Fractions: All Four Operations
Fractions: All Four Operations covers adding and subtracting fractions with different denominators, including mixed numbers, by converting to a common denominator, and multiplying and dividing fractions, including multiplying a fraction by a whole number and dividing a proper fraction by a whole number.
Before you start
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Method
- To add or subtract fractions with different denominators, find a common denominator (often the lowest common multiple of the two denominators), convert each fraction, then add or subtract only the numerators.
- For mixed numbers, either convert both numbers to improper fractions first, or add or subtract the whole number parts and fraction parts separately, regrouping if the fraction part becomes greater than one whole, or is not big enough to subtract from.
- To multiply a fraction by a whole number, multiply the numerator by the whole number and keep the denominator the same, then simplify if possible.
- To multiply two proper fractions together, multiply the numerators together and multiply the denominators together, then simplify the result.
- To divide a proper fraction by a whole number, multiply the denominator by that whole number, keeping the numerator the same.
- Always check whether the final answer can be simplified, and convert an improper fraction back to a mixed number if the question expects one.
- Estimate first by rounding each fraction to the nearest whole number or half, so an unreasonable answer can be spotted quickly.
Worked example
Work out 5 1/4 - 2 5/6, giving your answer as a mixed number in its simplest form.
- Convert both mixed numbers to improper fractions: 5 1/4 = 21/4, and 2 5/6 = 17/6.
- Find a common denominator for 4 and 6: the lowest common multiple is 12.
- Convert both fractions to twelfths: 21/4 = 63/12, and 17/6 = 34/12.
- Subtract the numerators: 63/12 - 34/12 = 29/12.
- Convert the improper fraction back to a mixed number: 29 divided by 12 = 2 remainder 5, so the answer is 2 5/12.
Practice questions
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Q1Work out 2/3 + 1/5.Show answer
Answer: 13/15
Q2Work out 7/8 - 1/3.Show answer
Answer: 13/24
Q3Work out 3/5 x 8.Show answer
Answer: 4 4/5 (24/5)
Q4Work out 2/3 x 3/7.Show answer
Answer: 2/7
Q5Work out 4/5 divided by 4.Show answer
Answer: 1/5
Q6Work out 3 1/2 + 2 5/8, giving your answer as a mixed number.Show answer
Answer: 6 1/8
Q7A ribbon is 4 1/3 metres long. A piece 1 3/4 metres long is cut off. Work out the length of ribbon remaining, giving your answer as a mixed number.Show answer
Answer: 2 7/12 metres
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Work out 5/6 - 3/8. Give your answer in its simplest form.
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Work out 2/9 x 3/5. Give your answer in its simplest form.
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A baker has 6 3/4 kg of flour. She uses 2 1/2 kg to make bread, then divides the remaining flour equally between 5 identical cake tins. Work out how much flour goes into each cake tin, giving your answer as a fraction of a kilogram in its simplest form.
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Free printable worksheet
Want more practice on paper? Download the fractions: all four operations 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.
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