# Equal Fractions Concept

The equal fractions concept is perhaps one of the most important concepts students must know for primary school Math. I have seen so many questions, again and again, which test this concept and students always get stuck.

Many students are confused about when to make the denominators the same and when to make the numerators the same.

Here is a simple rule:

If both fractions refer to the same whole, you can make the denominators the same.

**Example of Making Denominators The Same**

John gives away 1/2 of his sugar to his brother and 1/4 of his sugar to his sister. What fraction of his sugar does he give away in total?

In this question, both fractions refer to the same total.

Hence, we simply add 1/2 and 1/4 together to get the answer.

What if both fractions refer to different wholes?

**Example of Equal Fractions Concept**

*1/2 of boys is equal to 1/3 of girls. What is the ratio of boys to girls?*

Since the numerator of both fractions are the same, you can easily compare the denominator and that will be the answer:

Boys : Girls

= 2 : 3

**What if the numerators are different?**

Example,

*1/2 of boys is equal to 2/3 of girls. What is the ratio of boys to girls?*

In this case, you convert 1/2 to 2/4 to make the numerators the same.

Then you compare the denominators.

2/4 of boys = 2/3 of girls

So, boys : girls = 4 : 3

This concept is so useful that it can be applied to many different problem sums.

Let’s look at an example.

*There are 836 students in a school. 7/10 of the boys and 7/8 of the girls take bus to school. The number of boys who do not take bus is twice the number of girls who do not take bus. How many girls do not take bus?*

**Solutions**

Fraction of boys who do not take bus = 1 – 7/10 = 3/10

Fraction of girls who do not take bus = 1 – 7/8 = 1/8

Since “the number of boys who do not take bus is **twice** the number of girls who do not take bus”,

3/10 of boys = 2 x 1/8 of girls

3/10 of boys = 1/4 of girls

Now, we apply the equal fractions concept.

1/4 = 3/12

3/10 of boys = 3/12 of girls

Boys : Girls = 10 : 12 = 5 : 6

Since “there are 836 students in a school”,

11 u = 836

1 u = 76

Total girls = 6 x 76 = 456

Girls who do not take bus = 1/8 x 456 = 57 (Answer)

As you can see, using the equal fractions concept is useful, direct and simple. There is no need for complicated Algebra workings.

Do learn **when** and **how** to apply the equal fractions concept. It will be very useful in your P5 and P6 Math exam papers. We will cover it extensively in our tuition classes too.

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