Converting from Percents to Fractions, Decimals and Part-to-Whole ... - Free Printable

Let's solve the problem step by step. The task is to convert percents to fractions, decimals, and ratios, using part-to-whole relationships.

We'll go through each row and convert the given percent into:

- Fraction: Write the percent over 100 and simplify.
- Decimal: Divide the percent by 100.
- Ratio: Express as a part-to-whole ratio (e.g., 87.5:100), then simplify.

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🔁 Conversion Rules:

- Percent → Decimal: Divide by 100
e.g., 87.5% = 87.5 ÷ 100 = 0.875
- Percent → Fraction: Write as %/100, then simplify
e.g., 87.5% = 87.5/100 = 875/1000 = 7/8 (after simplifying)
- Ratio: Use the decimal or fraction form and express as a ratio of part to whole (usually over 100 or simplified).

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Now let’s fill in the table:

| Fraction | Decimal | Percent | Ratio |
|---------|--------|--------|-------|
| 1. | | 87.5% | |
| 2. | | 70% | |
| 3. | | 20% | |
| 4. | | 25% | |
| 5. | | 50% | |
| 6. | | 12.5% | |
| 7. | | 36% | |
| 8. | | 80% | |
| 9. | | 10% | |
| 10. | | 75% | |

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✔ Step-by-step Solutions:

#### 1. 87.5%
- Decimal: 87.5 ÷ 100 = 0.875
- Fraction: 87.5/100 = 875/1000 = 7/8 (simplify by dividing numerator and denominator by 125)
- Ratio: 87.5:100 → multiply both by 8 to eliminate decimals: 700:800 → simplify to 7:8

✔ Row 1:
Fraction: 7/8
Decimal: 0.875
Ratio: 7:8

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#### 2. 70%
- Decimal: 70 ÷ 100 = 0.7
- Fraction: 70/100 = 7/10
- Ratio: 70:100 = 7:10

✔ Row 2:
Fraction: 7/10
Decimal: 0.7
Ratio: 7:10

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#### 3. 20%
- Decimal: 20 ÷ 100 = 0.2
- Fraction: 20/100 = 1/5
- Ratio: 20:100 = 1:5

✔ Row 3:
Fraction: 1/5
Decimal: 0.2
Ratio: 1:5

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#### 4. 25%
- Decimal: 25 ÷ 100 = 0.25
- Fraction: 25/100 = 1/4
- Ratio: 25:100 = 1:4

✔ Row 4:
Fraction: 1/4
Decimal: 0.25
Ratio: 1:4

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#### 5. 50%
- Decimal: 50 ÷ 100 = 0.5
- Fraction: 50/100 = 1/2
- Ratio: 50:100 = 1:2

✔ Row 5:
Fraction: 1/2
Decimal: 0.5
Ratio: 1:2

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#### 6. 12.5%
- Decimal: 12.5 ÷ 100 = 0.125
- Fraction: 12.5/100 = 125/1000 = 1/8
- Ratio: 12.5:100 → multiply by 8: 100:800 → simplify to 1:8

✔ Row 6:
Fraction: 1/8
Decimal: 0.125
Ratio: 1:8

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#### 7. 36%
- Decimal: 36 ÷ 100 = 0.36
- Fraction: 36/100 = 9/25 (divide numerator and denominator by 4)
- Ratio: 36:100 = 9:25

✔ Row 7:
Fraction: 9/25
Decimal: 0.36
Ratio: 9:25

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#### 8. 80%
- Decimal: 80 ÷ 100 = 0.8
- Fraction: 80/100 = 4/5
- Ratio: 80:100 = 4:5

✔ Row 8:
Fraction: 4/5
Decimal: 0.8
Ratio: 4:5

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#### 9. 10%
- Decimal: 10 ÷ 100 = 0.1
- Fraction: 10/100 = 1/10
- Ratio: 10:100 = 1:10

✔ Row 9:
Fraction: 1/10
Decimal: 0.1
Ratio: 1:10

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#### 10. 75%
- Decimal: 75 ÷ 100 = 0.75
- Fraction: 75/100 = 3/4
- Ratio: 75:100 = 3:4

✔ Row 10:
Fraction: 3/4
Decimal: 0.75
Ratio: 3:4

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✔ Final Answer Table:

| Fraction | Decimal | Percent | Ratio |
|---------|--------|--------|--------|
| 1. | 7/8 | 87.5% | 7:8 |
| 2. | 7/10 | 70% | 7:10 |
| 3. | 1/5 | 20% | 1:5 |
| 4. | 1/4 | 25% | 1:4 |
| 5. | 1/2 | 50% | 1:2 |
| 6. | 1/8 | 12.5% | 1:8 |
| 7. | 9/25 | 36% | 9:25 |
| 8. | 4/5 | 80% | 4:5 |
| 9. | 1/10 | 10% | 1:10 |
| 10. | 3/4 | 75% | 3:4 |

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📝 Summary Tips:

- Always write percent as a fraction over 100 first.
- Simplify fractions by finding the greatest common divisor (GCD).
- Ratios are based on part-to-whole — so they match the fraction format (e.g., 7/8 → 7:8).
- For decimals, just divide the percent by 100.

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