Math 8
Percent, Ratio, and Rate.
Date:_________________
Name:________________
Block:_________
Lesson 5.6: Equivalent Ratios.
Making Connections:
The ratio of triangles to squares is 4:3.
That is, for every 4 triangles, there are 3 squares.
The ratio of triangles to squares is 8:6.
That is, for every 8 tri angles, there are 6 squares.
The ratios 8:6 and 4:3 are called equivalent ratios.
Equivalent ratios are equal. 8:6 = 4:3
An equivalent ratio can be formed by multiplying or dividing the terms of a ratio
by the same number.
We can show this with the terms of the ratios in rows.
Example 1) Write 2 ratios equivalent to each given ratio below.
a) 18:12
b) 4:5
c) 12:3:9
Example 2) Write each ratio in simplest form.
a) 6:18
b) 10:25
c)
d) 15:60:45
16:12:20
Example 3) Find pairs of equivalent ratios. How do you know they are equivalent?
a) 3:15:21
b) 3:6
c) 2:7
d)
9:18
e)
f) 12:15:21
g) 20:5
h)
8:28
j) 2:10:14
k) 24:30:42
l)
5:9
2:5
i) 10:18
Example 4) Write a ratio, in simplest form, to compare the items in each sentence.
a) On the bus, there are 14 girls and 12 boys.
b) In the garden, there are 12 rose bushes and 4 lilac bushes.
c) On the bookshelf, there are 7 mystery books, 28 non-fiction books, and 21
science-fiction books.
d) In a parking lot, there were 6 American cars, 12 Japanese cars, and 9
Korean cars.
Example 5) How many equivalent ratios are there for 3:4 in which the sum of all
the digits is less than 10? Write the ratios you find.
Ans: There are infinite many equivalent ratios for 3 : 4, and their sums of all digits
are less than 10. 30 : 40; 150 : 200; 300 : 400; 1500 :2000, ........ect.
Example 6) Use the ratios below.
a) Use the ratios in row A.
If there are 16 clubs, how many
hearts are there?
A
B
C
♣♣♣♣


D
►►►


►►►►
►►
◘◘◘◘◘◘
b) Use the ratios in row B. If there are 24 diamonds, how many spades are
there?
c) Use the ratios in row C. If there are 50 cards, how many arrows are there?
d) Use the ratios in row D. If there are 54 cards, how many squares are there?