Ratios
A class has 12 boys and 8 girls.
Write the ratio of boys to girls in simplest form.
12 : 8 → divide both by 4 → 3 : 2
A car travels 180 miles in 3 hours.
What is the car’s speed in miles per hour?
180 ÷ 3 = 60 miles per hour
What percent of 50 is 25?
25÷50=0.5=50%
✅ Answer: 50%
You have 12 cookies, and each bag holds 3 cookies.
How many bags can you fill?
12÷3=4
✅ Answer: 4 bags
A rectangle model is divided into 10 equal parts.
Seven parts are shaded to represent 0.7, and four parts of another identical rectangle are shaded to represent 0.4.
If you combine both shaded parts, what total decimal does the shading represent?
0.7 + 0.4 = 1.1
✅ Answer: 1.1 (one whole and one-tenth)
The ratio of apples to oranges in a fruit basket is 4 : 5.
If there are 20 apples, how many oranges are there?
4 : 5 = 20 : x
4/5=20/x
4x=100 → x=25
Answer: 25 oranges
A printer makes 120 copies in 4 minutes.
How many copies does it make in 10 minutes at the same rate?
Find the rate per minute: 120 ÷ 4 = 30 copies per minute
In 10 minutes → 30 × 10 = 300 copies
Write each form of 75%.
a) As a fraction
b) As a decimal
a) 75%=75/100=3/4
b) 75%=0.75
✅ Answer: 3/4, 0.75
You ate 2 slices of a pizza that had 8 equal slices.
What fraction of the pizza did you eat?
2/8 = 1/4
✅ Answer: You ate ¼ of the pizza.
Add 3.45 and 2.8.
3.45+2.80=6.25
✅ Answer: 6.25
In a pet store, the ratio of cats to dogs is 3 : 2.
If there are 15 animals in total, how many are cats and how many are dogs?
3 + 2 = 5 parts
15 ÷ 5 = 3 per part
Cats = 3 × 3 = 9, Dogs = 2 × 3 = 6
Answer: 9 cats and 6 dogs
Runner A runs 400 meters in 80 seconds.
Runner B runs 600 meters in 120 seconds.
Who is faster?
Runner A → 400 ÷ 80 = 5 m/s
Runner B → 600 ÷ 120 = 5 m/s
Answer: Both runners have the same speed.
What percent is equal to the fraction 3/20?
3/20 = 15/100 = 15%
A ¾-pound bag of nuts is divided equally among 3 friends.
How many pounds of nuts does each friend get?
3/4 ÷ 3 = 3/4(1/3) = 3/12 = 1/4
A grid represents 1.0 as 10 shaded columns.
If 0.8 of the grid is shaded and 0.3 of it is erased, what decimal amount remains shaded?
0.8 − 0.3 = 0.5
✅ Answer: 0.5 remains shaded.
Recipe A uses 2 cups of sugar for every 3 cups of flour.
Recipe B uses 5 cups of sugar for every 7 cups of flour.
Which recipe is sweeter (has a higher sugar-to-flour ratio)?
Recipe A → 2/3 ≈ 0.67
Recipe B → 5/7 ≈ 0.71
Answer: Recipe B is sweeter.
A cyclist rides at a speed of 15 miles per hour.
Convert this speed to feet per second.
(1 mile = 5280 feet, 1 hour = 3600 seconds)
15 miles/hour × (5280 ft / 1 mile) × (1 hour / 3600 s)
= (15 × 5280) ÷ 3600
= 22 feet per second (approx.)
A rectangular bar diagram represents 100 students.
If 30% of the bar is shaded to represent students who play sports, and another 20% is shaded to represent those who play an instrument, how many students do neither?
30% + 20% = 50% play sports or instruments.
100% – 50% = 50% do neither.
50% of 100 = 50 students
✅ Answer: 50 students
How many ½-cup servings are in 3 cups of rice?
3 ÷ 1/2 = 3(2) = 6
Subtract 7.25 − 3.68.
7.25−3.68=3.57
✅ Answer: 3.57
A paint mixture has red, blue, and white paint in the ratio 3 : 2 : 5.
If you have 30 liters of paint in total,
how many liters of each color are there?
what is the ratio of blue paint to the total amount of non-blue paint?
3 + 2 + 5 = 10 parts
Each part = 30 ÷ 10 = 3 liters
Red = 3×3 = 9 L, Blue = 2×3 = 6 L, White = 5×3 = 15 L
Non-blue = 9 + 15 = 24 L
Blue : Non-blue = 6 : 24 → 1 : 4
Answer:
Red = 9 L, Blue = 6 L, White = 15 L; Ratio of Blue to Non-blue = 1 : 4
Train A travels 90 kilometers in 1.5 hours.
Train B travels 60 miles in 1 hour.
Which train is faster?
(Use 1 mile ≈ 1.6 kilometers.)
Train A → 90 ÷ 1.5 = 60 km/h
Train B → 60 miles × 1.6 = 96 km
Speed = 96 ÷ 1 = 96 km/h
Answer: Train B is faster (96 km/h vs. 60 km/h).
A laptop originally costs $800. It is on sale for 25% off.
What is the sale price?
Formula:
Sale Price=Original Price−(Percent×Original Price)
Solution:
25% of 800 = 0.25 × 800 = 200
Sale price = 800 – 200 = $600
✅ Answer: $600
You have 3/4 of a yard of ribbon.
Each bow you make uses 1/8 of a yard.
How many bows can you make?
3/4 ÷ 1/8 = 3/4(8) = 6
Find the product of 0.6 × 0.75 by converting to equivalent fractions.
0.6=6/10=3/5,0.75=75/100=3/4
Multiply:
3/5(3/4) = 9/20 = 0.45
✅ Answer: 0.45