Dividing Mixed Number By Fraction Calculator Math

Mixed Number Divided By Fraction Formula:

\[ (m \frac{n}{o}) \div \frac{a}{b} = \frac{(m \times o + n)}{o} \times \frac{b}{a} \]

Result:

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1. What is Mixed Number Divided By Fraction?

Dividing a mixed number by a fraction is a common arithmetic operation that combines concepts of mixed numbers, improper fractions, and fraction division. The process involves converting the mixed number to an improper fraction, then multiplying by the reciprocal of the divisor fraction.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ (m \frac{n}{o}) \div \frac{a}{b} = \frac{(m \times o + n)}{o} \times \frac{b}{a} \]

Where:

\( m \) — Whole number part of mixed number
\( n \) — Numerator of mixed number fraction part
\( o \) — Denominator of mixed number fraction part
\( a \) — Numerator of divisor fraction
\( b \) — Denominator of divisor fraction

Explanation: The mixed number is first converted to an improper fraction, then we multiply by the reciprocal of the divisor fraction.

3. Importance of This Calculation

Details: This calculation is fundamental in various mathematical applications including algebra, physics, and engineering problems where mixed quantities need to be divided by fractions.

4. Using the Calculator

Tips: Enter the whole number, numerator and denominator of the mixed number, then enter the numerator and denominator of the fraction you're dividing by. All denominators must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What if my mixed number is negative?
A: The calculator handles positive numbers only. For negative numbers, apply the negative sign to the whole number part.

Q2: Can I divide a fraction by a mixed number?
A: Yes, but you would need to convert the mixed number to a fraction first, then multiply by its reciprocal.

Q3: What if the result is an improper fraction?
A: The calculator shows both decimal and simplified fraction forms. You can convert improper fractions to mixed numbers if needed.

Q4: Why do we multiply by the reciprocal?
A: Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal (flipped numerator and denominator).

Q5: What if denominators are zero?
A: The calculator prevents division by zero by requiring denominators to be positive integers.