Introduction to Ratios worksheet - Free Printable

Of course! Let's solve the problems step by step, following the instructions to show your work in the larger boxes and write the final answer in the smaller boxes.

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## 1. Writing Ratios – Complete the table to write the ratios in three different ways.

We need to convert between Words, Colon (a:b), and Fraction (a/b) forms.

a) Words: "4 to 5"

- Colon: 4:5
- Fraction: $\frac{4}{5}$

✔ Final Answer:
- Colon: 4:5
- Fraction: $\frac{4}{5}$

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b) Colon: 12:18

- Words: "12 to 18"
- Fraction: $\frac{12}{18}$ → *This can be simplified, but the question only asks for equivalent forms, not simplest form yet.*

✔ Final Answer:
- Words: 12 to 18
- Fraction: $\frac{12}{18}$

*(Note: We’ll simplify this in Part 2.)*

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c) Fraction: $\frac{15}{7}$

- Words: "15 to 7"
- Colon: 15:7

✔ Final Answer:
- Words: 15 to 7
- Colon: 15:7

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d) Colon: 14:3

- Words: "14 to 3"
- Fraction: $\frac{14}{3}$

✔ Final Answer:
- Words: 14 to 3
- Fraction: $\frac{14}{3}$

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e) Words: "seven to twenty"

- Colon: 7:20
- Fraction: $\frac{7}{20}$

✔ Final Answer:
- Colon: 7:20
- Fraction: $\frac{7}{20}$

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## 2. Simplest Form – Write the following ratios as fractions and reduce them to their simplest form.

To simplify a ratio written as $a:b$, write it as a fraction $\frac{a}{b}$, then divide numerator and denominator by their Greatest Common Factor (GCF).

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a) 14:16 → $\frac{14}{16}$

- GCF of 14 and 16 is 2
- $\frac{14 ÷ 2}{16 ÷ 2} = \frac{7}{8}$

✔ Final Answer: $\frac{7}{8}$

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b) 4:8 → $\frac{4}{8}$

- GCF of 4 and 8 is 4
- $\frac{4 ÷ 4}{8 ÷ 4} = \frac{1}{2}$

✔ Final Answer: $\frac{1}{2}$

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c) 2:12 → $\frac{2}{12}$

- GCF of 2 and 12 is 2
- $\frac{2 ÷ 2}{12 ÷ 2} = \frac{1}{6}$

✔ Final Answer: $\frac{1}{6}$

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d) 6:18 → $\frac{6}{18}$

- GCF of 6 and 18 is 6
- $\frac{6 ÷ 6}{18 ÷ 6} = \frac{1}{3}$

✔ Final Answer: $\frac{1}{3}$

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e) 24:18 → $\frac{24}{18}$

- GCF of 24 and 18 is 6
- $\frac{24 ÷ 6}{18 ÷ 6} = \frac{4}{3}$

✔ Final Answer: $\frac{4}{3}$

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f) 54:68 → $\frac{54}{68}$

- GCF of 54 and 68 is 2
- $\frac{54 ÷ 2}{68 ÷ 2} = \frac{27}{34}$

✔ Final Answer: $\frac{27}{34}$

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g) 65:110 → $\frac{65}{110}$

- GCF of 65 and 110 is 5
- $\frac{65 ÷ 5}{110 ÷ 5} = \frac{13}{22}$

✔ Final Answer: $\frac{13}{22}$

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h) 42:22 → $\frac{42}{22}$

- GCF of 42 and 22 is 2
- $\frac{42 ÷ 2}{22 ÷ 2} = \frac{21}{11}$

✔ Final Answer: $\frac{21}{11}$

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i) 80:15 → $\frac{80}{15}$

- GCF of 80 and 15 is 5
- $\frac{80 ÷ 5}{15 ÷ 5} = \frac{16}{3}$

✔ Final Answer: $\frac{16}{3}$

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j) 26:130 → $\frac{26}{130}$

- GCF of 26 and 130 is 26
- $\frac{26 ÷ 26}{130 ÷ 26} = \frac{1}{5}$

✔ Final Answer: $\frac{1}{5}$

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k) $\frac{1}{2} : 7$ → This is a ratio with a fraction.

To simplify, write it as a fraction: $\frac{\frac{1}{2}}{7} = \frac{1}{2} \div 7 = \frac{1}{2} \times \frac{1}{7} = \frac{1}{14}$

✔ Final Answer: $\frac{1}{14}$

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l) $5 : \frac{1}{4}$ → Ratio with a fraction.

Write as a fraction: $\frac{5}{\frac{1}{4}} = 5 \div \frac{1}{4} = 5 \times 4 = 20$

So as a fraction: $\frac{20}{1}$

✔ Final Answer: $\frac{20}{1}$ or just 20

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## ✔ Final Answers Summary:

1. Writing Ratios Table:

| | WORDS | COLON | FRACTION |
|-------|---------------|---------|--------------|
| a) | 4 to 5 | 4:5 | $\frac{4}{5}$ |
| b) | 12 to 18 | 12:18 | $\frac{12}{18}$ |
| c) | 15 to 7 | 15:7 | $\frac{15}{7}$ |
| d) | 14 to 3 | 14:3 | $\frac{14}{3}$ |
| e) | seven to twenty | 7:20 | $\frac{7}{20}$ |

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2. Simplest Form:

a) $\frac{7}{8}$
b) $\frac{1}{2}$
c) $\frac{1}{6}$
d) $\frac{1}{3}$
e) $\frac{4}{3}$
f) $\frac{27}{34}$
g) $\frac{13}{22}$
h) $\frac{21}{11}$
i) $\frac{16}{3}$
j) $\frac{1}{5}$
k) $\frac{1}{14}$
l) $\frac{20}{1}$

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Let me know if you’d like to see the working shown in box format as on the worksheet!