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Math  /  Numbers & Operations

Question15. Which is equivalent to the expression below? 3−2÷1163^{-2} \div 1 \frac{1}{6} A. 221\frac{2}{21} C. 736\frac{7}{36} B. −221-\frac{2}{21} D. −736-\frac{7}{36}

Studdy Solution

STEP 1

1. The expression involves exponents and division.
2. The fraction 1161 \frac{1}{6} can be converted to an improper fraction.
3. The final expression should be simplified to match one of the given options.

STEP 2

1. Simplify the exponent 3−23^{-2}.
2. Convert the mixed number 1161 \frac{1}{6} into an improper fraction.
3. Perform the division of the simplified exponent by the improper fraction.
4. Simplify the resulting fraction to match one of the given options.

STEP 3

Simplify the exponent 3−23^{-2}: 3−2=132=19 3^{-2} = \frac{1}{3^2} = \frac{1}{9}

STEP 4

Convert the mixed number 1161 \frac{1}{6} into an improper fraction: 116=1⋅6+16=76 1 \frac{1}{6} = \frac{1 \cdot 6 + 1}{6} = \frac{7}{6}

STEP 5

Perform the division of 19\frac{1}{9} by 76\frac{7}{6}: 19÷76=19⋅67 \frac{1}{9} \div \frac{7}{6} = \frac{1}{9} \cdot \frac{6}{7}

STEP 6

Simplify the multiplication: 1⋅69⋅7=663=221 \frac{1 \cdot 6}{9 \cdot 7} = \frac{6}{63} = \frac{2}{21}

STEP 7

Compare the result with the given options: 221 \frac{2}{21} This matches option A.
Solution: A. 221\frac{2}{21}

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