Patterns And Relations Worksheet - Grade 7 Page 33
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46When we write one quantity equal to another quantity, we have an equation.
Each quantity may be a number or an algebraic expression.
For example, 3x
2 is an algebraic expression; 11 is a number.
When we write 3x
2
11, we have an equation.
An equation is a statement that two quantities are equal.
Each side of the equation has the same value.
In an equation, the variable represents a specific unknown number.
When we find the value of the unknown number, we solve the equation.
Example
Write an equation for each sentence.
a) Three more than a number is 15.
b) Five less than a number is 7.
c) A number subtracted from 5 is 1.
d) A number divided by 3 is 10.
e) Eight added to 3 times a number is 26.
A Solution
a) Three more than a number is 15.
b) Five less than a number is 7.
Let x represent the number.
Let z represent the number.
Three more than x: x
3
Five less than z: z
5
The equation is: x
3
15
The equation is: z
5
7
c) A number subtracted from 5 is 1.
d) A number divided by 3 is 10.
Let g represent the number.
Let j represent the number.
j
g subtracted from 5: 5
g
j divided by 3:
3
j
The equation is: 5
g
1
The equation is:
10
3
e) Eight added to 3 times a number is 26.
Let h represent the number.
3 times h: 3h
8 added to 3h: 3h
8
The equation is: 3h
8
26
Write an equation for each sentence.
1.
a) Eight more than a number is 12.
b) Eight less than a number is 12.
Write a sentence for each equation.
2.
n
a) 12
n
19
b) 3n
18
c) 12
n
5
d)
6
2
36
UNIT 1: Patterns and Relations
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