1Cademy - Procedure for Locating Fractions on a Number Line

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Procedure for Locating Fractions on a Number Line

To plot fractions on a number line, choose a strategy based on the fraction's type:

Whole numbers (such as $4$ and $-3$ ) are plotted first, as they align directly with the labeled integer tick marks.
Proper fractions have an absolute value less than $1$ , placing them between two consecutive integers (either between $0$ and $1$ , or $0$ and $-1$ ). Subdivide that unit interval into the number of equal parts indicated by the denominator, then count outward from zero to the appropriate part. For example, $\frac{3}{4}$ lies between $0$ and $1$ ; splitting that segment into $4$ equal parts allows the point to be marked at the third tick. Similarly, $-\frac{1}{4}$ falls between $0$ and $-1$ ; it is marked $1$ part to the left of $0$ .
Improper fractions have an absolute value greater than $1$ , locating them beyond the $[-1, 1]$ interval. Converting an improper fraction into a mixed number helps identify the consecutive integers it lies between. For instance, $\frac{6}{5} = 1\frac{1}{5}$ , making it easy to plot just past $1$ on the way to $2$ . Likewise, $\frac{7}{3} = 2\frac{1}{3}$ falls between $2$ and $3$ , while $-\frac{5}{2} = -2\frac{1}{2}$ falls exactly halfway between $-2$ and $-3$ .

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Updated 2026-05-02

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References

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OpenStax

Elementary Algebra @ OpenStax

Ch.1 Foundations - Elementary Algebra @ OpenStax

Algebra

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Prealgebra

Intermediate Algebra @ OpenStax

Ch.1 Foundations - Intermediate Algebra @ OpenStax

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