# 1.06 Review: Order of operations with rational numbers

Worksheet
Order of operations with rational numbers
1

Evaluate the following:

a

- 7 + 9.1

b

4 - 6.1

c

- 13 + 45.31

d

29 - 36.71

e

- 6 \times 0.8

f

- 13.8 \times 9

g

- 2 + 1.9 + 7.3

h

- 6.8 - \left( - 1.1 \right) + 8.8

i

2.8 + 6 \times \left( - 9.5 \right)

j
\left(3 - 15\right) \times \left( - 14 + 9\right)
k

36.53 \times 63 \div 9

l

6.42 - 8.2 \times 0.7 + 4.67

m

24.7 - 9.9 - 8.2 \div \left( - 2 \right)

n

9 \times \left( - 6 \right) + 28 \div \left( - 7 \right)

o

\dfrac{\,\,\,9}{- 36} \left(9 + \left( - 6 \right)\right)

p

86 + \dfrac{3}{10} \times \left( - 2 \right)

q

\dfrac{3}{5} \times \dfrac{2}{3} + \dfrac{5}{15}

r

\left(\dfrac{2}{3} + \dfrac {3}{5}\right) \times \dfrac{3}{7}

s
- \left( - 4 \right)^{3} - \left( - 10 \right)^{2} - 122
t
3^{3} - \left( - 2 \right)^{3} + 59
2

State the first step to simplify the following expressions:

a
- 6\div 2 \times 4
b
- 14\div\left(5 - 3 \times 4\right)
3

Explain why the following statement is incorrect, and find the correct answer:

6-\left(-60\right)\div\left(-3\right)=-22
4

Complete the following statements:

a

- 3 \times 4 - ⬚ = - 14

b

2 - \left( - 3 \times ⬚\right) = 17

c

⬚ + 5 \times 2 = 4

d

\left( - 17 - 3\right) \div ⬚ = - 4

e

⬚ \div 2.5 + 5.6 = 14

f

2 \times ⬚ + 12.6 \div \left( - 3 \right) = - 8

g
\left(⬚ - \dfrac{1}{4}\right) \div \dfrac{1}{2} = \dfrac{7}{10}
h
\dfrac{5}{7} \times \left(\dfrac{1}{3} + ⬚ - \dfrac{1}{2}\right) = \dfrac{10}{21}
Applications
5

Convert the following temperatures:

a

Given that F = - 4\degree, find the value of C using the formula C = \dfrac{5}{9} \left(F - 32\right).

b

Given that C = - 30\degree, find the value of F using the formula F = \dfrac{9}{5}C + 32.

6

David buys 3 shirts at \$19.90 each, and a pair of jeans for \$20.50. The shop has a sale on, and so he receives a \$8.02 discount. Find the total amount he spends. 7 How much would you pay for eight t-shirts if they cost \$46.88 each, and you receive a discount of \$9.47? 8 Three items weighing 3.41\text{ lb}, 2.58\text{ lb} and 5.79\text{ lb} are to be posted but are too heavy to send. By how much does the total weight exceed the 11.38\text{ lb} limit? 9 After an earthquake, \dfrac{4}{7} of all claims were paid within a month. Of the remaining claims not paid \dfrac{4}{5} of them were paid within the second month. Calculate the fraction of all claims paid in the second month. 10 At the end of last month, a dam was \dfrac{4}{7} full. Over the current month, \dfrac{37}{56} of the dam's capacity was used up by the town. Meanwhile, rain filled \dfrac{5}{8} of the dam's capacity over the duration of the month. Calculate the fraction of the dam filled at the end of this month. 11 A bottle is \dfrac{2}{7} full of cordial. If 230\text{ mL} of cordial is added to it, the bottle is \dfrac{5}{6} full. How much cordial does the bottle hold when full? 12 During a sale, a number of computers were sold. 6 computers were sold at a loss, which represents \dfrac{1}{6} of the total number of computers that were sold. If 89 computers were up for sale, how many weren't sold? 13 Caitlin is planning to make an investment. She is told by her bank manager that if she puts her money into their new account, she will have 1.6 times her investment, minus a fee of \$122, by the end of the year.

Calculate how much money she will have at the end of the year if she invests \$1000. 14 Vanessa earns \$900.35 a month, and deposits it in to her bank account. She also withdraws \\$200 a month to pay for rent.

a

How much, in total, does Vanessa deposit in her bank account in one full year?

b

How much, in total, does Vanessa withdraw from her bank account in one full year?

c

What is the total change in her bank account over the year?