How to Reduce Fractions

Some kids get scared when they see mathematical problems involving fractions as they're unable to think of fast and quick ways of simplifying fractions. Fraction simplification is a good math lesson to learn as that helps in easing calculations in math word problems. Since simplifying fraction involves division and multiplication, kids get a bit uncomfortable. I'm going to help kids with some information on reducing fractions so that they're able to understand this interesting mathematics lesson. Acquainting yourself on how to divide fractions is important so that you can learn to simplify fractions with ease.

How to Reduce Fractions to Simplest Form

Le's begin our exercise on how to simplify fractions by firstly knowing ways to reduce a fraction in its simplest form. Consider a problem,

Question: Reduce the fraction, 72 ÷ 56 to its simplest form.

Answer: 72 ÷ 56 = 9 ÷ 7

How to Solve:

Step#1: Since fraction simplification involves reducing the numerator and denominator to lowest forms such that they can't be further divided by a common factor, our task reduces to find the greatest common factor (GCF) of the numerator and denominator. That means,

72 = 1, 2, 3, 4, 8, 9, 12, 18, 36, 72
56 = 1, 2, 4, 7, 8, 14, 28, 56

Step#2: Now, that we have got the GCF as 8, we have to reduce numerator and denominator by dividing it by GCF or 8

72 ÷ 8 = 9
56 ÷ 8 = 7

Hence, the reduced fraction is: 9÷7. Isn't this simple?

How to Reduce Fractions with Variables

In our next step in learning fraction reductions, we are going to study the tricks to reduce fractions with variables. We all know variables are not a fixed parameter like numbers that their values can vary depending on our choice. For instance, consider the expression, x² + 4x + 3. Putting different values of 'x' in the given expression we can get different values of this function. So how to reduce variables in fractions. It's fairly simple. All we have got to do is to find factors of the variables. Having said that, I would like to emphasize that you should be good in factorizing. You must be aware of factor by grouping method that helps in simplification of algebraic expressions.

Question#1: 46 x³y ÷ x²y³

How to Solve:

Step#1: You guessed correctly - 46 x³y = 46. x. x. x. y

Step#2: Similarly, denominator, x²y³ = x.x.y.y.y

Step#3: Now, it is easier to divide, 46. x. x. x. y and x.x.y.y.y. Therefore, 46. x. x. x. y÷x.x.y.y.y = 46. x ÷ y.y

Step#4: Answer = 46x ÷ y²

Question#2: Simplify: x² + 4x ÷ x + 4

How to Solve:

Step#1: Numerator = x² + 4x = x(x+4) [Taking 'x' common]

Step#2: Denominator = x + 4 (nothing to simplify)

Step#3: Therefore, x(x+4) ÷ (x + 4)

Step#4: x

Hence, the answer is x.

This was a very simple problem but when you have to solve more complex problems then ensure that you remember numerous algebraic formula as that will help in factorizing algebraic expressions more smartly. Given below is a table containing some of the most basic formula in algebra that must be remembered by you.

Serial Number	Algebraic Formula
1	(a+b)2 = a2 + b2 + 2ab
2	(a - b)2 = a2 + b2 -2ab
3	(a + b)3 = a3 + b3 + 3ab2 + 3a2b
4	a3 + b3 = (a + b)3 - 3a2b - 3ab2
5	(a-b)3 = a3- b3 - 3a2b + 3ab2
6	a3- b3 = (a - b)3 + 3ab(a+b)
7	(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
8	(a + b)2 + (a - b)2 = 2(a2 + b2)
9	(a2- b2) = (a - b)(a + b)
10	(a3 + b3) = (a + b)(a2 - ab+ b2)
11	(a3 - b3) = (a - b)(a2 + b2 + ab)

How to Reduce Improper Fractions

By now, you must have been able to understand the perfect way to reduce fractional numbers. In cas of improper fractions, all you have got to do is to simplify the fraction by the same steps as mentioned above. Improper fractions are those wherein the numerator is higher than the denominator. For example, 90÷64 and 74÷43 are improper fractions as in the both fractions, the value of numerator is greater than the denominator. So just like basic simplification, you have to first find greatest common factor to get the answer.

How to Reduce Mixed Fractions

Reducing mixed fractions isn't a difficult task either. I have explained how to reduce mixed fractions further.

Question: Reduce: 3⁴/₂₈ (read as '3 whole 4 by 28')

Step#1: Convert the mixed fraction to normal fraction form. Here it will be (28 x 3 + 4) ÷ 28 = 88 ÷ 28

Step#2: 88 = 1, 2, 4, 8, 11, 22, 44, 88; 28 = 1, 2, 4, 7, 14, 28

Step#3: Greatest Common Factor of 88 and 28 = 4

Step#4: Dividing 88 and 28 respectively by 4, we get the answer as, 44÷7

This was all about how to reduce fractions. To enjoy studying mathematics, the first step is to practice it with interest