Question

Prove the pairs of fractions are equivalent without using a rectangular diagram:

24/32 and 27/36
a) They are not equivalent.
b) Simplify both fractions to a common form.
c) Cross-multiply and compare the results.
d) Convert to decimal form and compare.

Answer 1

To prove that the fractions 24/32 and 27/36 are equivalent, simplify both fractions to lowest terms and cross-multiply to compare the results.

Step-by-step explanation:

To prove that the fractions 24/32 and 27/36 are equivalent, we can follow these steps:

1. Simplify both fractions to lowest terms. 24/32 simplifies to 3/4 and 27/36 simplifies to 3/4 as well.
2. Since both fractions are now in the same form, cross-multiply and compare the results.
3. For 3/4, the cross-multiplication is 3 x 4 = 12.
4. Since both fractions have the same product of 12, they are equivalent.

Therefore, the pairs of fractions 24/32 and 27/36 are equivalent.