To combine the ratios $x:y = 3:5$ and $y:z = 2:7$, what is the correct first step?

Multiply the first ratio by 2 and the second by 5.

Add the corresponding parts of the ratios.

Multiply the first ratio by 5 and the second by 2.

Multi-way Ratios Practice — Grade 4 amc_math

Lesson 2: Multi-way Ratios — Practice Questions

1. If the ratio of $p$ to $q$ is $3:4$ and the ratio of $q$ to $r$ is $6:5$, what is the combined ratio $p:q:r$?
2. In a recipe, the ratio of flour to sugar is $5:2$. The ratio of sugar to butter is $3:1$. What is the combined ratio of flour to sugar to butter?
- A. 15:6:2
- B. 5:2:1
- C. 5:6:2
- D. 8:5:3
3. Given that the ratio $a:b = 7:3$ and the ratio $b:c = 9:4$, determine the three-part ratio $a:b:c$. Your answer should be in the form x:y:z. ___
4. To combine the ratios $x:y = 3:5$ and $y:z = 2:7$, what is the correct first step?
- A. Multiply the first ratio by 2 and the second by 5.
- B. Add the corresponding parts of the ratios.
- C. Multiply the first ratio by 5 and the second by 2.
- D. Write the ratio as 3:5:2:7.
5. In a collection of animals, the ratio of dogs to cats is $5:6$. The ratio of cats to birds is $4:3$. What is the ratio of dogs to cats to birds? ___
6. A collection of 180 marbles is shared in the ratio $4:2:3$. How many marbles does the first share contain? ___
7. A prize of 250 dollars is divided among three winners in the ratio $5:1:4$. What is the value of the second prize in dollars? ___
8. A total of 200 students are assigned to three projects in the ratio $1:3:6$. How many students are assigned to the third project?
- A. 20
- B. 60
- C. 120
- D. 180
9. In a mixture with parts in the ratio $3:7:2$, what fraction of the total does the second component represent?
- A. $\frac{7}{10}$
- B. $\frac{7}{12}$
- C. $\frac{3}{12}$
- D. $\frac{2}{7}$
10. A recipe for a fruit punch uses juices in the ratio $2:5:3$. If the total volume is 150 ounces, how many ounces of the third juice are needed? ___