Start by multiplying the numerators together and then the denominators. For example, to multiply 2/3 by 4/5, you multiply 2 × 4 to get 8, and 3 × 5 to get 15. The result is 8/15.
Always simplify the result if possible. For example, 6/9 can be simplified by dividing both the numerator and the denominator by 3, giving you 2/3.
Check for mistakes by reviewing each step. Confirm that you correctly multiplied the top and bottom numbers and simplified the final answer. Practicing with multiple problems helps to build accuracy.
Practice with Fraction Multiplication Problems
Begin by identifying the numerators and denominators. For example, in the problem 3/7 × 2/5, multiply 3 × 2 to get 6, and 7 × 5 to get 35. The result is 6/35.
Simplify the answer when possible. In the case of 4/8 × 2/3, first multiply the numerators (4 × 2 = 8) and the denominators (8 × 3 = 24). The result, 8/24, simplifies to 1/3 when both the numerator and denominator are divided by 8.
Practice a variety of problems with different numbers to build confidence. Start with smaller values and gradually move to more complex problems as you become more comfortable with the steps.
How to Multiply Fractions Step by Step
First, identify the numerators (top numbers) and denominators (bottom numbers) of the two values. Multiply the numerators together and then the denominators.
For example, consider 3/4 and 2/5. Multiply the numerators: 3 × 2 = 6. Then, multiply the denominators: 4 × 5 = 20. The result is 6/20.
Simplify the result if possible. In this case, both the numerator and denominator can be divided by 2. 6 ÷ 2 = 3 and 20 ÷ 2 = 10, so the final answer is 3/10.
| Example | Numerators | Denominators | Product | Simplified |
|---|---|---|---|---|
| 3/4 × 2/5 | 3 × 2 = 6 | 4 × 5 = 20 | 6/20 | 3/10 |
Common Mistakes to Avoid When Multiplying Fractions
One common mistake is forgetting to multiply both the top and bottom numbers. For instance, in 3/8 × 2/5, it’s easy to only multiply the numerators (3 × 2 = 6) and ignore the denominators. The correct process involves also multiplying the denominators: 8 × 5 = 40, giving 6/40 as the result.
Another error is not simplifying the answer. After getting the result, like 6/40, always check for common factors. Here, both numbers can be divided by 2, leading to 3/20.
Some people also incorrectly add or subtract the numerators and denominators instead of multiplying them. This can cause significant mistakes. Always stick to multiplication for both the top and bottom values.
Practice Problems for Multiplying Fractions
1. 2/3 × 3/4 = ?
Solution: Multiply the numerators (2 × 3 = 6) and the denominators (3 × 4 = 12). The result is 6/12, which simplifies to 1/2.
2. 5/8 × 4/7 = ?
Solution: Multiply the numerators (5 × 4 = 20) and the denominators (8 × 7 = 56). The result is 20/56, which simplifies to 5/14.
3. 7/9 × 2/3 = ?
Solution: Multiply the numerators (7 × 2 = 14) and the denominators (9 × 3 = 27). The result is 14/27, which cannot be simplified further.
4. 1/2 × 5/6 = ?
Solution: Multiply the numerators (1 × 5 = 5) and the denominators (2 × 6 = 12). The result is 5/12.
How to Simplify Fraction Products After Multiplication
After obtaining the product, check if the numerator and denominator share common factors. If they do, simplify the result by dividing both the numerator and denominator by their greatest common divisor (GCD).
For example, consider 6/15 × 4/10. Multiply the numerators: 6 × 4 = 24, and the denominators: 15 × 10 = 150. The result is 24/150. Now, simplify:
- Find the GCD of 24 and 150, which is 6.
- Divide both the numerator and denominator by 6: 24 ÷ 6 = 4, 150 ÷ 6 = 25.
- The simplified result is 4/25.
Here are a few more steps to keep in mind:
- Always look for the largest common factor between the numerator and denominator.
- If the numbers are prime or cannot be simplified further, leave the product as is.
- If both the numerator and denominator are divisible by the same number, reduce the fraction by that factor.