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Are these ratios equivalent?\newline1010 teachers to 88 students\newline88 teachers to 1111 students\newlineChoices:\newline(A)yes\newline(B)no

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Q. Are these ratios equivalent?\newline1010 teachers to 88 students\newline88 teachers to 1111 students\newlineChoices:\newline(A)yes\newline(B)no
  1. Identify Ratios: Identify the ratios given in the problem.\newlineFirst ratio: 1010 teachers to 88 students, written as 10:810:8.\newlineSecond ratio: 88 teachers to 1111 students, written as 8:118:11.
  2. Simplify Ratios: Simplify both ratios to check if they are equivalent.\newlineFor the first ratio, simplify 10:810:8 by dividing both numbers by their greatest common divisor, which is 22.\newline10÷2=510 \div 2 = 5, 8÷2=48 \div 2 = 4, so the simplified ratio is 5:45:4.\newlineFor the second ratio, 8:118:11 cannot be simplified further as 88 and 1111 are coprime.
  3. Compare Simplified Ratios: Compare the simplified ratios.\newlineFirst ratio is 5:45:4, and the second ratio is 8:118:11.\newlineSince 5:4≠8:115:4 \neq 8:11, the ratios are not equivalent.

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