**1.) Determine if 2 ratios are equivalent.**

Are these two ratios equivalent? 63 : 27 = 49 : 21

At first glance it may appear that these two ratios are not equivalent.

However, you will be able to prove your answer by simplifying both ratios to lowest terms.

Step 1: Simplify the first ratio.

Divide both terms of the ratio by the G.C.F 9.

Are these two ratios equivalent? 63 : 27 = 49 : 21

At first glance it may appear that these two ratios are not equivalent.

However, you will be able to prove your answer by simplifying both ratios to lowest terms.

Step 1: Simplify the first ratio.

Divide both terms of the ratio by the G.C.F 9.

**63 : 27 = 7 : 3**

Step 2: Simplify the second ratio.

Divide both terms of the ratio by the G.C.F 7.

Step 2: Simplify the second ratio.

Divide both terms of the ratio by the G.C.F 7.

**49 : 21 = 7 : 3**

Both ratios simplify to 7 : 3, therefore, the ratios

63 : 27 and 49 : 21 are equivalent.

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2.) Determine the missing term, x.

98 : 112 = 63 : x

Step 1: Simplify the first ratio.

Divide both terms of the ratio by the G.C.F 14.

Both ratios simplify to 7 : 3, therefore, the ratios

63 : 27 and 49 : 21 are equivalent.

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2.) Determine the missing term, x.

98 : 112 = 63 : x

Step 1: Simplify the first ratio.

Divide both terms of the ratio by the G.C.F 14.

98 : 112 = 7 : 8

Step 2: Use the simplified ratio to calculate the second ratio's missing term.

Multiply the first term of the ratio by 9

because 7 x 9 = 63.

Multiply the second term of the ratio by 9 to keep it equivalent, so 8 x 9 = 72.

7 : 8 = 63 : x The missing term is 72, so x = 72.

98 : 112 = 63 : 72

98 : 112 = 7 : 8

Step 2: Use the simplified ratio to calculate the second ratio's missing term.

Multiply the first term of the ratio by 9

because 7 x 9 = 63.

Multiply the second term of the ratio by 9 to keep it equivalent, so 8 x 9 = 72.

7 : 8 = 63 : x The missing term is 72, so x = 72.

98 : 112 = 63 : 72