Ratios and proportions
A recipe calls for 2 cups of sugar for every 3 cups of flour. What is the ratio of sugar to flour?
2:3
What is ¾ written as a decimal?
What is ¾ written as a decimal?
→ 0.75
Write an expression for “5 more than a number x.”
Write an expression for “5 more than a number x.”
→ x + 5
What is the opposite of -7?
What is the opposite of -7?
→ 7
You buy 3 pencils for $1.50. What is the price of 1 pencil?
You buy 3 pencils for $1.50. What is the price of 1 pencil?
→ $0.50
If 4 apples cost $6, how much would 6 apples cost at the same rate?
If 4 apples cost $6, how much would 6 apples cost at the same rate?
→ $9
What is the product of 0.4 × 0.6?
What is the product of 0.4 × 0.6?
→ 0.24
Simplify: 2(3 + 4).
Simplify: 2(3 + 4).
→ 14
On a number line, which is greater: -2 or -5?
On a number line, which is greater: -2 or -5?
→ -2
A classroom has 12 boys and 8 girls. What fraction of the class are boys?
A classroom has 12 boys and 8 girls. What fraction of the class are boys?
→ 3/5
A car travels 60 miles in 2 hours. What is its unit rate in miles per hour?
A car travels 60 miles in 2 hours. What is its unit rate in miles per hour?
→ 30 miles per hour
Divide 3 ÷ ½.
Divide 3 ÷ ½.
→ 6
Evaluate 3a + 4 when a = 5.
Evaluate 3a + 4 when a = 5.
→ 19
Plot the point (3, -4). Which quadrant is it in?
Plot the point (3, -4). Which quadrant is it in?
→ Quadrant IV
If a runner completes ¾ of a 12-mile race, how far has she run?
If a runner completes ¾ of a 12-mile race, how far has she run?
→ 9 miles
A map scale says 1 inch = 5 miles. If two cities are 3.5 inches apart on the map, how far are they in real life?
A map scale says 1 inch = 5 miles. If two cities are 3.5 inches apart on the map, how far are they in real life?
→ 17.5 miles
If you spend 0.75 of an hour reading, how many minutes did you read?
If you spend 0.75 of an hour reading, how many minutes did you read?
→ 45 minutes
The expression 2n + 8 represents the total cost for n movie tickets. How much would 5 tickets cost?
The expression 2n + 8 represents the total cost for n movie tickets. How much would 5 tickets cost?
→ $18
Find the distance between the points (-2, 3) and (4, 3).
Find the distance between the points (-2, 3) and (4, 3).
→ 6 units
A water tank is ⅔ full and holds 60 gallons when full. How many gallons are in the tank?
A water tank is ⅔ full and holds 60 gallons when full. How many gallons are in the tank?
→ 40 gallons
In a school the ratio of teachers to students is 1 : 22. If the school has 1,056 students, how many teachers should there be to maintain the ratio?
In a school the ratio of teachers to students is 1 : 22. If the school has 1,056 students, how many teachers should there be to maintain the ratio?
→ 48 teachers (because 1,056 ÷ 22 = 48)
A number multiplied by 0.125 yields 3. What is the original number?
A number multiplied by 0.125 yields 3. What is the original number?
→ 24 (because 3 ÷ 0.125 = 24)
Simplify the expression: 4(2x − 3) + 5x
Simplify the expression: 4(2x − 3) + 5x
→ 13x − 12
A submarine is at −120 meters below sea level. It then ascends 45 meters, descends 30 meters, and ascends again 60 meters. What is its final depth?
A submarine is at −120 meters below sea level. It then ascends 45 meters, descends 30 meters, and ascends again 60 meters. What is its final depth?
→ Starting at −120, +45 → −75, −30 → −105, +60 → −45 meters
A fundraiser collected $540 from selling tickets at $9 each. If the venue took $120 for costs and the remaining money is split equally among 3 charities, how much does each charity receive?
A fundraiser collected $540 from selling tickets at $9 each. If the venue took $120 for costs and the remaining money is split equally among 3 charities, how much does each charity receive?
→ Ticket income: 540 ÷ 9 = 60 tickets → $540; subtract cost 120 → $420 remaining → split 3 ways → $140 each