Complex Ratios
What is the definition of a ratio in mathematics?
A ratio is a comparison of two quantities by division.
What is a unit rate?
A unit rate is a comparison of two different quantities where the denominator is 1.
What is a commission?
A commission is a fee or percentage paid to a person for making a sale or completing a transaction.
What is simple interest?
Simple interest is a type of interest calculated on the initial principal only.
What is absolute value?
Absolute value is the distance from 0 on a number line.
If a recipe calls for 4 cups of flour and 6 cups of sugar, what is the ratio of flour to sugar in simplest form?
2:3 or 2/3
If a recipe calls for 3 cups of flour and makes 12 cookies, how many cups of flour are needed to make 36 cookies using the same ratio?
9 cups (Using proportion 3 cups: 12 cookies = x cups: 36 cookies)
If a salesperson earns a 5% commission on a $500 sale, how much commission do they earn?
$25 (Calculating 5% of $500)
If you borrow $500 at an interest rate of 5% per year, how much interest will you owe after one year?
$25 (Calculating 5% of $500)
Calculate |-5 + 3|.
2 (First perform the addition inside the absolute value bars, then take the absolute value of the result.)
If a bike travels 30 miles in 2 hours, how far will it travel in 5 hours at the same speed?
75 miles (Using the unit rate of 15 miles per hour, multiply by 5 hours.)
If 4 gallons of paint cover an area of 120 square feet, how many gallons of paint are needed to cover an area of 300 square feet using the same rate?
10 gallons (using the proportion 4 gallons: 120 sft = x gallons: 300 sft)
If the sales tax rate is 8% and you buy a $120 item, how much sales tax do you pay?
$9.60 (Calculating 8% of $120)
If you invest $800 at an interest rate of 4% per year for 3 years, how much interest will you earn?
If you invest $800 at an interest rate of 4% per year for 3 years, how much interest will you earn?
Evaluate |-12 - (-4)|
8 (First simplify the expression within the absolute value bars, then find the absolute value of the result.)
If a car travels 240 miles in 4 hours at a constant speed, how long will it take to travel 450 miles at the same speed?
7.5 hours (Using the unit rate of 60 miles per hour, divide 450 by 60 to find the time in hours.)
A map scale shows 1 inch represents 20 miles. If two cities are 180 miles apart, how far apart should they be on the map?
9 inches (Using the scale 1 inch: 20 miles = x inches: 180 days)
If a meal costs $50 and you want to leave a 20% tip, how much will the tip be?
$10 (Calculating 20% of $50)
If you deposit $1,200 into a savings account with an annual interest rate of 3.5%, how much will you have in the account after 2 years?
$1,254 (I = Prt)
A submarine is at a depth of -50 meters below sea level. It ascends 30 meters. What is its new depth, considering sea level as zero?
The submarine's new depth is -20 meters. (Thinking in terms of distances above and below sea level, adding 30 meters to -50 meters brings the submarine 20 meters above sea level.)
If 5 computers can complete a task in 8 hours, how many hours will it take for 20 computers to complete the same task, assuming all work at the same rate?
2 hours
If the number of computers quadruples, the time taken should decrease by a factor of 4, or you can say the time taken should be one-fourth of the original time. Since 8 is the original time then 1/4 of 8 is 2.
If 5 workers can complete a job in 10 days, how many workers are needed to complete the same job in 4 days?
12.5 workers (This question involves the concept that if the time to complete the job decreases, more workers are needed. Using the inverse proportion 5 workers: 10 days = x workers: 4 days)
Emily earns a 15% commission on sales. If she wants to earn a commission of $750, how much in sales does she need to generate?
$5,000 (Calculating the sales needed by using the inverse operation of finding 15% of a value to determine the total sales for a $750 commission.)
Sam invests $2,500 at a certain rate of interest and earns $600 in interest after 5 years. What was the annual interest rate?
4.8% (Calculating the annual interest rate using the simple interest formula: I=Prt)
A temperature drops 15 degrees below zero. Then, it rises 18 degrees. What is the final temperature above or below zero?
The final temperature is 3 degrees above zero. (Considering the temperature scale where negative values are below zero, the initial drop of 15 degrees, followed by an increase of 18 degrees, brings the final temperature 3 degrees above zero.)