http://www.ck12.org Chapter 7. Similarity
b) 9m:900cm
c) 164 galgal
First, change each ratio so that each part is in the same units. Remember that there are 12 inches in a foot.
a)
(^7) @@f t
(^14) in
·
(^12) in
(^1) @@f t
=
84
14
=
6
1
The inches and feet cancel each other out.Simplified ratios do not have units.
b) It is easier to simplify a ratio when written as a fraction.
(^9) Zm
(^900) cm
·
(^100) cm
(^1) Zm
=
900
900
=
1
1
c)
4 ZgalZ
16 ZgalZ=
1
4
Example C
A talent show has dancers and singers. The ratio of dancers to singers is 3:2. There are 30 performers total, how
many of each are there?
To solve, notice that 3:2 is a reduced ratio, so there is a number,n, that we can multiply both by to find the total
number in each group. Represent dancers and singers as expressions in terms ofn. Then set up and solve an equation.
dancers= 3 n,singers= 2 n−→ 3 n+ 2 n= 30
5 n= 30
n= 6There are 3· 6 =18 dancers and 2· 6 =12 singers.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter7FormsofRatiosB
Concept Problem Revisited
Everything needs to be scaled down by a factor of 181 ( 144 in÷ 8 in). Change everything into inches and then
multiply by the scale factor.
Bed: 36 in by 75 in−→2 in by 4.167 in