Let's solve each problem step by step. For each phrase, we will:
1.
Express the rate (as a fraction: quantity A per quantity B).
2.
Find the unit rate (how much of one quantity per one unit of the other — e.g., miles per gallon, dollars per book, etc.).
We’ll round each unit rate to the nearest hundredth (two decimal places).
---
1) 120 miles on 9 gallons of gas
-
Rate: $ \frac{120 \text{ miles}}{9 \text{ gallons}} $
-
Unit Rate: $ \frac{120}{9} = 13.\overline{3} \approx 13.33 $ miles per gallon
✔ Rate: 120 miles / 9 gallons
✔ Unit Rate:
13.33 miles per gallon
---
2) 12 dollars for 7 books
-
Rate: $ \frac{12 \text{ dollars}}{7 \text{ books}} $
-
Unit Rate: $ \frac{12}{7} \approx 1.714 \approx 1.71 $ dollars per book
✔ Rate: 12 dollars / 7 books
✔ Unit Rate:
1.71 dollars per book
---
3) mowed 5 yards for $35.00
-
Rate: $ \frac{5 \text{ yards}}{35 \text{ dollars}} $
-
Unit Rate: $ \frac{5}{35} = \frac{1}{7} \approx 0.1429 \approx 0.14 $ yards per dollar
Alternatively, if you want
dollars per yard, it would be $ \frac{35}{5} = 7 $ dollars per yard.
But since the phrase is “mowed 5 yards for $35”, the natural interpretation is
cost per yard, so:
✔ Rate: 5 yards / $35
✔ Unit Rate:
7.00 dollars per yard
> Note: The question says "express as a rate and unit rate." Usually, the unit rate is
per one unit of the second quantity, so here it’s
dollars per yard.
So:
-
Rate: $ \frac{5 \text{ yards}}{35 \text{ dollars}} $
-
Unit Rate: $ \frac{35}{5} = 7.00 $ dollars per yard
✔ Rate: 5 yards / $35
✔ Unit Rate:
7.00 dollars per yard
---
4) 5 calculators cost $200.00
-
Rate: $ \frac{5 \text{ calculators}}{200 \text{ dollars}} $
-
Unit Rate: $ \frac{200}{5} = 40 $ dollars per calculator
✔ Rate: 5 calculators / $200
✔ Unit Rate:
40.00 dollars per calculator
---
5) 8 dollars for 4 cans of tuna
-
Rate: $ \frac{8 \text{ dollars}}{4 \text{ cans}} $
-
Unit Rate: $ \frac{8}{4} = 2.00 $ dollars per can
✔ Rate: 8 dollars / 4 cans
✔ Unit Rate:
2.00 dollars per can
---
6) 7 movie tickets cost $35.00
-
Rate: $ \frac{7 \text{ tickets}}{35 \text{ dollars}} $
-
Unit Rate: $ \frac{35}{7} = 5.00 $ dollars per ticket
✔ Rate: 7 tickets / $35
✔ Unit Rate:
5.00 dollars per ticket
---
7) 9 inches of snow in 7 hours
-
Rate: $ \frac{9 \text{ inches}}{7 \text{ hours}} $
-
Unit Rate: $ \frac{9}{7} \approx 1.2857 \approx 1.29 $ inches per hour
✔ Rate: 9 inches / 7 hours
✔ Unit Rate:
1.29 inches per hour
---
8) 6 pencils for 13 dollars
-
Rate: $ \frac{6 \text{ pencils}}{13 \text{ dollars}} $
-
Unit Rate: $ \frac{13}{6} \approx 2.1667 \approx 2.17 $ dollars per pencil
✔ Rate: 6 pencils / $13
✔ Unit Rate:
2.17 dollars per pencil
---
9) 12 batteries cost 22 dollars
-
Rate: $ \frac{12 \text{ batteries}}{22 \text{ dollars}} $
-
Unit Rate: $ \frac{22}{12} \approx 1.8333 \approx 1.83 $ dollars per battery
✔ Rate: 12 batteries / $22
✔ Unit Rate:
1.83 dollars per battery
---
10) 12 chocolate bars cost 19 dollars
-
Rate: $ \frac{12 \text{ bars}}{19 \text{ dollars}} $
-
Unit Rate: $ \frac{19}{12} \approx 1.5833 \approx 1.58 $ dollars per bar
✔ Rate: 12 bars / $19
✔ Unit Rate:
1.58 dollars per bar
---
✔ Final Answers:
| # | Rate | Unit Rate |
|---|--------------------------|----------------------------|
| 1 | 120 miles / 9 gallons |
13.33 miles/gallon |
| 2 | 12 dollars / 7 books |
1.71 dollars/book |
| 3 | 5 yards / $35 |
7.00 dollars/yard |
| 4 | 5 calculators / $200 |
40.00 dollars/calculator |
| 5 | 8 dollars / 4 cans |
2.00 dollars/can |
| 6 | 7 tickets / $35 |
5.00 dollars/ticket |
| 7 | 9 inches / 7 hours |
1.29 inches/hour |
| 8 | 6 pencils / $13 |
2.17 dollars/pencil |
| 9 | 12 batteries / $22 |
1.83 dollars/battery |
|10 | 12 bars / $19 |
1.58 dollars/bar |
> All unit rates are rounded to the nearest hundredth.
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of unit rate and ratio worksheet.
