Question

Is the ratio 63:90 equivalent to 9:15

Answer 1

No

Explanation:

Since ratios are simply proportions, they may be represented in multiple ways as long as the relationship remains equal.

Simplifying Ratios

There are 2 ways to check if these ratios are equivalent. The first is to simplify both ratios and see if they match each other. Firstly, find the greatest common factor (GCF) between the 2 numbers.

• GCF of 63 and 90 = 9
• GCF of 9 and 15 = 3

Then, divide each ratio by its GCF

• 63:90 = 7:10
• 9:15 = 3:5

Since 7:10 is not equal to 3:5, we know that these ratios are not equal. It is important to note that this method only works when both ratios have been completely simplified.

Find the Relationship as a Decimal

Another to see if 2 ratios are equivalent is to see if their relationships are equal as decimals. To find the relationship of a ratio as a decimal, simply divide the 2 numbers within a ratio.

• 63 ÷ 90 = 0.7
• 9 ÷ 15 = 0.6

Clearly, the ratios do not have equal relationships. Thus, the ratios are also not equivalent.