Unit 11: Ratios, Rates, and Proportions
Comparing two amounts the same way every time — ratios, unit rates, comparison shopping, and scaling recipes and maps.
6 topics · 24 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What a Ratio Actually Compares
- How it worksHow do you write the ratio of 5 red marbles to 3 blue marbles in a bag using a colon?
- Common mistakeWhy isn't a ratio of 3 to 2 the same as saying there are only 5 things total?
- Going furtherWhat happens to the ratio of dogs to cats if 4 more cats join a group of 3 dogs and 2 cats?
Your turn1 of 2
A bag has a ratio of 4 red marbles to 4 blue marbles. If Sam refills it with 9 times as many of each color, how many red marbles are there now?Equivalent Ratios
- How it worksHow do you find an equivalent ratio by multiplying both numbers in a ratio by the same amount?
- Worked exampleFind an equivalent ratio to 3 cups of flour for every 2 cups of sugar using 6 cups of flour.
- Worked exampleFind out if the ratio 4 to 6 is equivalent to the ratio 10 to 15.
- Common mistakeWhy doesn't adding 3 to both numbers in the ratio 2 to 5 give you an equivalent ratio?
- Going furtherWhat happens to a recipe's ratio of 2 eggs to 1 cup of milk if you triple every ingredient?
Your turn1 of 2
A recipe mixes paint in a ratio of 4 parts blue to 4 parts yellow. If Tom makes 9 times as much of each color, how many parts blue does he use?Unit Rates
- How it worksHow do you find a unit rate by dividing a total amount by the number of single units?
- Worked exampleFind the unit rate in dollars per pound if 5 pounds of apples costs 10 dollars.
- Going furtherWhat happens to the unit rate if the same 10 dollars only buys 4 pounds of apples instead of 5?
- Ties togetherHow does finding a unit rate connect to the division you use to split a number into equal groups?
Your turn1 of 2
A farm stand sells 11 pounds of apples for 54 dollars. What is the price per pound?Comparison Shopping with Unit Rates
- How it worksHow do you compare two cereal boxes by finding the cost per ounce for each one?
- Going furtherWhat happens to which cereal box is the better deal if the smaller box goes on sale for half price?
- Ties togetherHow does comparing unit prices between two cereal boxes connect to comparing decimals like 0.19 and 0.21?
Your turn1 of 2
A box of cereal costs 8 dollars for 24 ounces. What is the cost per ounce?Solving a Proportion
- How it worksHow do you solve a proportion by cross-multiplying the two ratios and then dividing?
- Common mistakeWhy can't you solve 3 over 4 equals x over 12 by just adding 8 to the top and bottom?
- Worked exampleFind the missing number in the proportion 3 over 4 equals what number over 20.
- Worked exampleFind how many boys are in a class if the ratio of boys to girls is 2 to 3 and there are 15 girls.
- Going furtherWhat happens to the proportion 3 over 4 equals x over 20 if the 20 changes to 40 instead?
Your turn1 of 2
A recipe uses 7 cups of flour for every 7 cookies. How many cups of flour are needed to make 57 cookies?Scaling a Recipe or a Map
- How it worksHow do you scale up a recipe that serves 4 people so that it serves 12 people instead?
- Worked exampleFind how many cups of flour you need if a recipe uses 2 cups of flour for 6 cookies and you want 18 cookies.
- Common mistakeWhy doesn't tripling just the sugar in a recipe count as tripling the whole recipe?
- Ties togetherHow does scaling a map's distance connect to the equivalent ratios you use to scale a recipe?
Your turn1 of 2
Nina's recipe uses 4 cups of flour for 9 cookies, and she wants to make 57 cookies. How many cups of flour does she need?