As a teacher, I have seen a frown on the faces of my students when I introduce equivalent fractions in the class. For them, it’s another difficult step they have to learn. Students panic at fractions.
And, I’m not the only teacher in this position. Many teachers agree too that their students are battling with understanding deeper fraction concepts.
But it doesn’t have to be so. To understand how to solve for an equivalent fraction, let’s refresh our memory of what a fraction is.
What Is Fraction?
Almost every kid from grade 2 can tell you that a fraction is part of a whole. So if you break an object into parts, one piece of the broken part is a fraction of the entire object. The most common explanation has always been a pizza or divided shapes.
Look at this Illustration,
You buy a medium-sized chicken pepperoni pizza that comes in 6 slices. If you’re three friends that share the pizza. Each of you’ll have two slices right?
Now, each person’s share is a fraction of the entire pizza. so yours is 2/6 of the pizza, because you took 2 out of the 6 slices.
But where does the equivalent come in?
Let’s find out.
What is an Equivalent Fraction?
Fractions can have different numbers but they still represent the same value, the same amount, when you multiply or divide them.
Their numerator (top number) and denominator (bottom number) are different but when you reduce them, they give you the same answer. They’re equal to each other. For instance ¼ = 2/8 = 4/16.
How?
Here’s how.
How to find an equivalent fraction
You can follow these two steps to solve questions on equivalent fractions.
Step 1
Multiplying or dividing the top and bottom number of the given fraction with the same whole number.
For example, the 2/6 pizza in our first illustration. If you multiply or divide the top and bottom numbers with the same whole number, you’ll get an equivalent fraction.
Let’s see,
If you are given 2/6 of an object, and you choose to multiply by 2 what do you get?
2×2 = 4
6×2 =12
This means 2/6 is equivalent to 4/12. This is because if you divide 4 and 12 by 2, you’ll get 2/6. Because 2, 4,6 and 12 have a common factor. That is, a common number that can divide them evenly.
To get a correct answer, you must always apply the rule. And that is, whatever you do to the numerator you must do to the denominator.
As long as you multiply or divide the numerator and denominator with the same whole number, you’ll get a correct answer.
See this example,
Write the fraction three-seventh as an equivalent fraction with a denominator of 21.
Here is the solution:
3/7 = /21 =
Let’s multiply with (3), the same number that if we use it to divide our answer will give us the same fraction we multiplied without a left over.
3 × 3 = 9
7 × 3 =21
Now go ahead and divide 9/21 by 3 and see if your answer is the same as our given fraction.
Step 2,
Another step to finding equivalent fractions is to use the cross multiply method. Here is how:
- Multiply the top left number with the bottom right number
- Multiply the top right number with the bottom left number.
Here is the formula;
a/b = c/d if a×d = b×c
4/16 × 3/12 =
4× 12 = 3/16
= 48 = 48
Try this exercise.
If you’re given 2/6 and 3/9 how would you cross multiply to get a correct answer?
Follow the cross multiply method to solve this.
Note that a fraction is equivalent if its values are the same.
Conclusion
A fraction is a part of a whole. An equivalent fraction is a fraction that has
different numbers but when simplified end up with the same value.
Fraction is an important part of maths that must be perfected. Most often, students are scared of fractions because they haven’t mastered the practical concepts.
But as with everything, practicing daily is what will help you get the hang of it.
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