ORDER OF OPERATIONS WORKSHEET WITH FRACTIONS AND DECIMALS

Problem 1 :

1  1/4 x 6 - (1/2)²

Solution :

= 1  1/4 x 6 - (1/2)²

Converting the mixed fraction to improper, we get

Problem 2 :

1.55 + (0.5)² - 4.9 ÷ 7

Solution :

Problem 3 :

1  2/7 x (2/3)² - (6/7²) ÷ (1/7)

Solution :

= 1  2/7 x (2/3)² - (6/7²) ÷ (1/7)

Converting the improper fraction to mixed fraction, we get

= (9/7) x (2/3)² - (6/7²) ÷ (1/7)

Using exponents, we get

= (9/7) x (4/9) - (6/49) ÷ (1/7)

Multiplying the first two fractions, we get

= 4/7 - (6/49) ÷ (1/7)

Dividing 6/49 by 1/7, we get

= 4/7 - (6/7)

= (4 - 6)/7

= -2/7

Problem 4 :

(2.4)² + 5.6 x 1.6

Solution :

= (2.4)² + 5.6 x 1.6

= 5.76 + 5.6 x 1.6

= 5.76 + 8.96

= 14.72

Problem 5 :

(1/2)² x (4/5) - (6/5)

Solution :

= (1/2)² x (4/5) - (6/5)

By using exponent, we get

= (1/4) x (4/5) - (6/5)

= (1/5) - (6/5)

= (1-6)/5

= -5/5

= -1

Example 6 :

18.14 + (0.5)³ ÷ 2.5 - 21.13

Solution :

Problem 7 :

1.9 - 3² x 0.3 + 16.1

Solution :

Problem 8 :

(1/3)² ÷ 1/9 + 2/3 -15/2 x 2/5

Solution :

= (1/3)² ÷ 1/9 + 2/3 -15/2 x 2/5

= (1/9) ÷ 1/9 + 2/3 -15/2 x 2/5

= 1 + 2/3 -15/2 x 2/5

= 1 + 2/3 - 3

= (3 + 2 - 9)/3

= -4/3

Problem 9 :

2.16 ÷ 6² - 13.06 + 1.2 x 0.5

Solution :

= 2.16 ÷ 6² - 13.06 + 1.2 x 0.5

= 2.16 ÷ 36 - 13.06 + 1.2 x 0.5

= 0.06 - 13.06 + 1.2 x 0.5

= 0.06 - 13.06 + 0.6

= -13 + 0.6

= -12.4

Problem 10 :

(2/3) ÷ (2/3) x 2² + 1 1/2

Solution :

= (2/3) ÷ (2/3) x 2² + 1 1/2

= (2/3) ÷ (2/3) x 2² + 1 1/2

= 1 x 4 + 1 1/2

= 4 + 3/2

= (8 + 3)/2

= 11/2

Problem 11 :

You buy 2.6 pounds of apples and 1.475 pounds of peaches. You hand the cashier a $20 bill. How much change will you receive?

Solution :

Cost of 1 pound of aple = $1.23

Quantity of apples = 2.6 pounds

Cost of 1 pound of peaches = $1.88

Quantity of peaches = 1.475 pounds.

1.23(2.6) + 1.88(1.475)

Amount given = 20

Change  20 - [1.23(2.6) + 1.88(1.475)]

= 20 - [3.198 + 2.773]

= 20 - 5.971

= $14.029

Problem 12 :

A car can travel 22.36 miles on one gallon of gasoline. 

a. How far can the car travel on 8.5 gallons of gasoline?

b. A hybrid car can travel 33.1 miles on one gallon of gasoline. How much farther can the hybrid car travel on 8.5 gallons of gasoline?

Solution :

a) One gallon of gasoline will cover the distance = 22.36 miles

8.5 gallons of gasoline will cover the distance = 8.5 x 22.36

= 190.06 miles

b)  Distance covered by 1 gallon of gasoline = 33.1 miles

Distance covered by 8.5 gallons of gasoline = 8.5 x 33.1

= 281.35 miles

Hybrid car will cover more distance, the difference = 281.35 - 190.06

= 91.29 miles

Problem 13 :

You buy 2.75 pounds of tomatoes. You hand the cashier a $10 bill. How much change will you receive?

Solution :

Step 1 :

Find the cost of the tomatoes. Multiply 1.89 by 2.75.

The cost of 2.75 pounds of tomatoes is $5.20.

Step 2:

Subtract the cost of the tomatoes from the amount of money you hand the cashier.

= 10.00 − 5.20

= $4.80

So, you will receive $4.80 in change.

Problem 14 :

What is the value of 2.44(4.5 − 3.175)?

a) 3.233     b) 3.599     c) 7.805      d) 32.33

Solution :

= 2.44(4.5 − 3.175)

= 2.44 (1.325)

= 3.233

So, option a is correct.

Problem 15 :

You work 1.15 hours on English homework and 1.75 hours on math homework. Your science homework takes 1.05 hours less than your math homework. How many hours do you work on homework?

Solution :

Time taken for English homework = 1.15 hours

Time taken for Math homework = 1.75 hours

Time taken for Science homework = 1.75 - 1.05

= 0.7 hours

Time taken for homework = 1.15 + 1.75 + 0.7

= 3.6 hours

Problem 16 :

Your meal at the school cafeteria costs $3.45. Your friend’s meal costs $3.90. You pay for both meals with a $10 bill. How much change do you receive?

Solution :

Use a verbal model to solve the problem. amount of change

= amount given − (cost of your meal + cost of friend’s meal)

= 10.00 − (3.45 + 3.90)

= 10.00 − 7.35

= 2.65

So, you receive $2.65.