Multiplying Fractions

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 multiply the denominators together. The product is then simplified if possible.

Front

What is the product of \( \frac{a}{b} \times \frac{c}{d} \)?

Back

The product is \( \frac{a \times c}{b \times d} \).

Front

What does it mean to simplify a fraction?

Back

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

Front

What is the greatest common divisor (GCD)?

Back

The GCD is the largest number that divides two or more numbers without leaving a remainder.

Front

How can you find the GCD of two numbers?

Back

You can find the GCD by listing the factors of each number and identifying the largest common factor, or by using the Euclidean algorithm.

Front

What is an improper fraction?

Back

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Front

What is a mixed number?

Back

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

Front

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

Back

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator.

Front

What is the relationship between fractions and division?

Back

Multiplying by a fraction is equivalent to dividing by its reciprocal. For example, \( \frac{a}{b} \times \frac{c}{d} \) is the same as \( a \div b \times c \div d \).