Multiply/Divide Fractions & Mixed Numbers

Front

What is a fraction?

Back

A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number).

Front

How do you multiply two fractions?

Back

To multiply two fractions, multiply the numerators together and the denominators together. For example, \( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \).

Front

What is the reciprocal of a fraction?

Back

The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, the reciprocal of \( \frac{a}{b} \) is \( \frac{b}{a} \).

Front

How do you divide fractions?

Back

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

Front

What is a mixed number?

Back

A mixed number is a whole number combined with a proper fraction, such as \( 2 \frac{1}{3} \).

Front

How do you convert a mixed number to an improper fraction?

Back

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Place this result over the original denominator. For example, \( 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3} \).

Front

What is the process for adding fractions with different denominators?

Back

To add fractions with different denominators, find a common denominator, convert each fraction, and then add the numerators. For example, \( \frac{a}{b} + \frac{c}{d} = \frac{a \times d + c \times b}{b \times d} \).

Front

What is the least common multiple (LCM)?

Back

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers.

Front

How do you simplify a fraction?

Back

To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).

Front

What is the greatest common divisor (GCD)?

Back

The greatest common divisor (GCD) of two or more numbers is the largest number that divides each of the numbers without leaving a remainder.