Learning how to reduce fractions is not a difficult task if the basic concepts of mathematics are clear. Here is some information about it…
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. Simplification or reduction of fractions is a handy lesson to learn, as it helps ease calculations in various types of problems.
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, 56/72 to its simplest form.
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,
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Factors of 72 = 1, 2, 3, 4, 8, 9, 12, 18, 36, 72
Step 2: Now that we have got the GCF as 8, we divide both the numerator and denominator by 8. The value of the fraction remains the same if we can divide both numerator and denominator by the same number, and makes solving them a lot easier.
56 ÷ 8 = 7
72 ÷ 8 = 9
Hence, the reduced fraction is: 7/9. Isn’t this simple?
How to Reduce Fractions with Variables
Now we are going to study how to reduce fractions with variables, also known as algebraic fractions. Variables, by definition, are not a fixed parameter like numbers, and their value can vary.
All we have to do when reducing algebraic fractions is to find the factors of the variables. Having said that, I would like to emphasize that you should be good in factorizing in order to reduce algebraic fractions.
Question 1: 46 x3y ÷ x2y3
How to Solve:
Step 1: The expression ’46 x3y’ can also be represented as 46(x)(x)(x)(y)
Step 2: Similarly, in the denominator, ‘x2y3‘ is the same as (x)(x)(y)(y)(y)
Step 3: Now cancel out the common variables in the numerator and denominator. Therefore, 46(x)(x)(x)(y)÷(x)(x)(y)(y)(y) = 46(x) ÷ (y)(y)
Step 4: Thus the reduced fraction is 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 = 1(x + 4) (nothing to simplify)
Step 3: Therefore, the fraction becomes x(x+4) ÷ 1(x + 4)
Step 4: Cancelling out the common elements, all that remains is x/1, which is the same as ‘x’.
This was a very simple problem, but when you have to solve more complex problems, ensure that you remember numerous algebraic formulae, as they will help in factorizing algebraic expressions. Given below is a table containing some of the most basic formulae in algebra that you must remember.
|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 case 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 is a simple task once you learn how to do it.
Question: Reduce: 31/7 (read as ‘3 whole 1 by 7’)
Convert the mixed fraction to normal form. Here it will be (7 x 3 + 1) ÷ 7 = 22 ÷ 7
If the resulting fraction can be reduced further, use the method in the first section of this article to reduce it. However, mixed fractions should not be open to further reduction when simplified.
This was all about how to reduce fractions. To enjoy studying mathematics, the first step is to take an interest in the magic of numbers.