Fraction on a Number Line Math Example 3

Follow the full solution, then compare it with the other examples linked below.

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Place

\frac{3}{8}

on a number line between 0 and 1. Between which two unit fractions does it fall?

1
Step 1: Divide the segment from 0 to 1 into 8 equal parts. Each part has length $\frac{1}{8}$ .
2
Step 2: Count 3 parts from 0 to locate $\frac{3}{8}$ . It sits at the 3rd tick mark.
3
Step 3: Compare with unit fractions: $\frac{1}{3} = \frac{8}{24}$ and $\frac{3}{8} = \frac{9}{24}$ and $\frac{1}{2} = \frac{12}{24}$ . So $\frac{1}{3} < \frac{3}{8} < \frac{1}{2}$ .

Answer

\frac{3}{8} \text{ falls between } \frac{1}{3} \text{ and } \frac{1}{2}

To compare fractions with different denominators, find a common denominator. Using 24ths:

\frac{1}{3} = \frac{8}{24}

\frac{3}{8} = \frac{9}{24}

, and

\frac{1}{2} = \frac{12}{24}

. This confirms

\frac{3}{8}

lies between the unit fractions

\frac{1}{3}

and

\frac{1}{2}

on the number line.

About Fraction on a Number Line

Locating and representing a fraction as a precise point on a number line by dividing the unit interval into equal parts.

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