Multiplying Fractions

Front

What is the product of two fractions?

Back

To find the product of 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

How do you decompose a fraction?

Back

To decompose a fraction, you can express it as a sum of two or more fractions with the same denominator. For example, \( \frac{4}{3} = \frac{2}{3} + \frac{2}{3} \).

Front

What is a unit fraction?

Back

A unit fraction is a fraction where the numerator is 1 and the denominator is a positive integer. For example, \( \frac{1}{3} \) is a unit fraction.

Front

How can you express a fraction as a multiple of a unit fraction?

Back

To express a fraction as a multiple of a unit fraction, divide the numerator by the denominator and multiply the unit fraction by that whole number. For example, \( \frac{8}{3} = 8 \times \frac{1}{3} \).

Front

What is the relationship between whole numbers and fractions in multiplication?

Back

When multiplying a whole number by a fraction, you can think of the whole number as being multiplied by the numerator of the fraction. For example, \( 9 \times \frac{1}{6} = \frac{9}{6} \).

Front

What is the product of a whole number and a fraction?

Back

The product of a whole number and a fraction is found by multiplying the whole number by the numerator of the fraction and keeping the same denominator. For example, \( 2 \times \frac{5}{7} = \frac{10}{7} \).

Front

How do you simplify a fraction?

Back

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD). For example, \( \frac{14}{6} \) can be simplified to \( \frac{7}{3} \).

Front

What is the importance of finding a common denominator when adding fractions?

Back

Finding a common denominator is important when adding fractions because it allows you to combine the fractions into a single fraction. Without a common denominator, you cannot directly add the fractions.

Front

What does it mean to multiply fractions?

Back

Multiplying fractions means finding the product of two or more fractions, which involves multiplying their numerators and denominators.

Front

Can you multiply a fraction by a whole number?

Back

Yes, you can multiply a fraction by a whole number by treating the whole number as a fraction with a denominator of 1. For example, \( 3 \times \frac{2}{5} = \frac{3 \times 2}{1 \times 5} = \frac{6}{5} \).