1989 AMC 8 第 13 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

13.

下列哪个式子等于

97×53\frac{9}{7 \times 53}

Which of the following is equal to

97×53?\frac{9}{7 \times 53}?

.9.7×53\dfrac{.9}{.7 \times 53}

.9.7×.53\dfrac{.9}{.7 \times .53}

.9.7×5.3\dfrac{.9}{.7 \times 5.3}

.97×.53\dfrac{.9}{7 \times .53}

.09.07×.53\dfrac{.09}{.07 \times .53}

答案:A
知识点:分数位值
难度评级:920
解答:

将分子 99 除以 1010,得到 .9.9。为了保持分数值不变,分母整体也要除以 1010,即把其中一个因数除以 1010

把分母中的因数 77 除以 1010,而另一个因数保持不变,便得到 .9.7×53\frac{.9}{.7 \times 53}。其他选项会使原式改变 1010 倍或 100100 倍。

所以正确答案是 A

To rewrite the numerator 99 as .9,.9, divide it by 10.10. To keep the fraction equal, divide the denominator by 1010 too, which means dividing one of its factors by 10.10.

Dividing the factor 77 by 1010 gives .9.7×53,\frac{.9}{.7 \times 53}, which equals the original. Each other choice changes the value by a factor of 1010 or 100.100.

Thus, the correct answer is A .

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