Multiplying 3 Fractions Calculator

Historical Background

Multiplying fractions has been a fundamental part of mathematics since the earliest recorded histories. Ancient mathematicians, like those from Babylon and Egypt, used fractions to solve problems related to trade, agriculture, and astronomy. The process of multiplying fractions, just like whole numbers, involves multiplying the numerators to get a new numerator and the denominators to get a new denominator.

Calculation Formula

The formula for multiplying three fractions is:

\[ \frac{X}{Y} \times \frac{W}{Z} \times \frac{A}{B} = \frac{X \times W \times A}{Y \times Z \times B} \]

To simplify the result, both the numerator and denominator are divided by their greatest common denominator (GCD):

\[ \text{Simplified Result} = \frac{(X \times W \times A) / \text{GCD}}{(Y \times Z \times B) / \text{GCD}} \]

Example Calculation

If the three fractions are \( \frac{2}{3} \), \( \frac{4}{5} \), and \( \frac{3}{7} \):

1. Multiply the numerators: \( 2 \times 4 \times 3 = 24 \).
2. Multiply the denominators: \( 3 \times 5 \times 7 = 105 \).
3. Find the GCD of 24 and 105, which is 3.
4. Divide both by their GCD:

\[ \text{Numerator} = \frac{24}{3} = 8 \] \[ \text{Denominator} = \frac{105}{3} = 35 \]

The simplified result is \( \frac{8}{35} \).

Importance and Usage Scenarios

Multiplying fractions is essential in various fields, including engineering, physics, finance, and everyday life. It's often used in scaling recipes, adjusting proportions, calculating probabilities, and working with ratios in scientific research.

Common FAQs

1. Can I multiply fractions with different denominators?

   • Yes, you multiply the numerators together and the denominators together directly, regardless of their values.

2. How do I simplify the resulting fraction?

   • Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that GCD.

3. What if one of the denominators is zero?

   • A denominator of zero makes the fraction undefined, so the multiplication would be invalid.

This calculator provides an easy way to multiply three fractions and get the simplified result quickly, aiding in mathematical computations and problem-solving tasks.