Lesson 3: Comparing fractions. Equivalent Fractions.
Lesson 3: Comparing Fractions. Equivalent Fractions
Find equivalent fractions and compare fractions.
A fraction is a part of a whole. A fraction has two components. The number on the top of the line is called the numerator. It tells how many equal parts of the whole are given. The number at the bottom of the fraction line (bar) is called the denominator. The denominator represents the total number of parts that make up a whole.
In this lesson you will learn about the concept of a fraction and comparing fractions with unlike denominators.
You will practice how to compare fractions with different denominators and why, in order to do that, you need to bring them to the Lowest Common Denominator (LCD).
To find the LCD you would need to find a number that is evenly divisible by the denominators of the fractions you are comparing. But remember, when the denominator changes, the numerator changes with it.
For example, how could you determine which one is greater, 3/4 or 2/5? In order to compare them, express both fractions in terms of the same number of parts that make up a whole.
The Lowest Common Multiple for 4 and 5 is 20. So, the Lowest Common Denominator is also 20. Now, express each fraction in terms of the denominator 20, preserving the ratio.
3/4 is equivalent to 15/20.
And 2/5 is equivalent to 8/20.
Now, that the denominators are the same, only compare the numerators. Compare them as natural numbers: 15 is greater than 8.
Thus, 15/20 is greater than 8/20.
Record it as 15/20 > 8/20.
In this lesson you will also discover how to compare fractions without using a number line and how to determine equivalent fractions.
Fractions Short Animation
Key ideas: Comparing Fractions. Equivalent Fractions
Equivalent fractions show the same amount: 2/3 = 4/6 = 8/12. Multiply or divide the numerator and denominator by the same number.
To simplify, divide the top and bottom by their GCF. To compare fractions with different denominators, rewrite them with a common denominator (the LCD), then compare numerators.
Worked examples
Example 1
Find a fraction equivalent to 2/3 with denominator 12.
- 3 × 4 = 12, so multiply the top by 4 too.
- 2/3 = 8/12
Example 2
Simplify 18/24.
- The GCF of 18 and 24 is 6.
- 18 ÷ 6 = 3 and 24 ÷ 6 = 4: 3/4
Example 3
Which is greater, 3/4 or 5/6?
- LCD = 12: 3/4 = 9/12 and 5/6 = 10/12.
- 5/6 is greater.
Example 4
Order 1/2, 3/8 and 5/12 from least to greatest.
- LCD = 24: 12/24, 9/24 and 10/24.
- 3/8 < 5/12 < 1/2
Common mistakes
- Multiplying only the numerator or only the denominator.
- Comparing fractions with different denominators by looking at the numerators only.
Questions students ask
How do I know a fraction is fully simplified?
When the only number that divides both the numerator and the denominator is 1.
Grade 6 Fraction Properties Quiz
Check your understanding
Try the quiz for this lesson. You’ll see right away if each answer is correct.