I can develop tape diagrams to aid me reason about problems including a ratio and also a total amount.I can solve troubles when I recognize a ratio and also a full amount.

You are watching: Part-to part and part-to whole ratios

### Lesson 15: Part-Part-Whole Ratios

Let’s watch at situations where friend can include the amounts in a proportion together.

Illustrative math Unit 6.2, great 15 (printable worksheets)

### Lesson 15 Summary

The adhering to diagram shows just how to usage a tape diagram to represent a ratio.

15.1 True or False: multiply by a Unit Fraction

True or false?

Scroll down the page for the solution to the fruit beat problem.

15.2 - Cubes the Paint

A recipe for maroon repaint says, “Mix 5 ml the red repaint with 3 ml the blue paint.”

Use snap cubes to stand for the quantities of red and blue paint in the recipe. Then, draw a sketch of your snap-cube depiction of the maroon paint.a. What amount does every cube represent?b. How many milliliters the maroon repaint will over there be?a. Expect each cube to represent 2 ml. Exactly how much that each shade paint is there?Red: _______ mlBlue: _______ mlMaroon: _______ mlb. Expect each cube represents 5 ml. Exactly how much that each color paint is there?Red: _______ mlBlue: _______ mlMaroon: _______ mla. Expect you need 80 ml that maroon paint. Just how much red and blue paint would girlfriend mix? Be all set to explain your reasoning.Red: _______ mlBlue: _______ mlMaroon: 80 mlb. If the initial recipe is because that one batch that maroon paint, how plenty of batches are in 80 ml of maroon paint?15.3 - Sneakers, Chicken, and Fruit Juice

Solve every of the complying with problems and also show your thinking. If you obtain stuck, think about drawing a tape diagram to stand for the situation.

The ratio of students wearing sneakers come those attract boots is 5 come 6. If there room 33 student in the class, and every one of them are wearing one of two people sneakers or boots, how plenty of of them room wearing sneakers?A recipe because that chicken marinade says, “Mix 3 components oil with 2 components soy sauce and 1 part orange juice.” If you need 42 cup of marinade in all, just how much of each ingredient must you use?Elena provides fruit beat by mixing 4 parts cranberry juice come 3 components apple juice to 2 parts grape juice. If one batch the fruit punch consists of 30 cup of to apologize juice, how huge is this batch of fruit punch?Are you prepared for more?

Using the recipe from earlier, how much fruit punch have the right to you do if you have 50 cup of cranberry juice, 40 cup of to apologize juice, and also 30 cups of grape juice?

15.3 -Invent Your own Ratio ProblemInvent another ratio trouble that deserve to be addressed with a tape diagram and solve it. If you gain stuck, consider looking ago at the difficulties you fixed in the earlier activity.Create a visual screen that includes:The brand-new problem the you wrote, there is no the solution.Enough work room for who to present a solution.Trade your display screen with another group, and also solve every other’s problem. Encompass a ice cream diagram as component of your solution. Be all set to re-publishing the systems with the class.When the systems to the difficulty you created is being common by one more group, inspect their answer for accuracy.Glossary Terms

tape diagramA tape diagram is a team of rectangles put together to stand for a relationship in between quantities.

For example, this tape diagram mirrors a ratio of 30 gallons of yellow paint to 50 gallons the blue paint.

If every rectangle to be labeled 5, rather of 10, climate the same snapshot could stand for the tantamount ratio the 15 gallons of yellow paint to 25 gallons of blue paint.

Lesson 15 exercise ProblemsHere is a tape diagram representing the proportion of red repaint to yellow repaint in a mixture that orange paint.a. What is the proportion of yellow paint to red paint?b. Just how many total cups the orange repaint will this mixture yield?At the kennel, the proportion of cat to dogs is . There room 27 pets in all. Below is a ice diagram representing this ratio.a. What is the worth of each small rectangle?b. How countless dogs space at the kennel?c. How many cats room at the kennel?Last month, there to be 4 sunny days for every rainy day. If there to be 30 job in the month, how plenty of days were rainy? describe your reasoning. If you get stuck, take into consideration using a tape diagram.Noah gone into a 100-mile cycle race. He to know he can ride 32 miles in 160 minutes. In ~ this rate, exactly how long will it take him to complete the race? use each table to find the answer. Next, explain which table girlfriend think works better in finding the answer.Table A:
 distance (miles) elapsed time (minutes) 32 160 1 100
Table B:
 distance (miles) elapsed time (minutes) 32 160 96 4 100
5. A cashier worked an 8-hour day, and also earned \$58.00. The double number line reflects the quantity she earned because that working different numbers of hours. For each question, describe your reasoning.a. Just how much does the cashier earn per hour?b. How much walk the cashier earn if she functions 3 hours?6. A grocery store sells bags that oranges in two various sizes.- The 3-pound bags the oranges cost \$4.- The 8-pound bags the oranges because that \$9.Which oranges expense less every pound? explain or present your reasoning.

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