 1.06 Positive and negative rational numbers

Worksheet
Compare and order rational positive and negative numbers
1

Complete the following statements with the correct inequality sign \gt or \lt:

a

\dfrac{8}{9} ⬚ \dfrac{9}{10}

b

- \dfrac{5}{6}⬚ - \dfrac{9}{10}

c

- \dfrac{8}{9}⬚\dfrac{6}{7}

d
\dfrac{5}{7} ⬚ \dfrac{7}{10}
e
-\dfrac{6}{11}⬚ -\dfrac{5}{9}
f

\dfrac{7}{8}⬚- \dfrac{5}{6}

g
\dfrac{3}{10}⬚ - \dfrac{7}{10}
h
-\dfrac{2}{5} ⬚\dfrac{1}{5}
2

Consider the fractions -\dfrac{2}{5}, -\dfrac{4}{5}, \dfrac{1}{5}

a

Plot the fractions on a number line.

b

Arrange the fractions from largest to smallest.

3

Consider the fractions -\dfrac{3}{7}, \dfrac{2}{7}, -\dfrac{4}{7}

a

Plot the fractions on a number line.

b

Arrange the fractions from smallest to largest.

4

Consider the fractions \dfrac{2}{9}, \dfrac{4}{9}, -\dfrac{2}{9}

a

Plot the fractions on a number line.

b

Arrange the fractions from largest to smallest.

5

Consider the fractions -\dfrac{7}{11} , \dfrac{2}{11},-\dfrac{3}{11}

a

Plot the fractions on a number line.

b

Arrange the fractions from smallest to largest.

Multiplication and division of rational positive and negative numbers
6

Find the product of the following fractions. Give your answers as simplified fractions.

a

\dfrac{2}{5} \times \dfrac{3}{7}

b

\dfrac{4}{7} \times \left( - \dfrac{9}{5} \right)

c

- \dfrac{5}{9} \times \dfrac{2}{11}

d

- \dfrac{2}{5} \times \left( - \dfrac{9}{7} \right)

e

\left(\dfrac{2}{9}\right)^{2}

f

\left( - \dfrac{9}{5} \right)^{2}

g

9 \times \left( - \dfrac{4}{5} \right)

h

- \dfrac{3}{7} \times \dfrac{4}{7}

i

- \dfrac{2}{9} \times \left( - \dfrac{2}{3} \right)

j

- \dfrac{2}{7} \times \dfrac{3}{8}

k

- \dfrac{11}{9} \times \left( - \dfrac{7}{44} \right)

l

\dfrac{2}{45} \times \left( - \dfrac{5}{6} \right)

m
\dfrac{10}{11} \times \left ( - \dfrac{9}{5} \right)
n

\dfrac{44}{15} \times \left( - \dfrac{12}{55} \right)

o

\dfrac{7}{4} \times \left( - \dfrac{9}{7} \right) \times \dfrac{5}{7}

p
\left(-\dfrac{12}{7}\right) \times \left(\dfrac{5}{8}\right)
7

Find the quotient of the following fractions. Give your answers as simplified fractions.

a

\dfrac{3}{7} \div \dfrac{5}{4}

b

\dfrac{2}{9} \div \left( - \dfrac{7}{5} \right)

c

\left( - \dfrac{3}{11} \right) \div \dfrac{8}{5}

d

\left( - \dfrac{3}{7} \right) \div \left( - \dfrac{5}{4} \right)

e

7 \div \left( - \dfrac{4}{7} \right)

f

\left( - \dfrac{3}{4} \right) \div 12

g

\left( - \dfrac{3}{7} \right) \div \dfrac{7}{8}

h

\left( - \dfrac{6}{7} \right) \div \dfrac{3}{4}

i

\left( - \dfrac{2}{7} \right) \div \left( - \dfrac{5}{63} \right)

j

\left( - \dfrac{7}{2} \right) \div \left( - \dfrac{21}{5} \right)

k

\left( - \dfrac{45}{4} \right) \div \dfrac{9}{28}

l

\dfrac{45}{28} \div \left( - \dfrac{25}{36} \right)

m

\dfrac{4}{81} \div \left( - \dfrac{20}{9} \right)

n

\left( - \dfrac{20}{27} \right) \div \left( - \dfrac{35}{24} \right)

Compare and order rational positive and negative decimals
8

For the each of the following pairs of decimals, state which decimal is bigger:

a

0.74 or 0.8

b

- 0.7 or - 0.67

c

- 0.74 or 0.8

d

0.67 or - 0.7

9

Consider the decimals 0.2, 0.5, -0.3

a

Plot the fractions on a number line.

b

Arrange the decimals from smallest to largest.

10

Consider the decimals -0.9, 0.3, -0.4

a

Plot the fractions on a number line.

b

Arrange the decimals from largest to smallest.

11

Consider the decimals -0.1, -0.42, -0.29

a

Plot the fractions on a number line.

b

Arrange the decimals from smallest to largest.

12

Consider the decimals 0.75, -0.5, 0.25

a

Plot the fractions on a number line.

b

Arrange the decimals from largest to smallest.

Multiplication and division of positive and negative decimals
13

Find the product of the following:

a

7.3 \times 7.9

b

6.4 \times \left( - 7.8 \right)

c

\left( - 4.3 \right) \times 9.7

d

\left( - 3.9 \right) \times \left( - 9.8 \right)

e
7.4 \times \left( - 4.1 \right)
f
\left( - 7.6 \right) \times 7.8
g
8 \times \left( - 2.4 \right)
h
\left( - 8 \right) \times \left( - 7.2 \right)
i
0.8 \times \left( - 0.5 \right)
j
\left( - 0.9 \right) \times 0.6
k
\left( - 0.6 \right) \times \left( - 0.8 \right)
l
1.99 \times \left( - 8 \right)
m
\left( - 2.77 \right) \times \left( - 2 \right)
n
\left( - 8.18 \right) \times 6
o
\left(-7.26 \right) \times 9
p
\left(-4.9\right) \times \left(-7.3 \right)
14

Find the quotient of the following:

a

4.16 \div 0.08

b

7.36 \div \left( - 0.08 \right)

c

\left( - 3.08 \right) \div 0.07

d

\left( - 8.28 \right) \div \left( - 0.09 \right)

e
9.2 \div \left( - 2 \right)
f
\left( - 29.4 \right) \div 3
g
\left( - 33.6 \right) \div \left( - 8 \right)
h
0.81 \div \left( - 0.9 \right)
i
\left( - 0.35 \right) \div 0.7
j
\left( - 0.27 \right) \div \left( - 0.9 \right)
15

Find the value of the following:

a

\left(3.7\right)^{2}

b

\left( - 6.4 \right)^{2}

c

\left(3.7\right)^{3}

d

\left( - 6.4 \right)^{3}

16

Determine whether the following calculations can be evaluated:

a

\dfrac{- 3.88}{2.99}

b

\dfrac{2.99}{0}

c

\dfrac{1.93}{2 - 2}

d

\dfrac{0}{- 1.93}

Applications
17

Jack owes \$47.59 to each of his 3 friends. If he paid off all of these debts at once, how much will his bank account balance decrease by? (Note whether the change is positive or negative by the sign of the number.) 18 Peggy owes \$98.96 in total to 4 friends.

a

Assuming she owes the same amount to each friend, how much does she owe one of them?

b

If Peggy pays just 3 of her friends back, how much money will come out of her bank account?

19

Jenny takes out a loan of \$2200. She pays back \$42.60 each month without interest. If she has made 5 repayments so far, how much does Jenny still owe?

20

At midnight, the temperature in Buffalo is 45.7 \, \degree \text{F} . Each hour the temperature decreases by 2.87 \degree. Find the temperature after 5 hours.

21

Hadi is studying temperatures around the world and notices that Antarctica has a temperature of -29.4\degree \text{C} while Egypt has a temperature of 29.4\degree \text{C}. He thinks that this means that they have the same temperature.

22

A diver is 3.5 \text{ m} below the surface of the water. He descends 1.47 \text{ m/s} for 3 seconds, then rises 0.46 \text{ m/s} for 6 seconds. Note that surface level is 0 \text{ m}, and 1 \text{ m} below is represented by - 1 \text{ m}.

a

Find the depth of the diver after 9 seconds.

b

The diver is running out of oxygen and needs to get to a depth of 0.35 \text{ m} below the surface within 4 seconds. How many metres does he need to rise each second, assuming he will rise at a constant speed?

23

Debbie is considering installing solar panels for her home. In direct sunlight, the solar panels generate 8.71 \text{ kWh} of electricity each hour, and on average her house gets 7 hours of sunlight a day. Any unused power is returned to the main grid and you receive \\33 cents per kWh.

Over a 24-hour period, a household's usage averages out to 1.87 \text{ kWh} each hour. How much will you expect to make each day by selling back electricity if you install the solar panels?

24

Kendra is looking at her bank statement and notices the following transactions:

a

What do the negative signs in front of the last two values indicate about the transaction?

b

If Kendra initially had \\$65.20 in her account, how much does she have after these transactions?

Outcomes

9.B3.2

Apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools.

9.B3.3

Apply an understanding of integers to explain the effects that positive and negative signs have on the values of ratios, rates, fractions, and decimals, in various contexts.

9.B3.4

Solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriate.