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Sequence in Arithmetic Operations of Same Precedence


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overview

The expression 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 (added first) and

 •  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.

One person carries out the later subtraction first 20-4-3 20-1 =19.
Another person carries out the initial subtraction first 20-4-3 =16-3 =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 20-1 =19.
The correct order of simplification is 20-4-3 =16-3 =13

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


Consider 36÷6÷3

It is wrong to simplify as 36÷6÷3 36÷2 =18

The correct order of simplification is 36÷6÷3 =6÷3 =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.

It is wrong to do 20-4+3 20-7 =13.

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

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


Consider 36÷6×3

It is wrong to simplify as 36÷6×3 36÷18 =2

The correct order of simplification is 36÷6×3 =6×3 =18.

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

examples

Simplify 4+6÷3×2
The answer is "8".

The division and multiplication are higher in precedence over addition. so 6÷3×2 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÷3×2

=4+2×2

=4+4

=8


Simplify 10-3-2×3.
The answer is "1". The multiplication is higher in precedence over subtraction and so 2×3 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.

10-3-2×3

=10-3-6

=7-6

=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