lesson
Take part of a part
1 · Learn
Multiplying proper fractions can mean taking part of an existing part. Multiply numerators and denominators, then simplify. An area model helps explain why one half of one third is one sixth.
Dividing a fraction by a positive whole number shares the fractional quantity equally. Multiply the denominator by the whole number; dividing both numerator and denominator would leave the original value unchanged.
2 · Worked example
3/4 × 2/5 = 6/20 = 3/10. Sharing 5/6 between 5 gives 5/30 = 1/6; five such shares rebuild 5/6.
3 · Your turn
Calculate 2/3 × 3/7 and 3/5 ÷ 4.
Check your answer
6/21 = 2/7; 3/20.
4 · Apply your learning
Draw a rectangle for the product and use fraction strips to reconstruct the shared amount.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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