Examples on Simplification

Examples on simplification are discussed, in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. Different types of questions on simplifications are explained here step by step.

1. Simplify: 37 - [5 + {28 - (19 - 7)}] 

Solution: 


37 - [5 + {28 - (19 - 7)}] 

= 37 - [5 + {28 - 12}]      [Removing the innermost bracket ( )] 

= 37 - [5 + 16]                [Removing braces { }]

= 37 - 21 

= 16. 


2. Simplify: 78 - [24 - {16 (5 - 4 - 1)}]

Solution:


78 - [24 - {16 - (5 – 4 - 1)}]

= 78 - [24 - {16 - (5 - 3)}]       [Removing vinculum]

= 78 -[24 - {16 - 2}]               [Removing parentheses]

= 78 - [24 – 14]                      [Removing braces]

= 78 - 10

= 68.



3. Simplify: 197 - [1/9{42 + (56 - 8 + 9)} +108]

Solution:


197 - [1/9 {42 + (56 - 8 + 9)} +108]

= 197 – [1/9 {42 + (56 – 17)} + 108]       [Removing vinculum]

= 197 - [1/9 {42 + 39} + 108]                [Removing parentheses]

= 197 - [(81/9) + 108]                          [Removing braces]

= 197 - [9 + 108]

= 197 - 117

= 80



4. Simplify: 39 – [23 – {29 – (17 – 9 – 3)}]

Solution:


39 - [23 - {29 – (17 – 9 – 3)}]

= 39 - [23 - {29 - (17 - 6)} ]      [Removing vinculum]

= 39 - [23 - {29 - 11}]              [Removing parentheses]

= 39 - [23—18]                         [Removing braces]

= 39 – 5

= 34



5. Simplify:

(i) 15 - (-5) {4 - 7 - 3} ÷ [3{5 + (-3) x (-6)}]

Solution:


15 - (-5) {4 - 7 - 3} ÷ [3{5 + (-3) x (-6)}]

= 15 - (-5) {4 - 4} ÷ [3 {5 + 18}]

= 15 - (-5) x 0 ÷ 3 x 23

= 15 - (-5) x 0 ÷ 69

= 15 - (-5) x 0       [Performing division 0 ÷ 69 = 01]

= 15


(ii) 95 - [144 ÷ (12 x 12) - (-4) - {3 – 17 - 10}]

Solution:


95 - [144 ÷ (12 x 12) - (-4) - {3 - 17 - 10}]

= 95 - [144 ÷ (12 x 12) - (-4) - {3 -7}]

= 95 - [144 ÷ 144 - (-4) - {3-7)]

= 95 - [1 - (-4) - (-4)]      [Performing division]

= 95 - [1 + 4 + 4]

= 95 - 9

= 86

Students can practice these examples on simplification which are discussed here step by step and then proceed to the worksheet for more practice.

 Numbers - Integers

Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification


 Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification













7th Grade Math Problems

From Examples on Simplification to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 01, 23 01:16 AM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  2. Days of the Week | 7 Days of the Week | What are the Seven Days?

    Nov 30, 23 10:59 PM

    Days of the Weeks
    We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…

    Read More

  3. Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical

    Nov 30, 23 01:08 PM

    Types of Lines
    What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…

    Read More