To give fractions common denominators, the most straightforward method is to multiply each fraction's numerator and denominator by the other fraction's denominator. This results in equivalent fractions that share the same denominator.
The Method Explained
- Identify the denominators: First, determine the denominators of the fractions you're working with.
- Cross-multiply: Multiply the numerator and denominator of the first fraction by the denominator of the second fraction.
- Repeat: Multiply the numerator and denominator of the second fraction by the denominator of the first fraction.
- Result: Both fractions will now have the same denominator, making them suitable for addition or subtraction.
Example
Let's consider the example from the reference where we need to find the common denominator for 3/5 and 2/3:
| Steps | Fraction 1 | Fraction 2 |
|---|---|---|
| Original fractions | 3/5 | 2/3 |
| Multiply by the other fraction’s denominator | (3 * 3)/(5 * 3) | (2 * 5)/(3 * 5) |
| Resulting fractions with common denominators | 9/15 | 10/15 |
As you can see, by multiplying both the numerator and denominator of each fraction by the denominator of the other fraction, we achieved the common denominator of 15.
Another Example
Let’s say you need to give 1/4 and 2/5 common denominators:
- Multiply 1/4 by 5/5: (1 5) / (4 5) = 5/20
- Multiply 2/5 by 4/4: (2 4) / (5 4) = 8/20
Now both fractions are over 20, and we can easily add or subtract them.
Additional insights:
- Lowest Common Denominator (LCD): While cross-multiplication always works, it might not yield the lowest common denominator. Sometimes you can find a smaller denominator that both fractions can convert to.
- Simplification: After operations with fractions, remember to simplify the results when needed.
