Comparing numbers and fractions, ordering on number line
Elementary Foundations • K-5
In everyday life, we constantly compare: Who is taller? Which bag has more candy? Is this fraction bigger or smaller? In this lesson, you will learn how to compare whole numbers and fractions, and how to place numbers in order on a number line.
We use three symbols to compare numbers:
| Symbol | Meaning | Example |
|---|---|---|
| > | is greater than | 8 > 5 (eight is greater than five) |
| < | is less than | 3 < 7 (three is less than seven) |
| = | is equal to | 4 = 4 (four equals four) |
Think of the > and < symbols as an alligator's mouth. The alligator is hungry and always wants to eat the bigger number. The open side of the symbol faces the larger number: 9 > 3 (mouth opens toward 9).
Always compare from left to right, starting with the largest place value.
A number line is a straight line with numbers placed at equal intervals. Numbers get larger as you move to the right and smaller as you move to the left.
Any number to the right of another number is greater. Any number to the left is smaller. This makes number lines perfect for putting numbers in order.
Find each number on the number line and read from left to right:
From least to greatest: 2, 4, 7, 9.
From greatest to least: 9, 7, 4, 2.
Comparing fractions requires a bit more thought. Here are the key strategies:
Same denominator: When two fractions have the same denominator, just compare the numerators. The larger numerator means the larger fraction.
Same numerator: When two fractions have the same numerator, the one with the smaller denominator is larger (bigger pieces).
Both fractions have the numerator 2. Compare the denominators: 4 < 6, which means fourths are larger pieces than sixths.
Two big pieces beat two small pieces!
It helps to know where common fractions fall compared to 1⁄2:
Students often think bigger numbers always mean bigger fractions. But 1⁄8 is NOT bigger than 1⁄3, even though 8 is bigger than 3. Remember: the denominator tells you the size of each piece. More pieces means smaller pieces!
1. Fill in the blank with >, <, or =: 345 ___ 354
Hundreds: 3 = 3. Tens: 4 < 5. So 345 < 354.
2. Order from least to greatest: 58, 85, 41, 14
14, 41, 58, 85. Compare the tens digits first: 1, 4, 5, 8.
3. Which is larger: 5⁄8 or 3⁄8?
5⁄8 is larger. Same denominator, so compare numerators: 5 > 3.
4. Which is larger: 1⁄2 or 1⁄4?
1⁄2 is larger. Same numerator, so the smaller denominator means bigger pieces.
5. Place these fractions in order from least to greatest: 3⁄4, 1⁄4, 2⁄4
1⁄4, 2⁄4, 3⁄4. All have the same denominator, so order the numerators: 1, 2, 3.
Summary: To compare whole numbers, start from the largest place value and work right. For fractions with the same denominator, compare numerators. For fractions with the same numerator, the smaller denominator means a larger fraction. Number lines help you visualize order.