Expanding Brackets

Expanding brackets are used to expand the numbers without changing its value and then removing the brackets by multiplying with each term inside the bracket. The brackets are used to expand the numbers, so that we can write the numbers in simplified form. This method of writing the numbers in expanded form helps to solve multiplication problems.

Sometimes, it is not easy to keep a track of steps involved in mathematical problems. Therefore, in Class 6 Mathematics, the concept of brackets is used to write the large numbers in a simple way and solve the problems quickly.

The concept of expansion of brackets will also be introduced while learning about algebraic expressions. Hence, it is necessary to learn the basics for the students.

How to Expand Brackets?

The process of expanding brackets is a simple one. We need to multiply out the numbers with the numbers present inside the brackets. So, basically we are removing the brackets here.

Let us see some examples here to learn how to expand the brackets.

Solved Examples

Example 1: Solve 7 × 110

Solution: 7 x 110

We can write, 110 as;

110 = 100 + 10

Therefore,

7 x 110 = 7 x (100 + 10)

Now expanding the brackets we get;

⇒ 7 x 100 + 7 x 10

⇒ 700 + 70

⇒ 770

Hence, 7 x 110 = 770.

Example 2: Solve 202 × 203

Solution: 202 × 203

We can write, 202 and 203 as:

202 = 200 + 2

203 = 200 + 3

Thus,

202 × 203 = (200 + 2) x (200 + 3)

⇒ 200 x (200 + 3) + 2 x (200 + 3)

Expanding brackets we get;

⇒ 200 x 200 + 200 x 3 + 2 x 200 + 2 x 3

⇒ 40000 + 600 + 400 + 6

⇒ 41006

Example 3: Solve 17 × 1009

Solution: 17 × 1009

17 = 10 + 7

1009 = 1000 + 9

⇒ (10 + 7) x (1000 + 9)

⇒ 10 x (1000 + 9) + 7 x (1000 + 9)

Expanding brackets we get;

⇒ 10 x 1000 + 10 x 9 + 7 x 1000 + 7 x 9

⇒ 10000 + 90 + 7000 + 63

⇒ 17153

Practice Problems

Solve by expanding brackets methods.

  1. 106 x 67
  2. 45 x 13
  3. 103 x 90
  4. 500 × 81
  5. 958 × 387

Frequently Asked Questions on Expanding Brackets

What is the rule of expanding brackets?

While expanding brackets the value outside the bracket is multiplied by each value inside the bracket followed by addition and subtraction.

How do we compare 4875 and 3542?

Given, 4875 and 3542 are the two numbers. Clearly, at the thousands place, 4 is greater than 3. Therefore, 4875 is greater than 3542.

How do we expand brackets for 3 x (9 + 18)?

Given, 3 x (9 + 18)
Multiply 3 by each term within the bracket followed by addition.
3 x 9 + 3 x 18 = 27 + 54 = 81

What is ascending order and descending order?

Ascending order means arranging the numbers from smallest to largest and descending order means arranging the numbers from largest to smallest.

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