Equivalent Ratios
Unit Rates
Ratio and Rate Word Problems
Greatest Common Factor (GCF)
100
Simplify the ratio 12:18 in its simplest form
2:3
2 to 3
2/3
100
A car travels 120 miles in 2 hours. What is the unit rate in miles per hour?
60 miles per hour
100
The ratio of cats to dogs at a shelter is 2:5. If there are 20 cats, how many dogs are there?
There would be 50 dogs at the shelter.
100
Find the greatest common factor (GCF) of 12 and 18
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
The GCF for 12 and 18 is 6
200
Complete the ratio table below to find the missing values.
9 apples cost $6
12 apples cost $8
200
A 12-ounce box of cereal costs $3.60. What is the unit price per ounce?
The unit price is $0.30 per ounce
200
A blue paint mix uses 2 pints of white paint for every 3 pints of blue paint. How many pints of white paint are needed if you use 12 pints of blue paint?
You would need 8 pints of white paint.
200
What is the GCF between two different prime numbers?
The GCF is 1
300
Are the ratios Equivalent? Explain Why or Why Not?
4/5 = 16/25
No, they are not equivalent since 4x4 = 16 and 5x4 = 20 not 25
300
Use the double number line to determine how many kilometers a cyclist travels in 4 hours if they maintain a constant speed.
The cyclist travels 60 kilometers in 4 hours
300
A faucet leaks 4 ounces of water every 5 minutes. How many ounces will it leak in one hour?
It will leak 48 ounces of water in 60 minutes aka 1 hour.
300
Find the greatest common factor (GCF) of 24 and 36
24: 1, 2, 3, 4, 6, 8, 12, 24
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The GCF is 12.
400
A recipe uses 3 cups of flour for every 2 cups of sugar. If you use 15 cups of flour, how many cups of sugar do you need?
For 15 cups of flour you will need 10 cups of sugar.
400
A printer can print 45 pages in 3 minutes. At this rate, how many pages can it print in 10 minutes?
The printer can make 150 copies in 10 minutes.
400
In a garden, the ratio of roses to tulips is 5 to 2. There are 14 tulips in the garden. How many roses are in the garden?
There are 35 roses in the garden.
400
Find the greatest common factor (GCF) between 16, 24, and 40
16: 1, 2, 4, 8, 16
24: 1, 2, 3, 4, 6, 8, 12, 24
40: 1, 2, 4, 5, 8, 10, 20, 40
The GCF is 8
500
The ratio of boys to girls at H. H. Wells band is 3:4. If there are 84 girls in the band, how many boys are in the band?
There would be 63 boys in the band.
500
Store A sells 5 pounds of apples for $7.50. Store B sells 8 pounds of apples for $11.20. Which store has the better buy? Show your work.
Store A
7.50/5 = 1.5
Store B
11.20/8=1.4
Store A would be $1.50 per pound, while store B would be $1.40 per pound. Store B has the better buy since it is $0.10 cheaper.
500
A plane flies 1,800 miles in 4 hours. A second plane flies 2,400 miles in 5 hours. Which plane is averaging a faster rate, and by how many miles per hour?
Plane A
1800/4=450 mph
Plane B
2400/5 = 480mph
480-450 = 30
Plane B is going faster by 30 mph.
500
Two ropes are 48 inches and 64 inches long. They are cut into equal pieces. How long is each piece?
48: 1,2,3,4,6,8,12,16,24,48
1 piece 48 inches
2 pieces 24 inches each
3 pieces 16 inches each
4 pieces 12 inches each
6 pieces 8 inches each
8 pieces 6 inches each
12 pieces 4 inches each
16 pieces 3 inches each
24 pieces 2 inches each
48 pieces 1 inch each
64: 1,2,4,8,16,32,64
1 piece 64 inches
2 pieces 32 inches each
4 pieces 16 inches each
8 pieces 8 inches each
16 pieces 4 inches each
32 pieces 2 inches each
64 pieces 1 inch each
The 48 inch rope is cut into 16 pieces each piece is 3 inches, while the 64 inch rope is also cut into 16 pieces, but each piece is 4 inches