Whole Numbers : Precedence of Arithmetic Operations

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Precedence of Arithmetic Operations

what you'll learn...

overview

The expression $3 \times 2 - 1$ $3xx2-1$ can possibly be simplified in two ways (considering a rule for the precedence order of operation is not established yet.)

• $3 \times 2 - 1 = 3 \times 1 = 3$ $3xx2-1 = 3xx1=3$ (subtracted first) and

• $6 - 1 = 5$ $6-1=5$ (multiplied first)

Which one is correct? To resolve this, the precedence order of arithmetic operations in a numerical expression is established as a rule.

one problem, many answers

Simplify $2 + 4 \times 3$ $2+4xx3$ .

• One person adds first and multiplies next, $2 + 4 \times 3$ $2+4xx3$ $= 6 \times 3$ $=6 xx 3$ $= 18$
• Another person multiplies first and then adds, $2+4xx3$ $=2 + 12$ $=14$

Which answer is the correct one?

To resolve this, a rule of precedence is accepted by all and agreed on. As per that rule,
• It is wrong to do $2+4xx3$ $=6 xx 3$ $= 18$
Addition $2+4$ is not to be performed first.

• $2+4xx3$ $=2 + 12$ $=14$
Multiplication $4xx3$ is performed first and then addition is performed.

Multiplication is higher in precedence to addition. In

$2+4xx3$ , the multiplication is to be simplified ahead of addition.

The word "precedence" means: priority over another; order to be observed.

In a numerical expression, the precedence order is:
• division and multiplication (both in the same level same level of precedence)
• addition and subtraction (both in the same level of precedence)

This is abbreviated as BODMAS (Division, Multiplication, Addition, Subtraction) or PEMDAS (Multiplication, Division, Addition, Subtraction).

The letters B O or P E are explained later

examples

Simplify $1+ 6xx3$ .
The answer is " $19$ ".
Multiplication is higher in precedence over addition. so

$quad 1+6xx3$

$quad =1+18$

$quad =19$ .

Simplify $9-6-:3$
The answer is " $7$ ". Division is higher in precedence over subtraction. So

$quad 9-6-:3$

$quad =9-2$

$quad =7$

Simplify $3+ 6-:3$ .
The answer is " $19$ ".
Division is higher in precedence over addition. so

$quad 3+6-:3$

$quad =3+2$

$quad =5$ .

summary

In a numerical expression, the precedence order is:

• division and multiplication (both in the same level same level of precedence)

• addition and subtraction (both in the same level of precedence)

This is abbreviated as BODMAS (Division, Multiplication, Addition, Subtraction) or PEMDAS (Multiplication, Division, Addition, Subtraction).

The letters B O or P E are explained later

Outline

The outline of material to learn whole numbers is as follows

Note: click here for detailed outline of Whole numbers

• Introduction

→ Numbers

→ Large Numbers

→ Expanded form

→ Face and place values

→ Approximation and Estimation

• Comparison

→ Comparing two numbers

→ Number line

→ Predecessor & Successor

→ Largest & Smallest

→ Ascending & Descending

• Addition Subtraction

→ Addtion: First Principles

→ Addition: Simplified Procedure

→ Subtraction: First Principles

→ Subtraction: Simplified Procedure

• Multiplication Division

→ Multiplication: First Principles

→ Multiplication: Simplified Procedure

→ Division: First Principles

→ Division: Simplified Procedure

• Numerical Expression

→ Introducing Numerical Expressions

→ Precedence

→ Sequence

→ Brackets