Multiplying fractions is straightforward: you multiply the numerators (top numbers) together and then multiply the denominators (bottom numbers) together.
Understanding the Process
When you see fractions, they represent parts of a whole. For example, 1/2 means one out of two equal parts. To multiply fractions, you're essentially finding a fraction of another fraction.
Step-by-step Guide
- Identify the Numerators and Denominators: Understand which numbers are at the top (numerators) and bottom (denominators) of each fraction.
- Multiply the Numerators: Multiply all the top numbers together. This result will be the new numerator.
- Multiply the Denominators: Multiply all the bottom numbers together. This result will be the new denominator.
- Simplify (If Needed): After multiplying, you might need to reduce the resulting fraction to its simplest form by finding common factors in the numerator and denominator.
Examples
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Example 1:
- Multiply 1/2 by 2/3:
- Multiply the numerators: 1 * 2 = 2
- Multiply the denominators: 2 * 3 = 6
- The result is 2/6. This fraction can be simplified to 1/3.
- Multiply 1/2 by 2/3:
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Example 2:
- Multiply 3/4 by 1/5:
- Multiply the numerators: 3 * 1 = 3
- Multiply the denominators: 4 * 5 = 20
- The result is 3/20. This fraction is in its simplest form.
- Multiply 3/4 by 1/5:
-
Example 3:
- Multiply 2/3 by 3/4
- Multiply the numerators: 2 * 3 = 6
- Multiply the denominators: 3 * 4 = 12
- The result is 6/12. This fraction can be simplified to 1/2.
- Multiply 2/3 by 3/4
Key Points
- No Need for Common Denominators: Unlike addition and subtraction, you do not need to find common denominators when multiplying fractions.
- Simplification: Always check if you can simplify the resulting fraction.
- Mixed Numbers: If you're multiplying mixed numbers (like 1 1/2), convert them to improper fractions (like 3/2) first.
- The reference states "When multiplying fractions, you first start with the two fractions you want to multiply. You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together". This method is what we have used.
Practical Application
Multiplying fractions is used in various real-life scenarios, such as:
- Recipes: Scaling recipes up or down.
- Construction: Calculating material quantities.
- Finance: Calculating proportions of investments.
By following these simple steps, multiplying fractions becomes a straightforward process. Remember to always simplify your final answer to get the most reduced fraction.
