Ratios and Rates worksheet with problems to convert phrases into rates and unit rates, suitable for math education.

Problem: Express each phrase as a rate and unit rate. Round your answer to the nearest hundredth.

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

#### Steps to Solve:
1. Identify the two quantities in the problem.
2. Write the rate as a fraction (Quantity 1 / Quantity 2).
3. Simplify the fraction to find the unit rate by dividing both the numerator and denominator by the denominator.
4. Round the result to the nearest hundredth if necessary.

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Solutions:

#### 1) 6 dollars for 2 cans of tuna
- Rate: $6 \text{ dollars} / 2 \text{ cans}$
- Unit Rate: Divide both parts by 2:
$$
\frac{6}{2} = 3 \text{ dollars per can}
$$
- Answer:
- Rate: $6 \text{ dollars}/2 \text{ cans}$
- Unit Rate: $3 \text{ dollars/can}$

#### 2) 13 chocolate bars cost 21 dollars
- Rate: $21 \text{ dollars} / 13 \text{ chocolate bars}$
- Unit Rate: Divide both parts by 13:
$$
\frac{21}{13} \approx 1.62 \text{ dollars per chocolate bar}
$$
- Answer:
- Rate: $21 \text{ dollars}/13 \text{ chocolate bars}$
- Unit Rate: $1.62 \text{ dollars/chocolate bar}$

#### 3) 13 dollars for 4 books
- Rate: $13 \text{ dollars} / 4 \text{ books}$
- Unit Rate: Divide both parts by 4:
$$
\frac{13}{4} = 3.25 \text{ dollars per book}
$$
- Answer:
- Rate: $13 \text{ dollars}/4 \text{ books}$
- Unit Rate: $3.25 \text{ dollars/book}$

#### 4) Mowed 5 yards for \$35.00
- Rate: $35 \text{ dollars} / 5 \text{ yards}$
- Unit Rate: Divide both parts by 5:
$$
\frac{35}{5} = 7 \text{ dollars per yard}
$$
- Answer:
- Rate: $35 \text{ dollars}/5 \text{ yards}$
- Unit Rate: $7 \text{ dollars/yard}$

#### 5) 145 miles on 9 gallons of gas
- Rate: $145 \text{ miles} / 9 \text{ gallons}$
- Unit Rate: Divide both parts by 9:
$$
\frac{145}{9} \approx 16.11 \text{ miles per gallon}
$$
- Answer:
- Rate: $145 \text{ miles}/9 \text{ gallons}$
- Unit Rate: $16.11 \text{ miles/gallon}$

#### 6) 12 batteries cost 20 dollars
- Rate: $20 \text{ dollars} / 12 \text{ batteries}$
- Unit Rate: Divide both parts by 12:
$$
\frac{20}{12} \approx 1.67 \text{ dollars per battery}
$$
- Answer:
- Rate: $20 \text{ dollars}/12 \text{ batteries}$
- Unit Rate: $1.67 \text{ dollars/battery}$

#### 7) 7 calculators cost \$190.00
- Rate: $190 \text{ dollars} / 7 \text{ calculators}$
- Unit Rate: Divide both parts by 7:
$$
\frac{190}{7} \approx 27.14 \text{ dollars per calculator}
$$
- Answer:
- Rate: $190 \text{ dollars}/7 \text{ calculators}$
- Unit Rate: $27.14 \text{ dollars/calculator}$

#### 8) 7 inches of snow in 6 hours
- Rate: $7 \text{ inches} / 6 \text{ hours}$
- Unit Rate: Divide both parts by 6:
$$
\frac{7}{6} \approx 1.17 \text{ inches per hour}
$$
- Answer:
- Rate: $7 \text{ inches}/6 \text{ hours}$
- Unit Rate: $1.17 \text{ inches/hour}$

#### 9) 7 movie tickets cost \$25.00
- Rate: $25 \text{ dollars} / 7 \text{ tickets}$
- Unit Rate: Divide both parts by 7:
$$
\frac{25}{7} \approx 3.57 \text{ dollars per ticket}
$$
- Answer:
- Rate: $25 \text{ dollars}/7 \text{ tickets}$
- Unit Rate: $3.57 \text{ dollars/ticket}$

#### 10) 8 pencils for 14 dollars
- Rate: $14 \text{ dollars} / 8 \text{ pencils}$
- Unit Rate: Divide both parts by 8:
$$
\frac{14}{8} = 1.75 \text{ dollars per pencil}
$$
- Answer:
- Rate: $14 \text{ dollars}/8 \text{ pencils}$
- Unit Rate: $1.75 \text{ dollars/pencil}$

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Final Answer:

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