Question

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11 multiple answer 1 point
select all of the expressions that have the same value as $523 \div 64$.
$5230 \div 640$
$52.3 \div 64$
$.523 \div .064$
$52300 \div 6400$
$52.3 \div 6.4$
12 multiple answer 1 point
select all of the expressions that have the same value as $386 \div 58$.
$38600 \div 580$
$3860 \div 580$
$3.86 \div 0.58$

Explanation:

Step1: Recall division rule

For $\frac{a}{b}$, if we multiply/divide $a$ and $b$ by the same non-zero number $k$, $\frac{ka}{kb}=\frac{a}{b}$.

Step2: Check $5230 \div 640$

Multiply numerator/denominator of $523\div64$ by 10: $\frac{523\times10}{64\times10}=\frac{5230}{640}$, so equal.

Step3: Check $52.3 \div 64$

Numerator divided by 10, denominator unchanged: $\frac{523\div10}{64}
eq\frac{523}{64}$, not equal.

Step4: Check $.523 \div .064$

Multiply numerator/denominator of $523\div64$ by $\frac{1}{1000}$: $\frac{523\div1000}{64\div1000}=\frac{0.523}{0.064}$, so equal.

Step5: Check $52300 \div 6400$

Multiply numerator/denominator of $523\div64$ by 100: $\frac{523\times100}{64\times100}=\frac{52300}{6400}$, so equal.

Step6: Check $52.3 \div 6.4$

Multiply numerator/denominator of $523\div64$ by $\frac{1}{10}$: $\frac{523\div10}{64\div10}=\frac{52.3}{6.4}$, so equal.

Answer:

• $5230 \div 640$
• $.523 \div .064$
• $52300 \div 6400$
• $52.3 \div 6.4$