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9.01 Introduction to equations

Worksheet
Numerical equations
1

What is an equation?

2

State whether the following equations are true or false:

a
22 + 6 = 4 \times 7
b
51 - 6 = 18 + 4 \times 8
c
5 \times 8 - 27 = 19
d
\dfrac{96}{8} = 106 - 94
e
8 + 16 = 6 \times 4
f
57 - 4 = 15 + 6 \times 7
g
5 \times 7 - 19 = 13
h
\dfrac{36}{6} = 52 - 46
i
55 - 24 = 7 \times 3
j
32 + 8 = 20 + 4 \times 6
k
3 \times 6 + 7 = 32-8
l
\dfrac{28}{4} + 7 = 30 - 16
Equations involving unknown values
3

Fill in the blank to make the following equations true:

a
4 + ⬚ = 8
b
3 \times ⬚ = 30
c
8 \times ⬚ = 35 - 3
d
⬚ \div 3 = 9 - 6
e
8 + ⬚ = 17
f
8 \times ⬚ = 88
g
4 \times ⬚ = 27 - 3
h
⬚ \div 6 = 9 - 3
i
⬚ + 18 = 35
j
⬚\times 11 = 77
k
⬚ \times 8 = 42 - 10
l
36\div ⬚ = 15-6
4

Consider the equation 3x+8 = 23.

a

Find the value of each expression:

i
3\times 1 +8
ii
3\times 2 +8
iii
3\times 7 +8
iv
3\times 6 +8
v
3\times 5 +8
b

Use your answers from part (a) to solve the equation 3x+8 = 23.

5

Find the value of the variable that will make the following equations true:

a
x + 18 = 30
b
8 x = 96
c
28 - x = 21
d
\dfrac{x}{9} = 3
e
12 + m = 25
f
s - 7 = 14
g
11 u = 66
h
\dfrac{m}{12} = 4
Word problems
6

For each of the following word sentences, write a matching equation:

a

The quotient of g and seven is equal to eleven.

b

The product of seven and y is equal to x less than twenty five.

c

The product of eight and s is taken away from sixty six. The result is equal to ten.

d

Sixteen less than m is equal to twenty six.

e

Twelve less than q is equal to twenty five.

f

The product of twelve and r is taken away from seventy two. The result is equal to thirty six.

g

The quotient of p and ten is equal to seven.

h

The product of five and q is equal to p less than twenty nine.

7

For each of the following equations, write a matching word sentence:

a

8 x = 32

b

\dfrac{63}{x} = 9

c

6 x + 4 = 60 - 20

d

5 y = 60

e

\dfrac{72}{p} = 8

f

8 x + 7 = 72 - 25

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Outcomes

MA4-11NA

creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane

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