Are these ratios equivalent? 7 tenors : 4 basses 14 tenors : 8 basses Choices: (A)yes (B)no

Step 1: Simplify Ratio: Step 1: Simplify the first ratio. Original ratio: 7 tenors : 4 basses. Simplified ratio: Divide both terms by their greatest common divisor (GCD), which is 1. Simplified ratio = 7/1 : 4/1 = 7 : 4.Step 2: Simplify Second Ratio: Step 2: Simplify the second ratio. Original ratio: 14 tenors : 8 basses. Simplified ratio: Divide both terms by their GCD, which is 2. Simplified ratio = 14/2 : 8/2 = 7 : 4.Step 3: Compare Ratios: Step 3: Compare the simplified ratios. First ratio: 7 : 4. Second ratio: 7 : 4. Since both simplified ratios are the same, the original ratios are equivalent.

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Are these ratios equivalent? $\newline$ $7$ tenors : $4$ basses $\newline$ $14$ tenors : $8$ basses $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Math Problems

Grade 6

Equivalent ratios: word problems

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Q. Are these ratios equivalent?

\newline

7

tenors :

4

basses

\newline

14

tenors :

8

basses

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Step $1$ : Simplify Ratio: Step $1$ : Simplify the first ratio. $\newline$ Original ratio: $7$ tenors : $4$ basses. $\newline$ Simplified ratio: Divide both terms by their greatest common divisor (GCD), which is $1$ . $\newline$ Simplified ratio = $\frac{7}{1}$ : $\frac{4}{1}$ = $7$ : $4$ .
Step $2$ : Simplify Second Ratio: Step $2$ : Simplify the second ratio. $\newline$ Original ratio: $14$ tenors : $8$ basses. $\newline$ Simplified ratio: Divide both terms by their GCD, which is $2$ . $\newline$ Simplified ratio = $\frac{14}{2}$ : $\frac{8}{2}$ = $7$ : $4$ .
Step $3$ : Compare Ratios: Step $3$ : Compare the simplified ratios. $\newline$ First ratio: $7 : 4$ . $\newline$ Second ratio: $7 : 4$ . $\newline$ Since both simplified ratios are the same, the original ratios are equivalent.