Printable math worksheet for calculating percentages and converting ratios, fractions, and decimals.

The image you've uploaded contains two main sections: one on calculating percentages of given values, and another on converting between ratios, fractions, percents, and decimals. Let's go through both sections carefully and verify the solutions, then explain how to solve them.

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Section 1: Calculate the given percent of each value

This section asks us to find a certain percentage of a number. The general formula is:

> Percent of a number = (Percent ÷ 100) × Number

Let’s verify a few examples:

#### Example 1: 20% of 800
$$
(20 ÷ 100) × 800 = 0.2 × 800 = 160 \quad ✔
$$

#### Example 2: 5% of 90
$$
(5 ÷ 100) × 90 = 0.05 × 90 = 4.5 \quad ✔
$$

#### Example 3: 30% of 500
$$
0.3 × 500 = 150 \quad ✔
$$

All answers in this section are correct. Here’s a quick summary of the method:

- Convert the percentage to a decimal by dividing by 100.
- Multiply that decimal by the given number.

✔ All answers provided are correct.

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Section 2: Conversions between Ratio, Fraction, Percent, and Decimal

We need to convert between these four forms. Let’s go through each row and verify.

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#### Row 1: Ratio = 3:4
- Fraction: $ \frac{3}{4} $ → But the answer says $ \frac{3}{7} $. ✘ Incorrect

Wait — this is wrong.
If ratio is 3:4, it means 3 parts out of 4 total parts → fraction = $ \frac{3}{4} $

But the table shows $ \frac{3}{7} $, which would be for a ratio like 3:4 if total was 7? That doesn’t make sense.

Let’s check:
- $ \frac{3}{4} = 0.75 = 75\% $
- But the table says 42.9% and 0.429 → That matches $ \frac{3}{7} \approx 0.4286 $

So the ratio must be 3:7, not 3:4.

➡️ Error: The ratio should be 3:7, not 3:4.

✔ Corrected:
- Ratio: 3:7
- Fraction: $ \frac{3}{7} $
- Percent: $ \frac{3}{7} \times 100 \approx 42.857\% \approx 42.9\% $
- Decimal: $ \approx 0.429 $

So the ratio is mislabeled as 3:4 instead of 3:7.

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#### Row 2: Ratio = 5:9
- Fraction: $ \frac{5}{9} $? But table says $ \frac{5}{14} $

Check:
- $ \frac{5}{14} \approx 0.357 \Rightarrow 35.7\% $ → matches
- But $ \frac{5}{9} \approx 0.555 \Rightarrow 55.5\% $ → does not match

So again, the fraction and ratio don't align.

Wait — the ratio is 5:9, but fraction is $ \frac{5}{14} $? That’s inconsistent.

Let’s suppose the ratio is 5:14 → then fraction = $ \frac{5}{14} \approx 0.357 \Rightarrow 35.7\% $

So likely, the ratio should be 5:14, not 5:9.

✘ So the ratio is incorrect.

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#### Row 3: Ratio = 2:6
- Fraction: $ \frac{2}{6} = \frac{1}{3} \approx 0.333 \Rightarrow 33.3\% $
- But table says: fraction = $ \frac{2}{8} = \frac{1}{4} = 0.25 = 25\% $

So inconsistency.

Wait — 2:6 simplifies to 1:3, so fraction is $ \frac{1}{3} $, but table says $ \frac{2}{8} $

And $ \frac{2}{8} = \frac{1}{4} = 0.25 = 25\% $ → matches the percent and decimal

So the ratio should be 2:8, not 2:6

✔ Therefore, ratio is wrong — should be 2:8

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#### Row 4: Ratio = 1:2
- Fraction: $ \frac{1}{2} = 0.5 = 50\% $
- But table says $ \frac{1}{3} \approx 0.333 = 33.3\% $

✘ Inconsistent

Wait — the fraction is $ \frac{1}{3} $, so ratio should be 1:3, not 1:2

So again, ratio is incorrect

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#### Row 5: Ratio = 4:6
- Simplify: $ \frac{4}{6} = \frac{2}{3} \approx 0.666... \Rightarrow 66.6\% $
- But table says: fraction = $ \frac{4}{10} = 0.4 = 40\% $

So inconsistency.

But $ \frac{4}{10} = 0.4 = 40\% $ → correct

So ratio should be 4:10, not 4:6

✔ So ratio is wrong — should be 4:10

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#### Row 6: Ratio = 2:2
- $ \frac{2}{2} = 1 = 100\% $
- But table says: fraction = $ \frac{2}{4} = 0.5 = 50\% $

So again, inconsistent

$ \frac{2}{4} = 0.5 = 50\% $ → correct
So ratio should be 2:4, not 2:2

✔ So ratio is wrong — should be 2:4

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✔ Summary of Errors

| Given Ratio | Should Be | Reason |
|------------|----------|--------|
| 3:4 | 3:7 | Because $ \frac{3}{7} \approx 0.429 $ |
| 5:9 | 5:14 | Because $ \frac{5}{14} \approx 0.357 $ |
| 2:6 | 2:8 | Because $ \frac{2}{8} = 0.25 $ |
| 1:2 | 1:3 | Because $ \frac{1}{3} \approx 0.333 $ |
| 4:6 | 4:10 | Because $ \frac{4}{10} = 0.4 $ |
| 2:2 | 2:4 | Because $ \frac{2}{4} = 0.5 $ |

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🔍 How to Convert Between Forms

Let’s use the correct version of one example:

#### Example: Ratio = 2:8
- Fraction: $ \frac{2}{8} = \frac{1}{4} $
- Decimal: $ \frac{1}{4} = 0.25 $
- Percent: $ 0.25 × 100 = 25\% $

So:
| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| 2:8 | 1/4 | 25% | 0.25 |

Same logic applies to others.

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✔ Final Answer:

#### Part 1: Percent Calculations
All answers are correct.

#### Part 2: Conversions
There are errors in the ratios listed. The ratios do not match the fractions, percents, or decimals.

Here are the corrected tables:

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✔ Corrected Conversion Tables

| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| 3:7 | 3/7 | 42.9% | 0.429 |

| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| 5:14 | 5/14 | 35.7% | 0.357 |

| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| 2:8 | 2/8 | 25% | 0.25 |

| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| 1:3 | 1/3 | 33.3% | 0.333 |

| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| 4:10 | 4/10 | 40% | 0.4 |

| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| 2:4 | 2/4 | 50% | 0.5 |

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📝 Conclusion

- Part 1 (Percent of Value): ✔ All answers are correct.
- Part 2 (Conversions): ✘ The ratios are incorrect; they should be adjusted to match the fraction, percent, and decimal values.

👉 Tip: When converting:
- Ratio → Fraction: Use the first number over the sum (e.g., 2:8 → 2/(2+8)? No! Wait — actually, ratio 2:8 means 2 parts out of 8 parts → fraction = $ \frac{2}{8} $)
- So ratio a:b → fraction = a/b (only if b is total parts)
- But often, ratio a:b means a parts to b parts → total = a+b → fraction = $ \frac{a}{a+b} $
- But in this case, the table uses $ \frac{a}{b} $, not $ \frac{a}{a+b} $

For example: ratio 2:8 → $ \frac{2}{8} $, not $ \frac{2}{10} $

So the interpretation here is: ratio a:b → fraction = a/b

Therefore, the ratios in the table should be written as a:b where b is the denominator.

So all the ratios are wrong because they don’t reflect the actual fraction.

✔ Correct approach:
- If fraction is $ \frac{2}{8} $, ratio is 2:8
- If fraction is $ \frac{1}{3} $, ratio is 1:3
- etc.

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✔ Final Verdict:

- Percent calculations: All correct.
- Conversion tables: Ratios are incorrectly labeled. They should be corrected to match the fraction column.

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