Rational Numbers on the Number Line
Grade 7 · Math · Study Guide
Place, compare, and order rational numbers — including fractions, decimals, and negatives — on the number line.
A rational number is any number that can be written as a fraction p/q, where p and q are integers and q ≠ 0. This includes all integers (like -5, 0, 7), fractions (like 3/4 or -2/3), and decimals that either end (like 0.75) or repeat (like 0.333...). Numbers like √2 and π are NOT rational — they are irrational.
The number line extends infinitely in both directions. Zero sits in the middle, positive numbers go right, and negative numbers go left. Every rational number has a specific location on this line. To plot a fraction like 3/4, you divide the space between 0 and 1 into 4 equal parts and count 3 of them to the right. For -3/4, you do the same but go left of zero.
To compare rational numbers, think about their position on the number line. Numbers further to the right are greater. So -1/2 > -3/4 because -1/2 is closer to zero (further right) than -3/4. A common trap is thinking a larger absolute value always means a larger number — for negatives, the opposite is true.
To convert a fraction to a decimal for plotting, divide the numerator by the denominator. 3/4 = 0.75. For mixed numbers like 2 1/3, the integer part tells you which pair of integers the number lives between — in this case, between 2 and 3 — then you locate the fractional part.
Ordering multiple rational numbers is easiest when you convert them all to decimals first. Then place them on a number line from least to greatest. This is a skill that connects directly to comparing quantities in real-world problems like temperature, elevation, and bank accounts.
| Rational Number | Decimal Form | Position on Number Line |
|---|---|---|
| -3/4 | -0.75 | Between -1 and 0, closer to -1 |
| -1/4 | -0.25 | Between -1 and 0, closer to 0 |
| 1/2 | 0.5 | Halfway between 0 and 1 |
| 5/4 | 1.25 | Between 1 and 2, closer to 1 |
| Comparison | True or False | Why |
|---|---|---|
| -1/2 > -3/4 | True | -1/2 = -0.5, -3/4 = -0.75; -0.5 is further right |
| -2 < -1/2 | True | -2 is far left; -1/2 is closer to zero |
| -5/6 > -4/6 | False | -5/6 = -0.833 is further left than -4/6 = -0.667 |
Key terms
- Rational number
- Any number that can be written as a fraction p/q where p and q are integers and q ≠ 0
- Number line
- A line where every point represents a number; positives go right, negatives go left of zero
- Absolute value
- The distance of a number from zero on the number line; always non-negative
- Opposite numbers
- Two numbers that are the same distance from zero but on opposite sides, like 3/4 and -3/4
- Comparing rational numbers
- On a number line, the number further to the right is always greater
Practice questions
Which of the following is NOT a rational number?
- -7
- 0.625
- √5
- 4/3
Show answer
Answer: √5
On the number line, -3/4 is to the right of -1.
Show answer
Answer: True
The rational number -0.5 is equivalent to the fraction ___.
Show answer
Answer: -1/2
Which list shows the numbers in order from least to greatest?
- -1/2, -3/4, 0.25, 1
- -3/4, -1/2, 0.25, 1
- 0.25, -1/2, -3/4, 1
- 1, 0.25, -1/2, -3/4
Show answer
Answer: -3/4, -1/2, 0.25, 1
The number -5/3 lies between -2 and -1 on the number line.
Show answer
Answer: True
Fun facts
- Ancient Greek mathematicians were shocked to discover that √2 could not be written as a fraction — they called it 'irrational' because it defied their mathematical worldview, and some say it was kept secret.
- Sea level is zero on the elevation number line. The lowest point on Earth, the Dead Sea at about -430 meters, is a real-world rational number plotted far below zero.
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