Which of the following is equal to (9)/(7 × 53)?

1989 AMC 8 Problem 13 — Solution

1989 AMC 8 Problem 13

Below is the professionally curated solution for Problem 13 of the 1989 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1989 AMC 8 solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:fraction place value

Difficulty rating: 920

13.

Which of the following is equal to

$\frac{9}{7 \times 53}?$

$\dfrac{.9}{.7 \times 53}$

$\dfrac{.9}{.7 \times .53}$

$\dfrac{.9}{.7 \times 5.3}$

$\dfrac{.9}{7 \times .53}$

$\dfrac{.09}{.07 \times .53}$

Solution:

To rewrite the numerator $9$ as $.9,$ divide it by $10.$ To keep the fraction equal, divide the denominator by $10$ too, which means dividing one of its factors by $10.$

Dividing the factor $7$ by $10$ gives $\frac{.9}{.7 \times 53},$ which equals the original. Each other choice changes the value by a factor of $10$ or $100.$

Thus, the correct answer is A .

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