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Are these ratios equivalent? $\newline$ $4$ crossword puzzles : $9$ word searches $\newline$ $7$ crossword puzzles : $10$ word searches $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Equivalent ratios: word problems

Full solution

Q. Are these ratios equivalent?

\newline

4

crossword puzzles :

9

word searches

\newline

7

crossword puzzles :

10

word searches

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Calculate Ratio $1$ : Step $1$ : Calculate the ratio for the first pair of values. $\newline$ To find if the ratios are equivalent, we first simplify each ratio. For the first ratio, $4$ crossword puzzles to $9$ word searches, we check if it can be simplified. The greatest common divisor (GCD) of $4$ and $9$ is $1$ , so the ratio $4:9$ is already in its simplest form.
Calculate Ratio $2$ : Step $2$ : Calculate the ratio for the second pair of values. $\newline$ For the second ratio, $7$ crossword puzzles to $10$ word searches, we check if it can be simplified. The GCD of $7$ and $10$ is $1$ , so the ratio $7:10$ is also in its simplest form.
Compare Simplified Ratios: Step $3$ : Compare the two simplified ratios. $\newline$ We compare $4:9$ and $7:10$ . To check if these ratios are equivalent, we cross-multiply $(4\times10$ and $9\times7)$ and see if the products are equal. $\newline$ $4 \times 10 = 40$ $\newline$ $9 \times 7 = 63$ $\newline$ Since $40$ is not equal to $63$ , the ratios $4:9$ and $7:10$ are not equivalent.

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