Dividing Fractions

A fraction represents a part of a whole and is expressed as a ratio of two integers, where the top number is the numerator and the bottom number is the denominator.

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For example, $$\frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$$ .

The reciprocal of a fraction $$\frac{a}{b}$$ is $$\frac{b}{a}$$ , obtained by swapping the numerator and denominator.

13 pieces can be cut, calculated as $$9 \text{ ft} \times \frac{3}{2} = 13$$ .

The quotient is 25, calculated as $$5 \times 5 = 25$$ .

Finding the quotient means determining how many times one number is contained within another, typically through division.

To convert a mixed number like $$2 \frac{1}{2}$$ to an improper fraction, multiply the whole number by the denominator and add the numerator: $$2 \times 2 + 1 = 5$$ , so it becomes $$\frac{5}{2}$$ .

Understanding division of fractions is crucial for solving real-world problems involving parts of a whole, such as recipes, measurements, and sharing.

Kamari spent 1/12 of an hour on each problem, calculated as $$\frac{1/3}{4} = \frac{1}{12}$$ .

A common mistake is to divide the numerators and denominators directly instead of multiplying by the reciprocal.