How To Divide Fractions In Decimal

Fraction Division Formula:

\[ \frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c} \]

Fraction Result:

Decimal Result:

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1. How To Divide Fractions

Dividing fractions involves multiplying by the reciprocal of the second fraction. The formula is:

\[ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c} \]

2. Converting To Decimal

After obtaining the resulting fraction, divide the numerator by the denominator to get the decimal equivalent:

\[ \text{Decimal} = \frac{\text{Numerator}}{\text{Denominator}} \]

3. Step-by-Step Example

Example: Calculate (3/4) ÷ (2/5)

Take the reciprocal of the second fraction: 5/2
Multiply the first fraction by this reciprocal: (3/4) × (5/2)
Multiply numerators: 3 × 5 = 15
Multiply denominators: 4 × 2 = 8
Resulting fraction: 15/8
Convert to decimal: 15 ÷ 8 = 1.875

4. Practical Applications

Real-world uses: This calculation is essential in cooking (adjusting recipes), construction (scaling measurements), and science (diluting solutions).

5. Frequently Asked Questions (FAQ)

Q1: Why do we flip the second fraction?
A: Dividing by a fraction is equivalent to multiplying by its reciprocal, which makes the calculation simpler.

Q2: What if denominators are zero?
A: Division by zero is undefined. The calculator prevents this by requiring denominators > 0.

Q3: How to handle mixed numbers?
A: Convert them to improper fractions first (e.g., 2½ becomes 5/2).

Q4: Why convert to decimal?
A: Decimal form is often easier to understand and use in further calculations.

Q5: Can this calculator handle negative fractions?
A: Yes, negative values can be entered in any numerator or denominator.