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Equivalent Fractions are defined as fractions that have different numerators and denominators but ultimately represent the same value. For example, both 2⁄12 and 6⁄36 are equivalent fractions because both give 1⁄6 when simplified.
In their simplest form, all fractions become the same, as shown in the example above. This lesson will help you understand more about finding equivalent fractions and checking if two fractions are equivalent or not.
What are Equivalent Fractions?
Two or more fractions are considered equivalent if they simplify to the same value. For example, let us consider the fractions like:
2⁄6, 4⁄12, 5⁄15, 10⁄30
Now let us simplify these fractions:
- 2⁄6 = 1⁄3
- 4⁄12 = 1⁄3
- 5⁄15 = 1⁄3
- 10⁄30 = 1⁄3
As we see, all these fractions simplify to 1⁄3, so they are equivalent fractions.
Equivalent Fractions Definition
Equivalent fractions are fractions that represent the same value, even though their numerators and denominators may differ. For instance, 12⁄24 simplifies to 1⁄2 and 10⁄20 also simplifies to 1⁄2. Thus, 12⁄24 and 10⁄20 are equivalent fractions because they represent the same proportion.
How to Find Equivalent Fractions?
By multiplying or dividing both the numerator and denominator by the same number, you can create equivalent fractions. This makes the fractions simplify to the same value. Let’s discuss two ways to find equivalent fractions:
- Multiply numerator and denominator by the same number.
- Divide numerator and denominator by the same number.
Multiply Numerator and Denominator by the Same Number
To find equivalent fractions, you can multiply both the numerator and denominator of a fraction by the same number. For example, if we want an equivalent fraction of 3⁄4, we can multiply both its numerator and denominator by 2. Therefore, 6⁄8 is another fraction that has the same value as 3⁄4.
Illustration:
3⁄4 × 2 = 6⁄8
3⁄4 × 3 = 9⁄12
3⁄4 × 4 = 12⁄16
3⁄4 × 5 = 15⁄20
Divide Numerator and Denominator by the Same Number
You can also find equivalent fractions by dividing both the numerator and the denominator by a common factor. For example, to find an equivalent fraction for 72⁄108, we can divide both by 2, resulting in 36⁄54.
For further simplification:
Divide 36⁄54 by 2: 18⁄27
Then divide 18⁄27 by 3: 6⁄9
Finally, divide 6⁄9 by 3: 2⁄3
So, some equivalent fractions for 72⁄108 are 36⁄54, 18⁄27, 6⁄9, and 2⁄3 in its simplest form.
How do you know if two fractions are equivalent?
To check if two fractions are equivalent, simplify them to their simplest forms. There are several methods to do this:
- Find a common denominator.
- Convert the fractions to decimal form.
- Use the cross-multiplication method.
- Use visual representation.
Finding a Common Denominator
Let’s use the example of 2⁄6 and 3⁄9. The Least Common Multiple (LCM) of 6 and 9 is 18. Multiply both fractions to get a denominator of 18:
2⁄6 × 3 = 6⁄18
3⁄9 × 2 = 6⁄18
Both fractions are now equal, so they are equivalent.
Converting to Decimal Form
We can also convert the fractions to decimals:
- 2⁄6 = 0.333
- 3⁄9 = 0.333
Since both decimals are the same, the fractions are equivalent.
Cross-Multiplication Method
By cross-multiplying 2⁄6 and 3⁄9, both products equal 18, proving the fractions are equivalent.
Visual Method
By visually representing the fractions as shaded portions of a shape, it’s easy to see that 2⁄6 and 3⁄9 cover the same area, confirming their equivalence.
Equivalent Fractions Chart
Charts and tables help represent concepts more clearly. For example, the following chart shows some fractions that are equivalent to 1⁄4:
- 2⁄8
- 3⁄12
- 4⁄16
Facts about Equivalent Fractions
- Two fractions are equivalent if their decimal or graphical values are the same.
- You can get an equivalent fraction by multiplying both the numerator and denominator by the same number.
- The cross-multiplication method is commonly used to check if two fractions are equivalent.
- Another way to check equivalency is by making the denominators of the fractions equal.
Equivalent Fractions FAQs
What are equivalent fractions?
Equivalent fractions are fractions that represent the same value, even if their numerators and denominators are different. For example, 1/2 is equivalent to 2/4 because both simplify to the same fraction.
How can I find equivalent fractions?
You can find equivalent fractions by multiplying or dividing both the numerator and denominator of a fraction by the same number. For example, multiplying 3/4 by 2 gives 6/8, which is equivalent to 3/4.
Why are equivalent fractions important?
Equivalent fractions are important because they help simplify problems and make calculations easier. They are used in various mathematical operations and are essential for comparing and ordering fractions.
