Multiplication of Fractions Calculator

Published on: March 10, 2024
Final Answer: Free • Full Steps: Free

This Multiplication of Fractions Calculator helps you multiply two fractions and shows the working clearly at every step. Multiplying fractions is the easiest of the four, because the bottom numbers do not have to match first. Multiply the two top numbers to get the new top number, then multiply the two bottom numbers to get the new bottom number. Then check whether the answer can be written with smaller numbers. Following the same pattern every time is what makes multiplying fractions easy to picture, check, and repeat on your own with any two fractions.

Step-by-step method

  1. Set up the problem.
  2. Multiply the top numbers, then multiply the bottom numbers.
  3. Do a simplifying of fractions at the end if you can.
See Example 1 Hide Example 1

Problem

\(\frac{3}{4} \times \frac{1}{2}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Multiply the top numbers, then multiply the bottom numbers.
  3. Do a simplifying of fractions at the end if you can.

Step 1

Step 1 - Set up the problem.

In this problem: We are multiplying \(\frac{3}{4}\) and \(\frac{1}{2}\).

\(\frac{3}{4} \times \frac{1}{2}\)

Step 2

Step 2 - Multiply the top numbers, then multiply the bottom numbers.

In this problem: Multiply the top numbers: \(3 \times 1 = 3\). Multiply the bottom numbers: \(4 \times 2 = 8\).

\(\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}\)

Step 3

Step 3 - Do a simplifying of fractions at the end if you can.

In this problem: The only number that divides both \(3\) and \(8\) is \(1\), and \(3 \div 1 = 3\), so nothing changes.

\(\frac{3}{8}\)

Final Answer

\(\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}\)
See Example 2 Hide Example 2

Problem

\(\frac{5}{10} \times \frac{2}{4}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Multiply the top numbers, then multiply the bottom numbers.
  3. Do a simplifying of fractions at the end if you can.

Step 1

Step 1 - Set up the problem.

In this problem: We are multiplying \(\frac{5}{10}\) and \(\frac{2}{4}\).

\(\frac{5}{10} \times \frac{2}{4}\)

Step 2

Step 2 - Multiply the top numbers, then multiply the bottom numbers.

In this problem: Multiply the top numbers: \(5 \times 2 = 10\). Multiply the bottom numbers: \(10 \times 4 = 40\).

\(\frac{5}{10} \times \frac{2}{4} = \frac{10}{40}\)

Step 3

Step 3 - Do a simplifying of fractions at the end if you can.

In this problem: The biggest number that divides both \(10\) and \(40\) is \(10\). Dividing each by it gives \(10 \div 10 = 1\) and \(40 \div 10 = 4\).

\(\frac{10}{40} = \frac{1}{4}\)

Final Answer

\(\frac{5}{10} \times \frac{2}{4} = \frac{1}{4}\)