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Expanding Brackets: Methods, Solved Examples, Practice Problems - Testbook

Last Updated on Jul 31, 2023
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Bracket expansion is a mathematical method that allows us to simplify numbers without altering their values. By multiplying each term inside the bracket, we can remove the brackets and present the numbers in an expanded form. This technique is especially handy when dealing with complex multiplication problems.

Keeping track of every step in a mathematical operation can be challenging. That's why the 6th grade Mathematics curriculum introduces the concept of brackets. This tool helps students simplify large numbers and solve problems more efficiently.

Students will also encounter bracket expansion when they start learning about algebraic expressions. It is crucial to understand the basics of this concept.

How Does Bracket Expansion Work?

Bracket expansion is a straightforward process. It involves multiplying the numbers outside the brackets with the numbers inside the brackets, effectively removing the brackets.

Let's look at some examples to better understand how to expand brackets.

Examples

Example 1: Solve 8 × 121

Solution: 8 x 121

We can express 121 as;

121 = 100 + 21

Therefore,

8 x 121 = 8 x (100 + 21)

Expanding the brackets, we get;

⇒ 8 x 100 + 8 x 21

⇒ 800 + 168

⇒ 968

Hence, 8 x 121 = 968.

Practice Problems

Try solving these problems using the method of bracket expansion.

  1. 109 x 68
  2. 46 x 14
  3. 104 x 91
  4. 501 × 82
  5. 959 × 388
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Frequently Asked Questions

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

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

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

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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