Are these ratios equivalent? 10 teachers to 8 students 8 teachers to 11 students Choices: (A)yes (B)no

Identify Ratios: Identify the ratios given in the problem. First ratio: 10 teachers to 8 students, written as 10:8. Second ratio: 8 teachers to 11 students, written as 8:11.Simplify Ratios: Simplify both ratios to check if they are equivalent. For the first ratio, simplify 10:8 by dividing both numbers by their greatest common divisor, which is 2. 10 ÷ 2 = 5, 8 ÷ 2 = 4, so the simplified ratio is 5:4. For the second ratio, 8:11 cannot be simplified further as 8 and 11 are coprime.Compare Simplified Ratios: Compare the simplified ratios. First ratio is 5:4, and the second ratio is 8:11. Since 5:4 ≠ 8:11, the ratios are not equivalent.

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Are these ratios equivalent? $\newline$ $10$ teachers to $8$ students $\newline$ $8$ teachers to $11$ students $\newline$ 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

10

teachers to

8

students

\newline

8

teachers to

11

students

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Identify Ratios: Identify the ratios given in the problem. $\newline$ First ratio: $10$ teachers to $8$ students, written as $10:8$ . $\newline$ Second ratio: $8$ teachers to $11$ students, written as $8:11$ .
Simplify Ratios: Simplify both ratios to check if they are equivalent. $\newline$ For the first ratio, simplify $10:8$ by dividing both numbers by their greatest common divisor, which is $2$ . $\newline$ $10 \div 2 = 5$ , $8 \div 2 = 4$ , so the simplified ratio is $5:4$ . $\newline$ For the second ratio, $8:11$ cannot be simplified further as $8$ and $11$ are coprime.
Compare Simplified Ratios: Compare the simplified ratios. $\newline$ First ratio is $5:4$ , and the second ratio is $8:11$ . $\newline$ Since $5:4 \neq 8:11$ , the ratios are not equivalent.