Fraction, Decimal and Percentage - Equivalents - Free Printable

Let's solve each part of the worksheet step by step and explain the solutions clearly.

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1) Convert these into mixed fractions to decimal numbers.

We convert mixed fractions to decimals by:
- Converting the fractional part to a decimal.
- Adding it to the whole number.

#### a. $ 3 \frac{1}{2} $
- $ \frac{1}{2} = 0.5 $
- $ 3 + 0.5 = 3.5 $
✔ Answer: 3.5

#### b. $ 12 \frac{1}{4} $
- $ \frac{1}{4} = 0.25 $
- $ 12 + 0.25 = 12.25 $
✔ Answer: 12.25

#### c. $ 35 \frac{1}{3} $
- $ \frac{1}{3} \approx 0.333... $
- $ 35 + 0.333... = 35.333... $
✔ Answer: 35.33 (or 35.\overline{3})

#### d. $ 75 \frac{1}{5} $
- $ \frac{1}{5} = 0.2 $
- $ 75 + 0.2 = 75.2 $
✔ Answer: 75.2

#### e. $ 8 \frac{3}{4} $
- $ \frac{3}{4} = 0.75 $
- $ 8 + 0.75 = 8.75 $
✔ Answer: 8.75

#### f. $ 29 \frac{3}{10} $
- $ \frac{3}{10} = 0.3 $
- $ 29 + 0.3 = 29.3 $
✔ Answer: 29.3

#### g. $ 86 \frac{2}{5} $
- $ \frac{2}{5} = 0.4 $
- $ 86 + 0.4 = 86.4 $
✔ Answer: 86.4

#### h. $ 90 \frac{2}{3} $
- $ \frac{2}{3} \approx 0.666... $
- $ 90 + 0.666... = 90.666... $
✔ Answer: 90.67 (approximately)

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2) Convert these into decimal numbers to mixed fractions.

We convert decimals to mixed fractions by:
- Separating the whole number part from the decimal part.
- Converting the decimal part into a fraction.
- Simplifying if needed.

#### a. $ 16.75 $
- Whole number: 16
- Decimal: 0.75 = $ \frac{75}{100} = \frac{3}{4} $
- So, $ 16 \frac{3}{4} $
✔ Answer: $ 16 \frac{3}{4} $

#### b. $ 15.5 $
- Whole number: 15
- Decimal: 0.5 = $ \frac{1}{2} $
- So, $ 15 \frac{1}{2} $
✔ Answer: $ 15 \frac{1}{2} $

#### c. $ 39.33 $
- Whole number: 39
- Decimal: 0.33 ≈ $ \frac{33}{100} $ → not simplified easily, but since $ \frac{1}{3} \approx 0.333 $, we can write:
- But 0.33 is approximate. Use $ \frac{33}{100} $ unless specified otherwise.
- So, $ 39 \frac{33}{100} $
✔ Answer: $ 39 \frac{33}{100} $
*(Note: If exact, $ 39.\overline{3} = 39 \frac{1}{3} $, but here it’s given as 39.33, so use $ \frac{33}{100} $)*

#### d. $ 86.25 $
- Whole number: 86
- Decimal: 0.25 = $ \frac{1}{4} $
- So, $ 86 \frac{1}{4} $
✔ Answer: $ 86 \frac{1}{4} $

#### e. $ 5.6 $
- Whole number: 5
- Decimal: 0.6 = $ \frac{6}{10} = \frac{3}{5} $
- So, $ 5 \frac{3}{5} $
✔ Answer: $ 5 \frac{3}{5} $

#### f. $ 7.9 $
- Whole number: 7
- Decimal: 0.9 = $ \frac{9}{10} $
- So, $ 7 \frac{9}{10} $
✔ Answer: $ 7 \frac{9}{10} $

#### g. $ 12.66 $
- Whole number: 12
- Decimal: 0.66 ≈ $ \frac{66}{100} = \frac{33}{50} $
- So, $ 12 \frac{33}{50} $
✔ Answer: $ 12 \frac{33}{50} $

#### h. $ 76.4 $
- Whole number: 76
- Decimal: 0.4 = $ \frac{4}{10} = \frac{2}{5} $
- So, $ 76 \frac{2}{5} $
✔ Answer: $ 76 \frac{2}{5} $

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3) Find the percentage.

To find a percentage of a number:
- Use the formula: $ \text{Percentage} \times \text{Number} \div 100 $

#### a. 50% of 40
- $ \frac{50}{100} \times 40 = 0.5 \times 40 = 20 $
✔ Answer: 20

#### b. 25% of 36
- $ \frac{25}{100} \times 36 = 0.25 \times 36 = 9 $
✔ Answer: 9

#### c. 10% of 78
- $ \frac{10}{100} \times 78 = 0.1 \times 78 = 7.8 $
✔ Answer: 7.8

#### d. 33% of 90
- $ \frac{33}{100} \times 90 = 0.33 \times 90 = 29.7 $
✔ Answer: 29.7

#### e. 66% of 90
- $ \frac{66}{100} \times 90 = 0.66 \times 90 = 59.4 $
✔ Answer: 59.4

#### f. 20% of 54
- $ \frac{20}{100} \times 54 = 0.2 \times 54 = 10.8 $
✔ Answer: 10.8

#### g. 40% of 88
- $ \frac{40}{100} \times 88 = 0.4 \times 88 = 35.2 $
✔ Answer: 35.2

#### h. 75% of 120
- $ \frac{75}{100} \times 120 = 0.75 \times 120 = 90 $
✔ Answer: 90

#### i. 30% of 130
- $ \frac{30}{100} \times 130 = 0.3 \times 130 = 39 $
✔ Answer: 39

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✔ Final Answers:

#### 1) Mixed Fractions to Decimals
a. 3.5
b. 12.25
c. 35.33 (or 35.3̄)
d. 75.2
e. 8.75
f. 29.3
g. 86.4
h. 90.67 (approx.)

#### 2) Decimals to Mixed Fractions
a. $ 16 \frac{3}{4} $
b. $ 15 \frac{1}{2} $
c. $ 39 \frac{33}{100} $
d. $ 86 \frac{1}{4} $
e. $ 5 \frac{3}{5} $
f. $ 7 \frac{9}{10} $
g. $ 12 \frac{33}{50} $
h. $ 76 \frac{2}{5} $

#### 3) Percentages
a. 20
b. 9
c. 7.8
d. 29.7
e. 59.4
f. 10.8
g. 35.2
h. 90
i. 39

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