Fraction Multiplication Calculator
Enter the numerators and denominators for two fractions below to multiply them and find their product.
Result:
"; outputHTML += "" + num1 + "/" + den1 + " × " + num2 + "/" + den2 + " = " + productNum + "/" + productDen + ""; if (simplifiedDen === 1) { outputHTML += "Simplified: " + simplifiedNum + ""; } else if (commonDivisor > 1) { outputHTML += "Simplified: " + simplifiedNum + "/" + simplifiedDen + ""; } else { outputHTML += "The fraction " + productNum + "/" + productDen + " is already in its simplest form."; } resultDiv.innerHTML = outputHTML; }Understanding Fraction Multiplication
Multiplying fractions is a fundamental operation in mathematics that allows you to find a part of a part. Unlike adding or subtracting fractions, you don't need a common denominator to multiply them. This calculator simplifies the process, providing you with the product in both unsimplified and simplified forms.
How to Multiply Fractions
The rule for multiplying fractions is straightforward:
- Multiply the numerators (the top numbers) together.
- Multiply the denominators (the bottom numbers) together.
The formula can be expressed as:
(a/b) × (c/d) = (a × c) / (b × d)
Where a and c are the numerators, and b and d are the denominators.
Simplifying the Resulting Fraction
After multiplying, the resulting fraction might not be in its simplest form. Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1. This makes the fraction easier to understand and work with.
To simplify a fraction:
- Find the Greatest Common Divisor (GCD) of the new numerator and the new denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
- Divide both the numerator and the denominator by their GCD.
For example, if you multiply 2/3 × 3/4, you get 6/12. The GCD of 6 and 12 is 6. Dividing both by 6 gives you 1/2, which is the simplified form.
Examples of Fraction Multiplication
Let's look at a few examples to illustrate the process:
Example 1: Simple Multiplication
Multiply 1/2 × 1/3
- Numerators:
1 × 1 = 1 - Denominators:
2 × 3 = 6 - Result:
1/6(already simplified)
Example 2: Multiplication Requiring Simplification
Multiply 2/5 × 10/12
- Numerators:
2 × 10 = 20 - Denominators:
5 × 12 = 60 - Result:
20/60 - Simplification: The GCD of 20 and 60 is 20. Dividing both by 20 gives
1/3.
Example 3: Resulting in a Whole Number
Multiply 3/4 × 8/6
- Numerators:
3 × 8 = 24 - Denominators:
4 × 6 = 24 - Result:
24/24 - Simplification: The GCD of 24 and 24 is 24. Dividing both by 24 gives
1/1, which simplifies to1.
Using the Calculator
Our Fraction Multiplication Calculator makes this process effortless:
- Enter the numerator of your first fraction in the "First Fraction Numerator" field.
- Enter the denominator of your first fraction in the "First Fraction Denominator" field.
- Enter the numerator of your second fraction in the "Second Fraction Numerator" field.
- Enter the denominator of your second fraction in the "Second Fraction Denominator" field.
- Click the "Calculate Product" button.
The calculator will instantly display the unsimplified product and its simplified form, making it a valuable tool for students, teachers, and anyone needing to quickly multiply fractions.