Dividing Fractions

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as $$\frac{5}{4}$$ .

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place that result over the original denominator. For example, $$5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4}$$ .

The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 5 is $$\frac{1}{5}$$ .

To find the reciprocal of a mixed number, first convert it to an improper fraction, then flip the fraction. For example, the reciprocal of $$2 \frac{1}{4}$$ is $$\frac{4}{9}$$ .

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

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. For example, $$\frac{6}{10}$$ can be simplified to $$\frac{3}{5}$$ .

To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify $$\frac{12}{20}$$ , divide both by 4 to get $$\frac{3}{5}$$ .

A common denominator is a shared multiple of the denominators of two or more fractions. It is used to add or subtract fractions.

To find a common denominator, identify the least common multiple (LCM) of the denominators. For example, for $$\frac{1}{4}$$ and $$\frac{1}{16}$$ , the LCM is 16.

The quotient of two fractions is the result of dividing one fraction by another. For example, $$\frac{3}{4} \text{ divided by } \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4} = \frac{3}{2}$$ .