Lesson 3: Fractions and Decimals on the Number Line

Property

To represent a fraction $\frac{1}{b}$ on a number line, partition the interval from 0 to 1 into $b$ equal parts. Each part has size $\frac{1}{b}$.
To represent a fraction $\frac{a}{b}$ on a number line, mark off $a$ lengths of $\frac{1}{b}$ from 0.
The resulting endpoint locates the number $\frac{a}{b}$.
This process is repeated on the left side of 0 for negative fractions.

Examples

• To locate $\frac{3}{4}$ on a number line, divide the unit from 0 to 1 into 4 equal parts and mark the end of the third part.
• The number $-\frac{7}{5}$ is located by marking off 7 lengths of size $\frac{1}{5}$ to the left of 0. This is the same as $-1\frac{2}{5}$.
• The point for $1.5$ is the same as $\frac{3}{2}$. It is found by marking 3 lengths of $\frac{1}{2}$ to the right of 0.

Explanation

To place a fraction like $\frac{2}{3}$ on a number line, first divide the space from 0 to 1 into 3 equal parts. Each part is $\frac{1}{3}$. Then, you simply count 2 of those parts over from zero.

Property

To place decimals and mixed numbers on a number line, convert them to equivalent forms that show their position clearly.
For decimals, identify which two consecutive integers the decimal falls between, then divide that unit interval into equal parts based on the decimal place value.
For mixed numbers like $a\frac{p}{q}$, locate the whole number part $a$, then add the fractional part $\frac{p}{q}$ by dividing the unit interval into $q$ equal parts and moving $p$ parts in the appropriate direction.

Examples