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, \( \frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d} \).

Front

How do you simplify a fraction?

Back

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

Front

What is an improper fraction?

Back

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as \( \frac{5}{4} \) or \( \frac{7}{7} \).

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, add the numerator, and place that result over the original denominator. For example, \( 6 \frac{1}{5} = \frac{6 \cdot 5 + 1}{5} = \frac{31}{5} \).

Front

What is the simplest form of a fraction?

Back

The simplest form of a fraction is when the numerator and denominator have no common factors other than 1. For example, \( \frac{4}{8} \) simplifies to \( \frac{1}{2} \).

Front

What is the first step in multiplying fractions?

Back

The first step in multiplying fractions is to multiply the numerators together.

Front

What is the second step in multiplying fractions?

Back

The second step in multiplying fractions is to multiply the denominators together.

Front

How do you find the product of \( \frac{3}{4} \) and \( \frac{13}{3} \)?

Back

To find the product, multiply the numerators: \( 3 \cdot 13 = 39 \) and the denominators: \( 4 \cdot 3 = 12 \). Thus, \( \frac{3}{4} \cdot \frac{13}{3} = \frac{39}{12} \), which simplifies to \( \frac{13}{4} \).

Front

What is the importance of simplifying fractions?

Back

Simplifying fractions makes them easier to understand and work with, especially in further calculations.

Front

What does it mean to multiply fractions in simplest form?

Back

Multiplying fractions in simplest form means that the final answer is expressed with the smallest possible numerator and denominator.