Are these ratios equivalent? 6 old erasers : 15 new erasers 8 old erasers : 19 new erasers Choices: (A)yes (B)no

Identify Ratios: Identify the given ratios and simplify them if possible. First ratio: 6 old erasers : 15 new erasers. Second ratio: 8 old erasers : 19 new erasers.Simplify Ratios: Check if the first ratio can be simplified by finding the greatest common divisor (GCD) of 6 and 15. GCD of 6 and 15 is 3. Simplified first ratio: (6 ÷ 3) : (15 ÷ 3) = 2 : 5.Check Simplification: Check if the second ratio can be simplified by finding the GCD of 8 and 19. GCD of 8 and 19 is 1 (since 19 is a prime number and does not divide 8). Simplified second ratio: 8 : 19.Compare Ratios: Compare the simplified ratios to see if they are equivalent. First simplified ratio: 2 : 5. Second simplified ratio: 8 : 19. Since 2/5 is not equal to 8/19, the ratios are not equivalent.

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Are these ratios equivalent? $\newline$ $6$ old erasers : $15$ new erasers $\newline$ $8$ old erasers : $19$ new erasers $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Grade 6

Equivalent ratios: word problems

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Q. Are these ratios equivalent?

\newline

6

old erasers :

15

new erasers

\newline

8

old erasers :

19

new erasers

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Identify Ratios: Identify the given ratios and simplify them if possible. $\newline$ First ratio: $6$ old erasers : $15$ new erasers. $\newline$ Second ratio: $8$ old erasers : $19$ new erasers.
Simplify Ratios: Check if the first ratio can be simplified by finding the greatest common divisor (GCD) of $6$ and $15$ . $\newline$ GCD of $6$ and $15$ is $3$ . $\newline$ Simplified first ratio: $(6 \div 3) : (15 \div 3) = 2 : 5$ .
Check Simplification: Check if the second ratio can be simplified by finding the GCD of $8$ and $19$ . $\newline$ GCD of $8$ and $19$ is $1$ (since $19$ is a prime number and does not divide $8$ ). $\newline$ Simplified second ratio: $8 : 19$ .
Compare Ratios: Compare the simplified ratios to see if they are equivalent. $\newline$ First simplified ratio: $2 : 5$ . $\newline$ Second simplified ratio: $8 : 19$ . $\newline$ Since $\frac{2}{5}$ is not equal to $\frac{8}{19}$ , the ratios are not equivalent.