USING THE ORDER OF OPERATIONS

The order of operations is a rule that tells the correct  sequence of steps for evaluating a math expression.

We can remember the order using PEMDAS :

Important Notes :

1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.

2. Multiplication does not always come before division. We have to do one by one in the order from left to right.

3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right.

Examples :

16 ÷ 4 x 3 = 4 x 3 = 12

18 - 3 + 6 = 15 + 6 = 21

In the above simplification, we have both division and multiplication. From left to right, we have division first and multiplication next.

So we do division first and multiplication next.

Practice Problems

Problem 1 :

Evaluate the given expression for x = 7.

4(x - 4)

Solution :

Substitute 7 for x.

= 4(7 - 4)

Subtract inside the parentheses.

= 4(3)

Multiply.

= 12

Problem 2 :

Evaluate the given expression for x = 7.

4x - 4

Solution :

Substitute 7 for x.

= 4(7) - 4

Multiply.

= 28 - 4

Subtract.

= 24

Problem 3 :

Evaluate the given expression for x = 3  and y = 5.

3x + 2y

Solution :

Substitute 3 for x and 5 for y.

= 3(3) + 2(5)

Multiply.

= 9 + 10

Add.

= 19

Problem 4 :

Evaluate the given expression for x = 9.

x² - x

Solution :

Substitute 9 for each x.

= 9² - 9

Evaluate the exponent.

= 81 - 9

Subtract.

= 72

Problem 5 :

Evaluate the given expression for m = 5  and n = 2.

m² + 2mn²

Solution :

Substitute 5 for m and 2 for n.

= 5² + 2(5)(2)²

Evaluate the exponents.

= 25 + 2(5)(4)

Multiply 2, 5 and 4.

= 25 + 40

Add.

= 65

Problem 6 :

Evaluate the given expression for m = 3.

(2m² + 5m - 7)/2

Solution :

Substitute 3 for m.

= [2(3)² + 5(3) - 7]/2

Evaluate the exponent.

= [2(9) + 5(3) - 7]/2

Multiply.

= [18 + 15 - 7]/2

Add 18 and 15.

= [33 - 7]/2

Subtract 7 from 33.

= 26/2

Divide.

= 13

Problem 7 :

Sylvia bought 4 bananas for 50 pence each and 2 apples for 80 pence each. How much did she spend ?

Solution :

Number of bananas she bought = 4

Number of apples = 2

Cost of each banana = 0.50

Cost of each apple = 0.80

Amount she spends = 4(0.50) + 2(0.80)

To evaluate, we have to multiply the terms and then add.

= 2 + 1.6

= $3.6

Problem 8 :

The price of rice is $2 per bag. Gary buys 6 bags. He pays using $20 note. How much change will he get ?

Solution :

Cost of bag of rice = $2

Number of bags = 6

Amount to be paid = 6(2)

Amount he gets as change = 20 - 6(2)

= 20 - 12

= $8

Problem 9 :

Everyday on the way to work Robert buys a coffee costing $2.50 and donut costing $1.50. He works 5 days per week. If he does this everyday for 4 weeks, how much will he spend ?

Solution :

Cost of coffee = $2.50

Cost of donut = $1.50

Number of days he works = 5

Number of weeks he works = 4

Amount he spends = 4 x 5(1.50 + 2.50)

= 4 x 5(4)

= 4 x 20

= 80

So, amount he spends is $80.

Problem 10 :

Hamza bought 4 new shirts for $15 each and 2 pairs of trousers for $25 each. How much did he spend ?

Solution :

Amount spends = 4(15) + 2(25)

= 60 + 50

= $110

So, amount he spends is $110.

Problem 11 :

Mark gets paid $100 per day. He works 5 days per week. On two of days he buys lunch, costing $4 each time. How much does he have left over after paying for his lunches ?

Solution :

Amount he has as left = 5(100) - 2(4)

= 500 - 8

= 492

Problem 12 :

Shay bought 4 packs of markers for $6 each and a box of colored chalk for $11. What was the total cost of the markers and chalk Shay bought?

A $35     B $17    C $50    D $68

Solution :

Total cost = 4(6) + 11

= 24 + 11

$35

So, the required total cost is $35.

Problem 13 :

Lousie pays $20 for materials to make earings. She makes 10 earings and sells 7 for each $5 and 3 for $2. How much profit does she make ?

Solution :

Profit = Selling price - cost price

= 7(5) + 3(2) - 20

= 35 + 6 - 20

= 41 - 20

= 21

So, the profit is $21.

There are 597 children participating in a county science fair. They are put into groups of six children. How many groups will participate? and what is the number of children 

A) 60, 2   B) 98, 3   c)  99, 3   D)  150, 0

Solution :

Total number of children = 597

Number of children in each group = 6

Number of groups = (597/6)

Quotient = 99, remainder = 3

So, number of groups = 99

and

number of children left over = 3

Option C is correct.

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