Hello all,
I am teaching fractions, but I am not sure how to explain to the children why multiplying the denominators to find a multiple is needed before comparing fractions.
Below is the problem and answer, along with my attempted reasoning, which I am not sure is sound.
Problem: Which of these fractions is greater? 3/4 or 2/6
Answer: We have to first multiply 4 and 6 together to get 24, and then multiply the numerators and denominators of 3/4 and 2/6 by 6 and 4 respectively to find out which fraction is greater. 3/4 will be greater than 2/6.
Reason: We need to find the multiple of 4 and 6 to make sure that the wholes which 3/4 and 2/6 are part of are indeed equal sizes. If we didn't know the size of the wholes being compared, 2/6 may be greater than 3/4.
2/6 of a 30cm long pizza/chocolate bar would give each person 10 slices/pieces, but 3/4 of a 10cm long pizza/chocolate bar would give each 7.5 slices/pieces.
Also, I am not sure how to explain why working out the multiple of 24 would ensure that a quarter of the 3/4 and a sixth of the 2/6 would be equal-sized, if 1/4 and 1/6 of 24 is 6 and 4 respectively.
Many thanks for the help.
I am teaching fractions, but I am not sure how to explain to the children why multiplying the denominators to find a multiple is needed before comparing fractions.
Below is the problem and answer, along with my attempted reasoning, which I am not sure is sound.
Problem: Which of these fractions is greater? 3/4 or 2/6
Answer: We have to first multiply 4 and 6 together to get 24, and then multiply the numerators and denominators of 3/4 and 2/6 by 6 and 4 respectively to find out which fraction is greater. 3/4 will be greater than 2/6.
Reason: We need to find the multiple of 4 and 6 to make sure that the wholes which 3/4 and 2/6 are part of are indeed equal sizes. If we didn't know the size of the wholes being compared, 2/6 may be greater than 3/4.
2/6 of a 30cm long pizza/chocolate bar would give each person 10 slices/pieces, but 3/4 of a 10cm long pizza/chocolate bar would give each 7.5 slices/pieces.
Also, I am not sure how to explain why working out the multiple of 24 would ensure that a quarter of the 3/4 and a sixth of the 2/6 would be equal-sized, if 1/4 and 1/6 of 24 is 6 and 4 respectively.
Many thanks for the help.