Multiplying and Dividing Fractions 5th grade

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction 1/2, 1 is the numerator and 2 is the denominator.

To multiply fractions, multiply the numerators together and the denominators together. For example, $$\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}$$ .

The reciprocal of a fraction is obtained by flipping the numerator and denominator. For example, the reciprocal of $$\frac{2}{3}$$ is $$\frac{3}{2}$$ .

To divide fractions, multiply by the reciprocal of the second fraction. For example, $$\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}$$ .

Simplifying a fraction means reducing it to its lowest terms. For example, $$\frac{4}{8}$$ simplifies to $$\frac{1}{2}$$ .

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

A mixed number is a whole number combined with a fraction. For example, $$2 \frac{1}{2}$$ is a mixed number.

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the numerator of the fraction. For example, $$\frac{9}{4} = 2 \frac{1}{4}$$ .

A common denominator is a shared multiple of the denominators of two or more fractions. It is used to add or subtract fractions. For example, the common denominator of $$\frac{1}{3}$$ and $$\frac{1}{4}$$ is 12.

To add fractions with different denominators, first find a common denominator, convert the fractions, and then add the numerators. For example, $$\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$$ .