Ratios & Proportions
What is the ratio of 8 apples to 12 oranges? (Simplify)
8:12 simplifies to 2:3
Write ¾ as a decimal.
¾ as a decimal = 0.75
Simplify: 4(3 + 5)
4(3 + 5) = 4(8) = 32
What is the area of a rectangle with a length of 8 cm and width of 5 cm?
Area = 8 × 5 = 40 cm²
What is the mean of the following numbers: 4, 8, 6, 2?
Mean = (4+8+6+2)/4 = 20/4 = 5
Solve: If 3 pencils cost $2, how much do 9 pencils cost?
9 pencils cost $6
Convert 0.6 into a fraction in simplest form.
0.6 = 3/5
Solve for x: x + 7 = 15
x + 7 = 15 → x = 8
Find the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm.
Perimeter = 6 + 8 + 10 = 24 cm
What is the median of 3, 7, 8, 10, 12?
Median of 3,7,8,10,12 = 8
Write 45% as a ratio.
45% as a ratio is 45:100 (or simplified 9:20)
What is 25% of 160?
25% of 160 = 40
Solve: 3x = 21
3x = 21 → x = 7
Identify the 3D shape: 6 square faces, 8 vertices, 12 edges.
Shape = Cube
If a number cube (die) is rolled, what is the probability of rolling a 5?
Probability of rolling 5 = 1/6 → 1/6
A recipe uses 2 cups of sugar for every 5 cups of flour. How much sugar is needed for 15 cups of flour?
2 cups sugar × (15 ÷ 5) = 6 cups of sugar
Solve: 5/8 + 1/4
5/8 + 1/4 = (5/8) + (2/8) = 7/8
Evaluate when x = 2: 5x² - 3x
5(2)² - 3(2) = 5(4) - 6 = 20 - 6 = 14
The area of a triangle is 24 cm² and its base is 8 cm. What is the height?
Area of triangle = (Base × Height) ÷ 2
24 = (8 × h) ÷ 2 → 24 = 4h → h = 6 cm
Find the mode: 2, 3, 2, 5, 7, 2, 8
Mode = 2
A car travels 180 miles in 3 hours. What is its unit rate in miles per hour?
180 ÷ 3 = 60 miles per hour
A shirt originally costs $40 and is on sale for 25% off. What is the sale price?
25% of $40 = $10 off → Sale price = $30
Write an expression for "three times a number decreased by 7."
Expression: 3x - 7
Find the volume of a rectangular prism with length 5 cm, width 3 cm, and height 2 cm.
Volume = 5 × 3 × 2 = 30 cm³
A spinner has 5 equal sections numbered 1–5. What is the probability of spinning an even number?
Even numbers: 2 and 4 → 2/5 → 2/5