Ratios Basics
What does the ratio 2:5 represent?
2 of one thing for every 5 of another.
Which ratio is equivalent to 3:4? (6:8, 8:10, 9:12)
6:8 and 9:12
A runner goes 10 miles in 2 hours. What is the unit rate?
5 miles/hour.
What percent is 25 out of 100?
25%
What is the GCF of 12 and 18
6.
Write the ratio of 8 red marbles to 12 blue marbles in simplest form.
2:3
A recipe calls for 2 cups flour and 3 cups sugar. How much sugar for 8 cups flour?
12 cups sugar
5 notebooks cost $7.50. What is the cost per notebook?
$1.50 each.
20% of 50 is what number?
10.
What is the LCM of 4 and 6?
12.
A class has 18 boys and 12 girls. What is the ratio of boys to total students?
18:30 → 3:5
Complete the ratio table:
| Flour | 2 | 4 | 6 | 8 |
| Sugar | 3 | 6 | 9 | ? |
12
400 miles on 16 gallons of gas — find miles per gallon.
25 mpg.
45 is 30% of what number?
150
Prime factorization of 48.
2⁴ × 3.
A pet store has 15 cats, 20 dogs, and 5 fish. What’s the ratio of cats to non-cats?
15:25 → 3:5
Explain why 12:18 and 4:6 are equivalent ratios.
Both simplify to 2:3 (divide by 6 or 2).
You type 720 words in 9 minutes. How many words per minute and per hour?
80 words/minute; 4,800 words/hour.
A store has a 25% off sale. If a jacket costs $48, what is the sale price?
$36 (48 − 12).
Use prime factorization to find the GCF of 36 and 60
36 = 2²×3², 60 = 2²×3×5 → GCF = 2²×3 = 12.
A mix uses 4 cups of juice for every 6 cups of soda. If you have 24 cups of soda, how much juice is needed to keep the ratio the same?
16 cups juice
A car travels 180 miles in 3 hours. Write an equivalent ratio for 1 hour and 5 hours, and explain your method.
60 miles per hour; 60:1 and 300:5.
A machine makes 120 parts in 15 minutes. How many parts in 2.5 hours?
120 ÷ 15 = 8 parts/min; 8 × 150 = 1,200 parts.
A laptop costs $800. It’s discounted 15% and then taxed 7.5%. What’s the final cost?
Discount = 15% of 800 = $120 → $680. Tax = 7.5% of 680 = $51 → $731
Two numbers have a GCF of 6 and an LCM of 60. One number is 12. What is the other number?
Use GCF×LCM = a×b → 6×60 = 12×b → b = 30.