lesson
Compare equal-sized parts
1 · Learn
Equivalent fractions keep the same value by multiplying or dividing numerator and denominator by the same non-zero number. Simplest form has no common factor greater than 1.
To compare unlike fractions, use a common denominator so their parts have the same size. Keep the whole equal when using drawings; half a small cake need not exceed a quarter of a much larger one.
Compare fractions above one in the same way. Seven quarters is 21/12, while five thirds is 20/12. So 7/4 is greater than 5/3. Both lie between one and two; changing to a common denominator does not change their positions.
2 · Worked example
7/12 and 5/8 become 14/24 and 15/24, so 5/8 is greater. Also 24/36 simplifies to 2/3 by dividing both numbers by 12.
3 · Your turn
Simplify 30/42. Which is greater, 3/4 or 7/10?
Check your answer
5/7. In twentieths, 3/4 = 15/20 and 7/10 = 14/20, so 3/4 is greater.
4 · Apply your learning
Make two equal-length fraction strips and show why changing only the denominator changes the value.
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
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