# 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( ), DP( ), M & AP( ), [ ], A & DP( ), AD

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( ), SP[ ], DP[ ], SMMD

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 & SP[ ], DP{ }, DP{ }, MM

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( ), DP( ), SP[ ], MMAS

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( ), SP[ ], MP{ }, MD

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&SP(), S&AP[ ], DP[ ], SP{ }, DD

Example 7 :

× {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&SP( ), SP[ ], MP{ }, AM

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&MP( ), AP[ ], MP[ ], SDM

Example 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( ), MP[ ], DP{ }, MM

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( ), AP[ ], DP[ ], MP{ }, MS

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