Jayden used the multiplication table below to determine that 8:14 is equivalent to 24:42.

Question

A multiplication table.

Which statement explains why Jayden’s reasoning is correct?
The ratio 8:14 is 4:7 times 2, and the ratio 24:42 is 4:7 times 6.
The terms 8 and 14 are multiples of 2, and the terms 24 and 42 are also multiples of 2 when the table is extended.
The term 24 is a multiple of the term 8, and the terms 14 and 42 are multiples of 7.
The ratio 8:14 is equivalent to 2:7, and the ratio 24:42 is also equivalent to 2:7.

Answer 1

The correct statement that explains why Jayden’s reasoning is correct is:

The ratio 8:14 is equivalent to 2:7, and the ratio 24:42 is also equivalent to 2:7.

This is because both ratios can be simplified to the same form, which confirms their equivalence. Specifically:

• 8:14 simplifies to 2:7 (by dividing both terms by 4).
• 24:42 simplifies to 2:7 (by dividing both terms by 12).

Since both ratios simplify to the same ratio, they are indeed equivalent.