Ratios and Rates worksheet for students to practice converting phrases into rates and unit rates.

To solve the problem, we need to express each phrase as a rate and then determine the unit rate. Here's how to approach each question step by step:

Definitions:

- Rate: A comparison of two quantities with different units.
- Unit Rate: A rate where the second quantity is reduced to 1 unit.

Steps:

1. Identify the two quantities in the phrase.
2. Write the rate as a fraction (Quantity 1 / Quantity 2).
3. Simplify the fraction to find the unit rate (divide both numerator and denominator by the denominator).

Let's solve each problem:

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1) 6 dollars for 2 cans of tuna

- Rate: $6 \text{ dollars} / 2 \text{ cans}$
- Unit Rate: Divide both numerator and denominator by 2:
$$
\frac{6}{2} = 3 \text{ dollars per can}
$$
- Answer:
- Rate: $6 \text{ dollars} / 2 \text{ cans}$
- Unit Rate: $3 \text{ dollars per can}$

---

2) 13 chocolate bars cost 21 dollars

- Rate: $21 \text{ dollars} / 13 \text{ chocolate bars}$
- Unit Rate: Divide both numerator and denominator by 13:
$$
\frac{21}{13} \approx 1.62 \text{ dollars per chocolate bar}
$$
- Answer:
- Rate: $21 \text{ dollars} / 13 \text{ chocolate bars}$
- Unit Rate: $1.62 \text{ dollars per chocolate bar}$

---

3) 13 dollars for 4 books

- Rate: $13 \text{ dollars} / 4 \text{ books}$
- Unit Rate: Divide both numerator and denominator by 4:
$$
\frac{13}{4} = 3.25 \text{ dollars per book}
$$
- Answer:
- Rate: $13 \text{ dollars} / 4 \text{ books}$
- Unit Rate: $3.25 \text{ dollars per book}$

---

4) Mowed 5 yards for \$35.00

- Rate: $35 \text{ dollars} / 5 \text{ yards}$
- Unit Rate: Divide both numerator and denominator by 5:
$$
\frac{35}{5} = 7 \text{ dollars per yard}
$$
- Answer:
- Rate: $35 \text{ dollars} / 5 \text{ yards}$
- Unit Rate: $7 \text{ dollars per yard}$

---

5) 145 miles on 9 gallons of gas

- Rate: $145 \text{ miles} / 9 \text{ gallons}$
- Unit Rate: Divide both numerator and denominator by 9:
$$
\frac{145}{9} \approx 16.11 \text{ miles per gallon}
$$
- Answer:
- Rate: $145 \text{ miles} / 9 \text{ gallons}$
- Unit Rate: $16.11 \text{ miles per gallon}$

---

6) 12 batteries cost 20 dollars

- Rate: $20 \text{ dollars} / 12 \text{ batteries}$
- Unit Rate: Divide both numerator and denominator by 12:
$$
\frac{20}{12} \approx 1.67 \text{ dollars per battery}
$$
- Answer:
- Rate: $20 \text{ dollars} / 12 \text{ batteries}$
- Unit Rate: $1.67 \text{ dollars per battery}$

---

7) 7 calculators cost \$190.00

- Rate: $190 \text{ dollars} / 7 \text{ calculators}$
- Unit Rate: Divide both numerator and denominator by 7:
$$
\frac{190}{7} \approx 27.14 \text{ dollars per calculator}
$$
- Answer:
- Rate: $190 \text{ dollars} / 7 \text{ calculators}$
- Unit Rate: $27.14 \text{ dollars per calculator}$

---

8) 7 inches of snow in 6 hours

- Rate: $7 \text{ inches} / 6 \text{ hours}$
- Unit Rate: Divide both numerator and denominator by 6:
$$
\frac{7}{6} \approx 1.17 \text{ inches per hour}
$$
- Answer:
- Rate: $7 \text{ inches} / 6 \text{ hours}$
- Unit Rate: $1.17 \text{ inches per hour}$

---

9) 7 movie tickets cost \$25.00

- Rate: $25 \text{ dollars} / 7 \text{ tickets}$
- Unit Rate: Divide both numerator and denominator by 7:
$$
\frac{25}{7} \approx 3.57 \text{ dollars per ticket}
$$
- Answer:
- Rate: $25 \text{ dollars} / 7 \text{ tickets}$
- Unit Rate: $3.57 \text{ dollars per ticket}$

---

10) 8 pencils for 14 dollars

- Rate: $14 \text{ dollars} / 8 \text{ pencils}$
- Unit Rate: Divide both numerator and denominator by 8:
$$
\frac{14}{8} = 1.75 \text{ dollars per pencil}
$$
- Answer:
- Rate: $14 \text{ dollars} / 8 \text{ pencils}$
- Unit Rate: $1.75 \text{ dollars per pencil}$

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Final Answer:

$$
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Problem} & \text{Rate} & \text{Unit Rate} \\
\hline
1 & 6 \text{ dollars} / 2 \text{ cans} & 3 \text{ dollars per can} \\
2 & 21 \text{ dollars} / 13 \text{ chocolate bars} & 1.62 \text{ dollars per chocolate bar} \\
3 & 13 \text{ dollars} / 4 \text{ books} & 3.25 \text{ dollars per book} \\
4 & 35 \text{ dollars} / 5 \text{ yards} & 7 \text{ dollars per yard} \\
5 & 145 \text{ miles} / 9 \text{ gallons} & 16.11 \text{ miles per gallon} \\
6 & 20 \text{ dollars} / 12 \text{ batteries} & 1.67 \text{ dollars per battery} \\
7 & 190 \text{ dollars} / 7 \text{ calculators} & 27.14 \text{ dollars per calculator} \\
8 & 7 \text{ inches} / 6 \text{ hours} & 1.17 \text{ inches per hour} \\
9 & 25 \text{ dollars} / 7 \text{ tickets} & 3.57 \text{ dollars per ticket} \\
10 & 14 \text{ dollars} / 8 \text{ pencils} & 1.75 \text{ dollars per pencil} \\
\hline
\end{array}
}
$$