Ratio and Proportions
A recipe uses 3 cups of flour for every 2 cups of sugar. What is the unit rate of flour per 1 cup of sugar?
1.5 cups flour per 1 cup sugar
Add: (-7) + 12 =
5
Simplify the expression: 5x + 3x − 4.
8x - 4
Solve for all values of x; 12x > 24
x > 2
Find the mean of the data set: 4, 7, 9, 10
7.5
A map scale shows 1 inch = 15 miles. If two cities are 4.8 inches apart on the map, how many miles apart are they?
72 miles
What is the absolute value of -8?
8
Solve for x: 4x − 7 = 21
x = 7
Solve for all values of x; 2x - 6 < -24
x < -9
A spinner has sections numbered 1–4 equally likely. What is the probability of landing on an even number?
1/2
Decide whether the following table represents a proportional relationship: (x: 2, 4, 6; y: 3, 6, 10). Explain your reasoning.
Not proportional: ratios 3/2 = 1.5, 6/4 = 1.5, 10/6 ≈ 1.666... so last pair breaks proportionality
Multiply: (-8) × 3/4 =
-6
Expand and simplify: 3(x + 5) − 2x
x + 15
Write and solve the inequality: 4 less than twice a number is at least -3.
2x - 4 >= -3
x >= 1/2
A box contains 3 red, 4 blue, and 5 green marbles. If one marble is drawn at random, what is the probability it is not blue? Express as a fraction in lowest terms.
Not blue = 3+5 = 8 out of 12 → 2/3
A car uses 6.5 gallons of gas to travel 260 miles. How many miles per gallon does the car get? Round to the nearest tenth.
40.0 mpg
Convert 7/12 to a decimal (rounded or repeating). Explain whether the decimal terminates or repeats.
0.5833... or 0.58̅3 (repeating); decimal repeats.
Write an equation for and solve: "Seven less than three times a number is 20."
3x - 7 = 20; x = 9
x <= 31.666.... so 31 bags.
Find the median for the data 5, 2, 7, 15, 18, 9, 12, 21
10.5
A school fundraiser raised $540 selling raffle tickets. Adult tickets cost $3 and student tickets cost $1.50. If 4 student tickets were sold total, how many were adult tickets? Show equation and solution.
3a + 4(1.50) = 540
a = 178
Divide and write the quotient as a simplified fraction and decimal: -9 ÷ 2.5. Show steps.
-9 ÷ 2.5 = -18/5 = -3.6
Solve the equation and check: 2/3 x + 5 = 11. Show algebraic steps.
x = 9
Spence wants to buy a gaming console for $350. They have $100 saved already and wins $30 per game they win. How many games at least do they need to win in order to afford the gaming console?
30x + 100 >= 350
x >= 8.33333 so 9 games
If there is a spinner with 3 equal sections (red, blue, and green) and there is a six-sided die, what is the probability of getting red and an odd number?
1/3 * 1/2 = 1/6