Multiplying and Dividing Fractions in Context
Multiplying and dividing fractions in context means using fraction multiplication and division to solve real word problems, such as splitting a quantity into equal fractional portions or finding how many smaller amounts fit inside a larger one. 11+ papers test whether a pupil can decide which operation a situation needs, not just whether they can calculate 2/3 x 3/4 in isolation, so this skill centres on reading the problem and choosing multiply or divide correctly.
Method
- Identify whether the situation needs multiplying (finding a fraction of a fraction, or repeated fractional amounts) or dividing (splitting a total into equal fractional-sized portions, or finding how many pieces fit inside a total).
- Turn any mixed numbers into improper fractions before calculating.
- For multiplying, multiply the numerators together and the denominators together, cancelling common factors first where possible.
- For dividing by a fraction, multiply by its reciprocal instead of dividing directly.
- Convert an improper fraction answer back into a mixed number, and attach the correct unit from the question.
- Check the answer's size makes sense in context: dividing by a fraction smaller than 1 gives a bigger number of pieces, not a smaller one.
Worked example
A market trader has 3/4 of a kg of cherries left. She wants to put them into small bags that each hold 1/8 of a kg. How many full bags can she make?
- Recognise this as a division problem: total amount divided by the size of each bag, 3/4 divided by 1/8.
- To divide by a fraction, multiply by its reciprocal instead: 3/4 x 8/1.
- Multiply the numerators: 3 x 8 = 24. Multiply the denominators: 4 x 1 = 4, giving 24/4.
- Simplify the fraction: 24/4 = 6.
- Final answer: she can make 6 full bags.
Practice questions
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Q1Work out 2/3 of 3/5, giving your answer in its simplest form.Show answer
Answer: 2/5 (2/3 x 3/5 = 6/15 = 2/5)
Q2A tank is 2/5 full of water. If 1/2 of the water in the tank is poured out, what fraction of the whole tank is now full?Show answer
Answer: 1/5 (2/5 x 1/2 = 2/10 = 1/5)
Q3How many 1/4-litre glasses can be filled from 3 litres of juice?Show answer
Answer: 12 (3 divided by 1/4 = 3 x 4 = 12)
Q4A ribbon is 5/6 m long. It is cut into pieces each 1/12 m long. How many pieces are cut?Show answer
Answer: 10 (5/6 divided by 1/12 = 5/6 x 12 = 60/6 = 10)
Q5Work out 3 1/2 x 2/7, giving your answer in its simplest form.Show answer
Answer: 1 (3 1/2 = 7/2, and 7/2 x 2/7 = 14/14 = 1)
Q6A recipe uses 2/3 of a cup of flour per batch. How many batches can be made from 6 cups of flour?Show answer
Answer: 9 (6 divided by 2/3 = 6 x 3/2 = 18/2 = 9)
Q7Explain why dividing 4 by 1/2 gives a bigger answer than dividing 4 by 2.Show answer
Answer: Dividing by a fraction smaller than 1 finds how many of the smaller pieces fit into the whole, so the answer is larger; 4 divided by 1/2 = 8, whereas 4 divided by 2 = 2, because half-sized pieces take more of them to make up 4.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A baker in Bristol has 5/8 of a bag of icing sugar left. Each cake needs 1/16 of a bag. How many cakes can she ice with the icing sugar she has left?
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A water butt contains 4 1/2 litres of water. Aisha uses 2/3 of the water to fill watering cans, then pours the remaining water into bottles that each hold 1/4 litre. How many full bottles can she fill from the remaining water?
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Work out 5/9 divided by 5/6, giving your answer in its simplest form.
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Free printable worksheet
Want more practice on paper? Download the multiplying and dividing fractions in context worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 41 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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