# Simplify – Definition with Examples

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.

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.

### 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.

## Solved Examples:

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

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

1

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

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

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

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

### What 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 $\frac{1}{3}$
4

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

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