Middle Years

# 1.01 Multiplying and dividing integers

Worksheet
Multiplication of integers
1

Are the following statements true or false?

a

The product of a positve number with a negative number is negative.

b

The product of an even number of negative numbers is negative.

2

State whether the following expressions will be positive or negative:

a

\left(-147\right) \times 183

b

\left(-151 \right) \times \left( - 185 \right)

c

\left( - 180 \right) \times \left( - 168 \right)

d

157 \times \left( - 142 \right)

3

Consider the equation 6 \times 4 = 24, and find the value of the following:

a

\left( - 6 \right) \times 4

b

6 \times \left( - 4 \right)

c

\left( - 6 \right) \times \left( - 4 \right)

4

Consider the equation 19 \times 17 = 323, and find the value of the following:

a

\left( - 19 \right) \times 17

b

19 \times \left( - 17 \right)

c

\left( - 19 \right) \times \left( - 17 \right)

5

Consider the equation 37 \times 31 = 1147, and find the value of the following:

a

\left( - 37 \right) \times 31

b

37 \times \left( - 31 \right)

c

\left( - 37 \right) \times \left( - 31 \right)

6

Consider the equation 3 \times 2 \times 5 = 30, and find the value of the following:

a

3 \times \left( - 2 \right) \times 5

b

\left( - 3 \right) \times 2 \times \left( - 5 \right)

c

\left( -3 \right) \times \left( - 2 \right) \times 5

d

\left( -3 \right) \times \left( - 2 \right) \times \left( - 5 \right)

7

Evaluate:

a

- 4^{2}

b

\left( - 4 \right)^{2}

c

\left( - 4 \right)^{3}

d

\left( - 12 \right)^{2}

e

- \left( - 12 \right)^{2}

f

- \left( - 8 \right)^{3}

g

\left( - 6 \right)^{3}

h
6 \times \left( - 6 \right)
i

5 \times \left( - 9 \right)

j

\left( - 12 \right) \times \left( - 10 \right)

k
\left( - 9 \right) \times 1
l
\left( - 9 \right) \times 0
m

\left(- 11 \right) \times 4

n
\left( - 4 \right) \times \left( - 11 \right)
o

\left( - 4 \right) \times \left( - 4 \right)

p

\left( - 4 \right) \times \left( - 4 \right) \times \left( - 4 \right)

q
4 \times \left( - 7 \right) \times 5
r
\left( - 3 \right) \times 4 \times \left( - 3 \right)
s
\left( - 6 \right) \times \left( - 8 \right) \times \left( - 3 \right)
t
\left(- 8 \right) \times \left( - 5 \right) \times \left( - 3 \right) \times 6
8

Solve the following equations:

a

\left( - 11 \right) \times r = - 66

b

n \times \left( - 3 \right) = - 36

c

7 \times q = - 28

d

t \times 7 = - 42

9

Complete the following equations:

a

⬚ \times \left( - 5 \right) = 55

b

-6\times ⬚=-66

c

⬚ \times 8 = - 56

d

7 \times ⬚ = - 84

10

Find the value of n in the following statements:

a

A number n is multiplied with - 3 to give 21.

b

A number n is multiplied with - 10 to give - 40.

11

Explain why there is no solution to the equation x^2=-1.

Division of integers
12

Is the quotient of a positive integer and a negative integer positive or negative?

13

State whether the following expressions will be positive or negative:

a

\left( - 2432 \right) \div 32

b

\left( - 855 \right) \div \left( - 15 \right)

c

1587 \div \left( - 23 \right)

d

\left( - 7614 \right) \div \left( - 81 \right)

14

Consider the equation 42 \div 7 = 6, and find the value of the following:

a

\left( - 42 \right) \div 7

b

42 \div \left( - 7 \right)

c

\left( - 42 \right) \div \left( - 7 \right)

15

Consider the equation 667 \div 29 = 23, and find the value of the following:

a

\left( - 667 \right) \div 29

b

-667 \div \left( - 29 \right)

c

\left( - 667 \right) \div \left( - 29 \right)

16

Consider the equation 924 \div 28 = 33, and find the value of the following:

a

\left( - 924 \right) \div 28

b

924 \div \left( - 28 \right)

c

\left( - 924 \right) \div \left( - 28 \right)

17

Evaluate:

a
\left( - 2 \right) \div \left( - 2 \right)
b
\left( - 2 \right) \div 1
c
4 \div \left( - 1 \right)
d
0 \div \left( - 36 \right)
e

12 \div \left( - 4 \right)

f

\left( - 20 \right) \div 4

g
21 \div \left( - 7 \right)
h
\left( - 22 \right) \div 11
i
\left( - 50 \right) \div \left( - 10 \right)
j

\left( - 72 \right) \div \left( - 9 \right)

k
\dfrac{- 5}{5}
l
\dfrac{- 11}{- 11}
m
\dfrac{10}{- 1}
n
\dfrac{42}{- 7}
o
\dfrac{- 60}{10}
p
\dfrac{- 48}{- 12}
18

Solve the following equations:

a

\left( - 108 \right) \div n = - 12

b

p \div \left( - 8 \right) = 11

c

\left( - 48 \right) \div t = 6

d

k \div 8 = - 6

19

Complete the following equations:

a

⬚ \div \left( - 6 \right) = - 9

b

⬚ \div 5 = -7

c

⬚ \div 5=-11

d

\left( - 72 \right) \div ⬚ = 9

20

Find the value of n in the following statements:

a

A number n, when divided by 3, gives - 9.

b

A number n when divided by - 5 gives - 4.

21

Evaluate:

a
\left(-4\right)\times 3\div \left(-2\right)
b
5\times\left(-3\right)\times\left(-7\right)
c
10\times 8\div \left(-5\right)
d
\left(-6\right)\times\left(-4\right)\times\left(-3\right)
e
\left(-14\right)\times \left(-4\right)\div 7
f
8\times\left(-15\right)\div 4
g
\left(18\div \left(-3\right)\right)\div \left(-2\right)
h
\left(-126\right)\div\left(\left(-6\right)\times\left(-3\right)\right)
Applications
22

Which quadrant(s) could the point \left(x, y\right) lie in if:

a
xy\gt 0
b
\dfrac{x^2}{y}\lt 0
23

In golf your score for each hole is determined by comparing it to the par (or expected) number of shots for that hole. Taking one less shot than expected will give a score of -1, one more shot will give +1, and so on.

Ivan played 18 holes of golf, and the frequency of each score he obtained is shown in the adjacent table:

a

Find Ivan's total score for his 6 scores of + 2.

b

Find Ivan's total score for his 5 scores of - 1.

c

Find Ivan's total score for the total 18 holes.

24

Victoria earns \$1100 a month, and deposits it into her bank account. She also withdraws \$200 a month to pay for rent.

a

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

b

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

c

Find the total change in her bank account over the year. An increase will be represented by a positive number and a decrease will be represented by a negative number.