd)", "description": "", "templateType": "anything", "can_override": false}, "rednumb": {"name": "rednumb", "group": "numerical fractions", "definition": "fh/gcdb", "description": "", "templateType": "anything", "can_override": false}, "reddenb": {"name": "reddenb", "group": "numerical fractions", "definition": "g/gcdb", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "numerical fractions", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "fh": {"name": "fh", "group": "numerical fractions", "definition": "f*h", "description": "", "templateType": "anything", "can_override": false}, "rednuma": {"name": "rednuma", "group": "numerical fractions", "definition": "ac/gcda", "description": "", "templateType": "anything", "can_override": false}, "gcdb": {"name": "gcdb", "group": "numerical fractions", "definition": "gcd(fh,g)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "numerical fractions", "definition": "random(2..12 except d)", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "numerical fractions", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "numerical fractions", "definition": "if(seed=0, rednuma/reddena, -rednumb/reddenb)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "numerical fractions", "variables": ["a", "b", "c", "d", "f", "g", "h", "ac", "bd", "gcda", "rednuma", "reddena", "fh", "gcdb", "rednumb", "reddenb", "seed", "ans"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\displaystyle\\frac{\\var{a}}{\\var{b}}\\text{ of } \\frac{\\var{c}}{\\var{d}}=$$\\displaystyle-\\frac{\\var{f}}{\\var{g}}\\text{ of } \\var{h}=$[[0]]
\n\n\n", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Finding a proportion/fraction of something means we need to multiply! Multiply the tops and the bottoms and look for common factors to cancel.
\n\n\\begin{align}\\displaystyle\\frac{\\var{a}}{\\var{b}}\\times \\frac{\\var{c}}{\\var{d}}&=\\frac{\\var{a}\\times\\var{c}}{\\var{b}\\times\\var{d}}\\\\[3pt]&=\\frac{\\var{ac}}{\\var{bd}}\\end{align}
\nWe can write this fraction on the computer using the slash, that is, $\\var{ac}/\\var{bd}$.
\n\nThis answer is correct but it is not reduced or simplified. We could write this fraction using smaller numbers on the top and bottom because $\\var{ac}$ and $\\var{bd}$ have a common divisor of $\\var{gcda}$. So we divide the top and bottom numbers by $\\var{gcda}$ to write our fraction in a simpler way.
\n\n
\\begin{align}\\displaystyle\\frac{\\var{ac}}{\\var{bd}}&=\\frac{\\var{ac}\\div\\var{gcda}}{\\var{bd}\\div\\var{gcda}}\\\\[3pt]&=\\frac{\\var{rednuma}}{\\var{reddena}}\\end{align}
\n\nTherefore a better answer to give would be $\\displaystyle\\frac{\\var{rednuma}}{\\var{reddena}}$, which we can enter as $\\var{rednuma}/\\var{reddena}$ .
\nActually, ideally we would write our answer as $\\var{rednuma}$.
\n\nWe actually recommend you look for common factors before multiplying, that way you can cancel them (divide out by them) before multiplying. See if you can find where the common factor of $\\var{gcda}$ comes from in the original question.
\nRecall that whole numbers can be written as fractions by putting them over $1$ and finding a proportion/fraction of something means we need to multiply! Multiply the tops and the bottoms and look for common factors to cancel.
\n\n\\begin{align}\\displaystyle-\\frac{\\var{f}}{\\var{g}}\\times \\var{h}&=-\\frac{\\var{f}}{\\var{g}}\\times \\frac{\\var{h}}{1}\\\\[3pt]&=-\\frac{\\var{f}\\times\\var{h}}{\\var{g}\\times 1}\\\\[3pt]&=-\\frac{\\var{fh}}{\\var{g}}\\end{align}
\nWe can write this fraction on the computer using the slash, that is, $-\\var{fh}/\\var{g}$.
\n\nThis answer is correct but it is not reduced or simplified. We could write this fraction using smaller numbers on the top and bottom because $\\var{fh}$ and $\\var{g}$ have a common divisor of $\\var{gcdb}$. So we divide the top and bottom numbers by $\\var{gcdb}$ to write our fraction in a simpler way.
\n\n
\\begin{align}\\displaystyle-\\frac{\\var{fh}}{\\var{g}}&=-\\frac{\\var{fh}\\div\\var{gcdb}}{\\var{g}\\div\\var{gcdb}}\\\\[3pt]&=-\\frac{\\var{rednumb}}{\\var{reddenb}}\\end{align}
\n\nTherefore a better answer to give would be $\\displaystyle-\\frac{\\var{rednumb}}{\\var{reddenb}}$, which we can enter as $-\\var{rednumb}/\\var{reddenb}$ .
\nActually, ideally we would write our answer as $-\\var{rednumb}$.
\n\nWe actually recommend you look for common factors before multiplying, that way you can cancel them (divide out by them) before multiplying. See if you can find where the common factor of $\\var{gcdb}$ comes from in the original question.
\nRandomly chooses one of the following
\na) Divide numerical fractions. Simplifying is discussed in the advice but not required to get full marks.
\nb) Divide a negative whole number by a fraction. Simplifying is discussed in the advice but not required to get full marks.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Write the following question down on paper and evaluate it without using a calculator. Write your answer as a fraction or whole number (not a decimal). Use / to signify a fraction or division, for example $\\frac{2}{3}$ is written 2/3.
\n", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b": {"name": "b", "group": "numerical fractions", "definition": "random(2..12 except a)", "description": "", "templateType": "anything", "can_override": false}, "ac": {"name": "ac", "group": "numerical fractions", "definition": "a*c", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "numerical fractions", "definition": "random(2..12 except f)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "numerical fractions", "definition": "random(2..12 except [a,b])", "description": "", "templateType": "anything", "can_override": false}, "reddena": {"name": "reddena", "group": "numerical fractions", "definition": "bd/gcda", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "numerical fractions", "definition": "random(2..12 except[a,b,c,10])", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "numerical fractions", "definition": "random(2..12 except [f,g])", "description": "", "templateType": "anything", "can_override": false}, "bd": {"name": "bd", "group": "numerical fractions", "definition": "b*d", "description": "", "templateType": "anything", "can_override": false}, "gcda": {"name": "gcda", "group": "numerical fractions", "definition": "gcd(ac,bd)", "description": "", "templateType": "anything", "can_override": false}, "rednumb": {"name": "rednumb", "group": "numerical fractions", "definition": "fh/gcdb", "description": "", "templateType": "anything", "can_override": false}, "reddenb": {"name": "reddenb", "group": "numerical fractions", "definition": "g/gcdb", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "numerical fractions", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "fh": {"name": "fh", "group": "numerical fractions", "definition": "f*h", "description": "", "templateType": "anything", "can_override": false}, "rednuma": {"name": "rednuma", "group": "numerical fractions", "definition": "ac/gcda", "description": "", "templateType": "anything", "can_override": false}, "gcdb": {"name": "gcdb", "group": "numerical fractions", "definition": "gcd(fh,g)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "numerical fractions", "definition": "random(2..12 except d)", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "numerical fractions", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "numerical fractions", "definition": "if(seed=0, rednuma/reddena, -rednumb/reddenb)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": [], "variable_groups": [{"name": "numerical fractions", "variables": ["a", "b", "c", "d", "f", "g", "h", "ac", "bd", "gcda", "rednuma", "reddena", "fh", "gcdb", "rednumb", "reddenb", "seed", "ans"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\displaystyle\\frac{\\var{a}}{\\var{b}}\\div \\frac{\\var{d}}{\\var{c}}=$$\\displaystyle-\\var{h}\\div\\frac{\\var{g}}{\\var{f}}=$[[0]]
\nNote, this is the same as asking how many $\\frac{\\var{d}}{\\var{c}}$$\\frac{\\var{g}}{\\var{f}}$s fit into $\\frac{\\var{a}}{\\var{b}}$.$-\\var{h}$.
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Instead of dividing by the second fraction, we multiply by the reciprocal of the second fraction (that is, the second fraction flipped upside-down), then look for common factors to cancel.
\n\n\\begin{align}\\displaystyle\\frac{\\var{a}}{\\var{b}}\\div \\frac{\\var{d}}{\\var{c}}&=\\frac{\\var{a}}{\\var{b}}\\times \\frac{\\var{c}}{\\var{d}}\\\\[3pt]&=\\frac{\\var{a}\\times\\var{c}}{\\var{b}\\times\\var{d}}\\\\[3pt]&=\\frac{\\var{ac}}{\\var{bd}}\\end{align}
\nWe can write this fraction on the computer using the slash, that is, $\\var{ac}/\\var{bd}$.
\n\nThis answer is correct but it is not reduced or simplified. We could write this fraction using smaller numbers on the top and bottom because $\\var{ac}$ and $\\var{bd}$ have a common divisor of $\\var{gcda}$. So we divide the top and bottom numbers by $\\var{gcda}$ to write our fraction in a simpler way.
\n\n
\\begin{align}\\displaystyle\\frac{\\var{ac}}{\\var{bd}}&=\\frac{\\var{ac}\\div\\var{gcda}}{\\var{bd}\\div\\var{gcda}}\\\\[3pt]&=\\frac{\\var{rednuma}}{\\var{reddena}}\\end{align}
\n\nTherefore a better answer to give would be $\\displaystyle\\frac{\\var{rednuma}}{\\var{reddena}}$, which we can enter as $\\var{rednuma}/\\var{reddena}$ .
\nActually, ideally we would write our answer as $\\var{rednuma}$.
\n\nWe actually recommend you look for common factors before multiplying, that way you can cancel them (divide out by them) before multiplying. See if you can find where the common factor of $\\var{gcda}$ comes from in the original question.
\nRecall that whole numbers can be written as fractions by putting them over $1$. Instead of dividing by the second fraction, we multiply by the reciprocal of the second fraction (that is, the second fraction flipped upside-down), then look for common factors to cancel.
\n\n\\begin{align}\\displaystyle-\\var{h}\\div\\frac{\\var{g}}{\\var{f}}&=-\\frac{\\var{h}}{1}\\div\\frac{\\var{g}}{\\var{f}}\\\\[3pt]&=-\\frac{\\var{h}}{\\var{1}}\\times \\frac{\\var{f}}{\\var{g}}\\\\[3pt]&=-\\frac{\\var{h}\\times\\var{f}}{1\\times \\var{g}}\\\\[3pt]&=-\\frac{\\var{fh}}{\\var{g}}\\end{align}
\nWe can write this fraction on the computer using the slash, that is, $-\\var{fh}/\\var{g}$.
\n\nThis answer is correct but it is not reduced or simplified. We could write this fraction using smaller numbers on the top and bottom because $\\var{fh}$ and $\\var{g}$ have a common divisor of $\\var{gcdb}$. So we divide the top and bottom numbers by $\\var{gcdb}$ to write our fraction in a simpler way.
\n\n
\\begin{align}\\displaystyle-\\frac{\\var{fh}}{\\var{g}}&=-\\frac{\\var{fh}\\div\\var{gcdb}}{\\var{g}\\div\\var{gcdb}}\\\\[3pt]&=-\\frac{\\var{rednumb}}{\\var{reddenb}}\\end{align}
\n\nTherefore a better answer to give would be $\\displaystyle-\\frac{\\var{rednumb}}{\\var{reddenb}}$, which we can enter as $-\\var{rednumb}/\\var{reddenb}$ .
\nActually, ideally we would write our answer as $-\\var{rednumb}$.
\n\nWe actually recommend you look for common factors before multiplying, that way you can cancel them (divide out by them) before multiplying. See if you can find where the common factor of $\\var{gcdb}$ comes from in the original question.
\n