Whole Numbers : Sequence in Arithmetic Operations of Same Precedence

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Sequence in Arithmetic Operations of Same Precedence

what you'll learn...

overview

The expression $3 - 1 + 1$ $3-1+1$ can possibly be simplified in two ways (considering a rule for the sequence of operation is not established yet.)

• $3 - 1 + 1 = 3 - 2 = 2$ $3-1+1 = 3-2 = 2$ (added first) and

• $3 - 1 + 1 = 2 + 1 = 3$ $3-1+1 = 2+1 = 3$ (subtracted first)

which one is correct? To resolve this, the sequence of arithmetic operations of same precedence value is established as a rule.

many answers, again

Consider $20 - 4 - 3$ $20-4-3$ .

One person carries out the later subtraction first $20 - 4 - 3$ $20-4-3$ $\neq 20 - 1$ $!=20-1$ $= 19$ $=19$ .
Another person carries out the initial subtraction first $20 - 4 - 3$ $20-4-3$ $= 16 - 3$ $= 16-3$ $= 13$ $=13$
Which answer is correct?

To resolve this, a rule of sequence is accepted by all and agreed on. As per the rule,
It is wrong to do $20 - 4 - 3$ $20-4-3$ $\neq 20 - 1$ $!=20-1$ $= 19$ $=19$ .
The correct order of simplification is $20 - 4 - 3$ $20-4-3$ $= 16 - 3$ $= 16-3$ $= 13$ $=13$

The two subtractions are in the same precedence level. This is to be handled from left to right sequence.

Consider $36 \div 6 \div 3$ $36-:6-:3$

It is wrong to simplify as $36 \div 6 \div 3$ $36-:6-:3$ $\neq 36 \div 2$ $!=36-:2$ $= 18$ $=18$

The correct order of simplification is $36 \div 6 \div 3$ $36-:6-:3$ $= 6 \div 3$ $=6 -:3$ $= 2$ $= 2$ .

The two divisions are in same precedence level. This is to be handled from left to right sequence. .

Sequence in Arithmetic Operations of Same Precedence: To simplify multiple arithmetic operations of same precedence, the operations are carried out in left to right sequence.

Consider $20 - 4 + 3$ $20-4+3$ .

It is wrong to do $20 - 4 + 3$ $20-4+3$ $\neq 20 - 7$ $!=20-7$ $= 13$ $=13$ .

The correct order of simplification is $20 - 4 + 3$ $20-4+3$ $= 16 + 3$ $= 16+3$ $= 19$ $=19$

The subtraction and addition are in the same precedence level. This is to be handled from left to right sequence.

Consider $36 \div 6 \times 3$ $36-:6xx3$

It is wrong to simplify as $36 \div 6 \times 3$ $36-:6xx3$ $\neq 36 \div 18$ $!=36-:18$ $= 2$ $=2$

The correct order of simplification is $36 \div 6 \times 3$ $36-:6xx3$ $= 6 \times 3$ $=6 xx3$ $= 18$ $= 18$ .

The division and multiplication are in same precedence level. This is to be handled from left to right sequence.

examples

Simplify $4 + 6 \div 3 \times 2$ $4+6-:3xx2$
The answer is " $8$ $8$ ".

The division and multiplication are higher in precedence over addition. so $6 \div 3 \times 2$ $6-:3xx2$ is to be simplified first.

In that, the division and multiplication are of same precedence, so it is simplified from left to right.

$4 + 6 \div 3 \times 2$ $4+6-:3xx2$

$= 4 + 2 \times 2$ $=4+2xx2$

$= 4 + 4$ $=4+4$

$= 8$ $=8$

Simplify $10 - 3 - 2 \times 3$ $10-3-2xx3$ .
The answer is " $1$ $1$ ". The multiplication is higher in precedence over subtraction and so $2 \times 3$ $2xx3$ is to be simplified first. Then the two subtraction are in the same precedence level and so they are simplified in the left to right sequence.

$10 - 3 - 2 \times 3$ $10-3-2xx3$

$= 10 - 3 - 6$ $=10-3-6$

$= 7 - 6$ $=7-6$

$= 1$ $=1$

summary

Sequence in Arithmetic Operations of Same Precedence: To simplify multiple arithmetic operations of same precedence, the operations are carried out in left to right sequence.

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