Sequence in Arithmetic Operations of Same Precedence

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 $20-4-3$ $\ne 20-1$ $=19$.

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 $20-4-3$ $\ne 20-1$ $=19$.

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 $36\xf76\xf73$

It is wrong to simplify as $36\xf76\xf73$ $\ne 36\xf72$ $=18$

The correct order of simplification is $36\xf76\xf73$ $=6\xf73$ $=2$.

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 $20-4+3$ $\ne 20-7$ $=13$.

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 $36\xf76\times 3$

It is wrong to simplify as $36\xf76\times 3$ $\ne 36\xf718$ $=2$

The correct order of simplification is $36\xf76\times 3$ $=6\times 3$ $=18$.

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

examples

Simplify $4+6\xf73\times 2$

The answer is "$8$".

The division and multiplication are higher in precedence over addition. so $6\xf73\times 2$ is to be simplified first.

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

$4+6\xf73\times 2$

$=4+2\times 2$

$=4+4$

$=8$

Simplify $10-3-2\times 3$.

The answer is "$1$". The multiplication is higher in precedence over subtraction and so $2\times 3$ 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.

$10-3-2\times 3$

$=10-3-6$

$=7-6$

$=1$

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__