Ratios and Rates worksheet for students to practice expressing ratios as fractions in simplest form.

Sure! Let’s solve each problem by expressing the given ratio as a fraction in simplest form.

To simplify a fraction, we divide both the numerator and denominator by their greatest common factor (GCF).

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1) 18 pounds to 22 pounds

→ Fraction: `18/22`
GCF of 18 and 22 is 2
→ `18 ÷ 2 = 9`, `22 ÷ 2 = 11`
✔ Answer: 9/11

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2) 12 pints to 36 pints

→ `12/36`
GCF = 12
→ `12 ÷ 12 = 1`, `36 ÷ 12 = 3`
✔ Answer: 1/3

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3) 16 feet out of 18 feet

→ `16/18`
GCF = 2
→ `16 ÷ 2 = 8`, `18 ÷ 2 = 9`
✔ Answer: 8/9

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4) 25 red bikes out of 60 bikes

→ `25/60`
GCF = 5
→ `25 ÷ 5 = 5`, `60 ÷ 5 = 12`
✔ Answer: 5/12

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5) 12 pennies to 24 pennies

→ `12/24`
GCF = 12
→ `12 ÷ 12 = 1`, `24 ÷ 12 = 2`
✔ Answer: 1/2

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6) 9 snow days out of 30 days

→ `9/30`
GCF = 3
→ `9 ÷ 3 = 3`, `30 ÷ 3 = 10`
✔ Answer: 3/10

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7) 12 blue cars out of 48 cars

→ `12/48`
GCF = 12
→ `12 ÷ 12 = 1`, `48 ÷ 12 = 4`
✔ Answer: 1/4

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8) 32 quarts to 48 quarts

→ `32/48`
GCF = 16
→ `32 ÷ 16 = 2`, `48 ÷ 16 = 3`
✔ Answer: 2/3

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9) 6 gallons to 42 gallons

→ `6/42`
GCF = 6
→ `6 ÷ 6 = 1`, `42 ÷ 6 = 7`
✔ Answer: 1/7

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10) 30 beetles out of 35 insects

→ `30/35`
GCF = 5
→ `30 ÷ 5 = 6`, `35 ÷ 5 = 7`
✔ Answer: 6/7

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11) 12 cups to 21 cups

→ `12/21`
GCF = 3
→ `12 ÷ 3 = 4`, `21 ÷ 3 = 7`
✔ Answer: 4/7

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12) 21 dimes to 24 dimes

→ `21/24`
GCF = 3
→ `21 ÷ 3 = 7`, `24 ÷ 3 = 8`
✔ Answer: 7/8

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13) 10 dimes out of 35 coins

→ `10/35`
GCF = 5
→ `10 ÷ 5 = 2`, `35 ÷ 5 = 7`
✔ Answer: 2/7

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14) 22 cakes out of 24 cakes

→ `22/24`
GCF = 2
→ `22 ÷ 2 = 11`, `24 ÷ 2 = 12`
✔ Answer: 11/12

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15) 10 nickels to 18 nickels

→ `10/18`
GCF = 2
→ `10 ÷ 2 = 5`, `18 ÷ 2 = 9`
✔ Answer: 5/9

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16) 21 inches to 28 inches

→ `21/28`
GCF = 7
→ `21 ÷ 7 = 3`, `28 ÷ 7 = 4`
✔ Answer: 3/4

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17) 20 points out of 45 points

→ `20/45`
GCF = 5
→ `20 ÷ 5 = 4`, `45 ÷ 5 = 9`
✔ Answer: 4/9

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18) 7 footballs to 56 fooballs

*(Note: “fooballs” is likely a typo — probably meant “footballs”)*
→ `7/56`
GCF = 7
→ `7 ÷ 7 = 1`, `56 ÷ 7 = 8`
✔ Answer: 1/8

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19) 18 rainy days out of 24 days

→ `18/24`
GCF = 6
→ `18 ÷ 6 = 3`, `24 ÷ 6 = 4`
✔ Answer: 3/4

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20) 60 miles out of 72 miles

→ `60/72`
GCF = 12
→ `60 ÷ 12 = 5`, `72 ÷ 12 = 6`
✔ Answer: 5/6

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## ✔ Final Answers Summary:

1) 9/11
2) 1/3
3) 8/9
4) 5/12
5) 1/2
6) 3/10
7) 1/4
8) 2/3
9) 1/7
10) 6/7
11) 4/7
12) 7/8
13) 2/7
14) 11/12
15) 5/9
16) 3/4
17) 4/9
18) 1/8
19) 3/4
20) 5/6

Let me know if you’d like these explained with visuals or step-by-step breakdowns for any specific one!