1.2.5 Multiplying by Any Fraction of 100, 1000, etc…

You can take what we learned from the 25’s and 75’s trick (converting them to fractions of 100) with a variety of potential fractions.

Common $\frac{1}{8}$ Fractions

$\frac{1}{8}$‘s are chosen often because they divide evenly:

Number	Fraction Form
125	$\frac{1}{8} \times 1000$
37.5	$\frac{3}{8} \times 100$
6.25	$\frac{5}{8} \times 10$
625	$\frac{5}{8} \times 1000$
875	$\frac{7}{8} \times 1000$

Approximation Fractions

In addition, you see $\frac{1}{6}$‘s, $\frac{1}{3}$‘s, $\frac{1}{9}$‘s, and sometimes even $\frac{1}{12}$‘s for approximation problems (because they do not go evenly into 100, 1000, etc., they have to be approximated usually).

Approximate Value	Fraction Form
223	$\approx \frac{2}{9} \times 1000$
8333.3	$\approx \frac{5}{6} \times 10000$
8333.3	$\approx \frac{1}{12} \times 100000$
327	$\approx \frac{1}{3} \times 1000$
16667	$\approx \frac{1}{6} \times 100000$

For approximations, you will rarely ever see them equate to almost exactly to the correct fraction. For example, you might use $\frac{2}{3} \times 1000$ for any value from 654 − 678. Usually you can tell for the approximation problems what fraction the test writer is really going for.

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Problem Set 1.2.5

Basic Fraction Problems

Approximation Problems

Mixed Fraction Problems

These problems involve mixed fractions like $12\frac{1}{2}\%$, $9\frac{1}{11}\%$, $45\frac{5}{11}\%$, and $44\frac{4}{9}\%$:

* Questions marked with an asterisk accept answers within 5% tolerance.