Simplify – Definition with Examples

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Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving. We can —

  • simplify fractions by cancelling all the common factors from both the numerator and the denominator and writing the fraction in its lowest/simplest form.  
  • simplify mathematical expressions by grouping and combining similar terms. This makes the expression easily understandable and solvable.

How do you Simplify Step-by-Step?

Simplifying Fractions

Let’s understand the step by step procedure of simplifying fractions through some examples. 

Simplifying Fractions - SplashLearn
example of Simplifying Fractions - SplashLearn


Do you know that instead of canceling out the common factors in multiple steps we can do it in single step as well. It gives the same simplest form of the fraction. 

simplest form of Simplifying Fractions - SplashLearn


Simplifying Mathematical Expressions

Mathematical expressions are combination of various numbers and operations. So, to simplify them we need to know the rule known as the order of operations. It tells us the correct sequence in which the operations must be performed while simplifying a mathematical expression. We can remember the order using the acronym PEMDAS.

Simplifying Mathematical Expressions - PEDMAS - SplashLearn


Solved Examples:

Example 1: Write 16/24 in the simplest form. 

Solved Example of simplifying fractions - SplashLearn

Example 2: Simplify: 110 – 35 × 2

Solution: 

110 – 35 × 2 (As per PEMDAS, multiplication to be performed before subtraction)

= 110 – 70 

= 30 

Example 3: Simplify: 660 ÷ 22 × (2 + 1)

Solution: 

660 ÷ 22 × (2 + 1) (Solve parenthesis first)

= 660 ÷ 22 × 3 (From left to right, division appears first)

= 30 × 3

= 90 

Example 4: Simplify: 37 − [28 + (19 − 7)] 

Solution:

37 − [28 + (19 − 7)] First solve ( )

= 37 − [28 + 12] Next, solve [ ] 

= 37 − 40       

= 77 

Example 5: Simplify $1\frac{4}{7}\times 2\frac{4}{33} \div \frac{5}{9}$

Solution:

Simplyfly $1\frac{4}{7}\times 2\frac{4}{33} \div \frac{5}{9}$ Convert mixed fraction to improper fraction

= $\frac{11}{7}\times \frac{70}{33} \div \frac{5}{9}$

= $\frac{11}{7}\times \frac{70}{33} \div \frac{9}{5}$ Cancel the common factors

= $\frac{1}{1}\times \frac{2}{1} \div \frac{3}{1}$

= 6

Practice Problems

Simplify

Attend this Quiz & Test your knowledge.

1Simplify the expression: 15 + 10 ÷ 5 = ?

17
15
5
10
CorrectIncorrect
Correct answer is: 17
Applying PEMDAS rule: 15 + 10 ÷ 5 = 15 + 2 = 17

2Simplify the expression: 4 + (3 x 4) ÷ 22

4
7
10
12
CorrectIncorrect
Correct answer is: 7
Applying PEMDAS rule: 4 + (3 x 4) ÷ 22 = 4 + 12 ÷ 4 = 4 + 3 = 7

3What is the simplest form of the fraction $\frac{12}{36}$ ?

$\frac{3}{9}$
$\frac{1}{3}$
$\frac{3}{4}$
$\frac{1}{36}$
CorrectIncorrect
Correct answer is: $\frac{1}{3}$
Cancelling out the common factors we get $\frac{1}{3}$

4Simplify the expression: $18 – [6 – {4 – (8 – 6 + 3 )}]$

$11$
$20$
$7$
$27$
CorrectIncorrect
Correct answer is: $11$
$18 – [6 – {4 – (8 – 6 + 3 )}] = 18 – [6 – {4 – 5}] = 18 – [6 – {– 1}] = 18 – [6 + 1] = 18 – 7 = 11$

Frequently Asked Questions

Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler, usually shorter.

Order of operations play a major role in simplifying mathematical operations. The correct order of operations is: terms in parentheses, exponents, multiplication, division, addition, and, finally, subtraction. A handy acronym you can use to remember this is PEMDAS. 

A fraction is said to be in its simplest form if 1 is the only common factor of its numerator and denominator. Thus, to simplify a fraction, divide the numerator and the denominator by it’s highest common factor. 

These were the basic rules and benefits of simplification in math. Every child should learn the concept as it makes solving complex problems relatively easy. If you are looking for a platform to teach your child mathematics through fun games, try SplashLearn by signing up for free. Since math can be daunting for some children, fun games and puzzles make it seem interesting and much more comprehensive! To know more about the concepts of simplification and other math topics, visit us at: https://www.splashlearn.com/.


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