Simplifications | Laws of Operations | Grade 3 Mathematics
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Operations

Simplifications

We already know about the operations on numbers. Here we will discuss the simplification of arithmetic expressions involving numbers.

Arithmetic Expressions:

An Arithmetic expression in math is a combination of operations (addition, subtraction, multiplication, division) and terms. There are different types of Arithmetic expressions.

Following are examples of some arithmetic expressions.

Examples:

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Orders of Operations

To simplify any arithmetic expression, we need to know the order of operations, that should be followed.

  1. First, do the operations in brackets.
  2. Multiplication and division should be done prior to any operations.
  3. Then addition and subtraction should be done after multiplication and division.
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Examples:

Simplify the followings.

  1. (62 ÷ 2 – 3) × 3 + 6 =
  2. 3 + 21 × 6 – (24 – 4) × 2 =

Answer:

  1. (62 ÷ 2 – 3) × 3 + 6
  2. 3 + 21 × 6 – (24 – 4) × 2
Boy

Laws of Operations

There are some laws which govern the order in which we perform the operations in arithmetic.

  • Commutative law
  • Associative law

Commutative Law:

The order of the numbers does not affect the result in addition, and in multiplication.

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Commutative law is not applicable for subtraction and division.

Examples:

  1. For addition, Boy
  2. For multiplication, Boy

This law is not applicable to subtraction and division.

Boy

Associative Law

This law states that the three numbers are independent of their grouping for addition and multiplication. Clearly, grouping or combination of three numbers doesn’t affect the result.

Associative law is not applicable for subtraction and division.

Examples:

  1. For addition, Boy
  2. For multiplication, Boy

This law is not applicable to subtraction and division.

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Application:

Examples 1:

Simplify.

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Answer:

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Examples 2:

Boy

Answer:

From grade 3:

249 – 200 students are not going to the summer camp.

From grade 2:

238 – 150 students are not going to the summer camp.

From grade 1

98 – 50 students are not going to summer camp

So, the total number of students who don’t want to go to the summer camp is

249 – 200 + 238 – 150 + 98 – 50

= 49 + 88 + 48

= 137 + 48 = 185

Boy

Answer:

Five brothers have given a total of (5 × Rs 60)

Two sisters have given a total of (2 × Rs 50)

The total amount in the fund

(5 × Rs 60) + (2 × Rs 50)

Each child will get

[(5 × Rs 60) + (2 × Rs 50)] ÷ 8

= (Rs 300 + Rs 100) ÷ 8

= Rs 400 ÷ 8

= Rs 50

Boy

Boy
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