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CanadaON
Grade 7

7.02 Building algebraic expressions

Worksheet
Variables, coefficients and algebraic expressions
1

For each of the following terms, choose the correct definition from the options below:

a

Variable

b

Coefficient

c

Expression

A

A numeral that is placed before and multiplies a variable in an algebraic term

B

A way to express a mathematical value that involves variables

C

A symbol, commonly a letter, that is used in the place of a numeric value

2

State the coefficient in the following terms:

a

4 x

b

- 4 y

c

6 y

d

- 6 y

e
-2x^2
f
8ab
g
9z
h
-11x^3
i
uv^2
j
\dfrac{4h}{3}
k
-i
l
\dfrac{-f}{5}
Basic operations in algebra
3

For each of the following terms, choose the correct definition from the options below:

a

Sum

b

Product

c

Difference

d

Quotient

e

Factor

f

Term

A

The result of multiplying two or more values or algebraic expressions.

B

The result of dividing a value or algebraic expression by another.

C

A single component of a product.

D

The result of adding two or more values or algebraic expressions.

E

A single component of a sum or subtraction.

F

The result of subtracting a value or algebraic expression from another.

4

Write an algebraic expression for each of the following statements:

a

7 multiplied by x

b

8 more than 5 x

c

3 less than 8 y

d

The product of 9 u and 8

e

The quotient of 8 u and 9

f

Four times y take away 9

g

8 more than the quotient of 9 and x

h

The difference of a and b, divided by 6

5

Write a word statement for each of the following expressions:

a
8x
b
p + 7
c
x - 6
d
\dfrac{p}{8}
e
b - 12
f
15 m
g
\dfrac{u}{15}
h
2 \left(b + 9\right)
i
9 y - 3
j
\dfrac{y}{3} + 5
k
12 - 3k
l
\dfrac{m+n}{d}
6

Explain what the expression m^2 means.

7

For each of the following expressions:

i

State the order in which the operations should be performed.

ii

Hence, simplify the expression.

a
3 \times u \div v + 8
b
5+ y \times x - 4
c
(4-k)\div 5
d
7-12 \div (3\times a)
8

Rewrite in expanded form:

a

3 k

b

- 5 k

c
2ab
d
6x^2
e

pqr

f

7m^2 n

g
-y^2
h
(ij)^3
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