EVALUATE THE FOLLOWING EXPRESSION USING PEMDAS

To evaluate the numerical expression, we need to know the order of operations.

What is an Order of Operations?

An Order of Operations is a rule that can be used to simplify or evaluate more than one operation.

There are many types of rules, we will use here the PEMDAS Rule.

Example 1 :

(20 + 80 ÷ 2 × 8) ÷ [(54 ÷ 9 + 14) ÷ 4]

Solution :

= (20 + 80 ÷ 2 × 8) ÷ [(54 ÷ 9 + 14) ÷ 4]

= (20 + 40 × 8) ÷ [(6 + 14) ÷ 4]

= (20 + 320) ÷ [20 ÷ 4]

= (20 + 320) ÷ 5

= 340 ÷ 5

= 68

P( ), D

P( ), M & A

P( ), [ ], A & D

P( ), A

D

Example 2 :

3 × [64 ÷ (13 - 5) - 4] × 42 ÷ 6

Solution :

= 3 × [64 ÷ (13 - 5) - 4] × 42 ÷ 6

= 3 × [64 ÷ 8 - 4] × 42 ÷ 6

= 3 × [8 - 4] × 42 ÷ 6

= 3 × 4 × 42 ÷ 6

= 12 × 42 ÷ 6

= 504 ÷ 6

= 84

P( ), S

P[ ], D

P[ ], S

M

M

D

Example 3 :

{24 ÷ [(8 × 3) ÷ 4] × 2} × (15 - 4)

Solution :

= {24 ÷ [(8 × 3) ÷ 4] × 2} × (15 - 4)

= {24 ÷ [24 ÷ 4] × 2} × 11

= {24 ÷ 6 × 2} × 11

= {4 × 2} × 11

= 8 × 11

= 88

P( ), M & S

P[ ], D

P{ }, D

P{ }, M

M

Example 4 :

[5 × (54 ÷ 6 - 3)] + 6 × 2 - 60

Solution :

= [5 × (54 ÷ 6 - 3)] + 6 × 2 - 60

= [5 × (9 - 3)] + 6 × 2 - 60

= [5 × 6] + 6 × 2 - 60

= 30 + 6 × 2 - 60

= 30 + 12 - 60

= 42 - 60

= -18

P( ), D

P( ), S

P[ ], M

M

A

S


Example 5 :

(78 - 6) ÷ {18 × [(7 - 8) × 2]}

Solution :

= (78 - 6) ÷ {18 × [(7 - 8) × 2]}

= 72 ÷ {18 × [-1 × 2]}

= 72 ÷ {18 × (-2)}

= 72 ÷ (-36)

= - 2

P( ), S

P[ ], M

P{ }, M

D

Example 6 :

{96 ÷ [36 ÷ 3 - (18 × 2 - 30)]} ÷ (31 - 16 + 1)

Solution :

= {96 ÷ [36 ÷ 3 - (18 × 2 - 30)]} ÷ (31 - 16 + 1)

= {96 ÷ [36 ÷ 3 - (36 - 30)]} ÷ (15 + 1)

= {96 ÷ [36 ÷ 3 - 6]} ÷ 16

= {96 ÷ [12 - 6]} ÷ 16

= {96 ÷ 6} ÷ 16

= 16 ÷ 16

= 1

P(), M&S

P(), S&A

P[ ], D

P[ ], S

P{ }, D

D

Example 7 :

2 × {11 + [2 × (10 - 15 + 8 × 3)] + 1}

Solution :

= 2 × {11 + [2 × (10 - 15 + 8 × 3)] + 1}

= 2 × {11 + [2 × (-5 + 24)] + 1}

= 2 × {11 + [2 × 19] + 1}

= 2 × {11 + 38 + 1}

= 2 × 50

= 100

P( ), M&S

P( ), S

P[ ], M

P{ }, A

M

Example 8 :

45 ÷ 15 × [(21 - 18) × (5 + 4 × 2) - 49]

Solution :

= 45 ÷ 15 × [(21 - 18) × (5 + 4 × 2) - 49]

= 45 ÷ 15 × [3 × (5 + 8) - 49]

= 45 ÷ 15 × [3 × 13 - 49]

=  45 ÷ 15 × [39 - 49]

= 45 ÷ 15 × (-10)

= 3 × (-10)

= -30

P( ), S&M

P( ), A

P[ ], M

P[ ], S

D

M

Example 9 :

9 ÷ 3 × {2 × [(16 × 4) ÷ 8]}

Solution :

= 9 ÷ 3 × {2 × [(16 × 4) ÷ 8]}

= 9 ÷ 3 × {2 × [64 ÷ 8]}

= 9 ÷ 3 × {2 × 8}

= 3 × 16

= 48

P( ), M

P[ ], D

P{ }, M

M

Example 10 :

100 - {4 × [3 × (19 + 1) ÷ 4]}

Solution :

= 100 - {4 × [3 × (19 + 1) ÷ 4]}

= 100 - {4 × [3 × 20 ÷ 4]}

= 100 - {4 × [3 × 5]}

= 100 - {4 × 15}

= 100 - 60

= 40

P( ), A

P[ ], D

P[ ], M

P{ }, M

S

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