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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.

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

One person carries out the later subtraction first $20-4-3$$20 - 4 - 3$ $\ne 20-1$$\ne 20 - 1$ $=19$$= 19$.
Another person carries out the initial subtraction first $20-4-3$$20 - 4 - 3$ $=16-3$$= 16 - 3$ $=13$$= 13$

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$$20 - 4 - 3$ $\ne 20-1$$\ne 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÷6÷3$$36 \div 6 \div 3$

It is wrong to simplify as $36÷6÷3$$36 \div 6 \div 3$ $\ne 36÷2$$\ne 36 \div 2$ $=18$$= 18$

The correct order of simplification is $36÷6÷3$$36 \div 6 \div 3$ $=6÷3$$= 6 \div 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$$20 - 4 + 3$ $\ne 20-7$$\ne 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÷6×3$$36 \div 6 \times 3$

It is wrong to simplify as $36÷6×3$$36 \div 6 \times 3$ $\ne 36÷18$$\ne 36 \div 18$ $=2$$= 2$

The correct order of simplification is $36÷6×3$$36 \div 6 \times 3$ $=6×3$$= 6 \times 3$ $=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÷3×2$$4 + 6 \div 3 \times 2$
The answer is "$8$$8$".

The division and multiplication are higher in precedence over addition. so $6÷3×2$$6 \div 3 \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÷3×2$$4 + 6 \div 3 \times 2$

$=4+2×2$$= 4 + 2 \times 2$

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

$=8$$= 8$

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

$10-3-2×3$$10 - 3 - 2 \times 3$

$=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