Question
Can you add or subtract fractions with unlike denominators without changing them
Answers
Answered by
GPT-4o mini
To add or subtract fractions with unlike denominators, you cannot directly perform the operation without changing the fractions. However, you can find a common denominator to make the addition or subtraction possible.
Here's how you can do it:
1. **Find the least common denominator (LCD)** of the fractions. This is the smallest number that both denominators can evenly divide into.
2. **Convert each fraction** to an equivalent fraction with the common denominator by multiplying the numerator and denominator by the appropriate value.
3. **Perform the addition or subtraction** with the new fractions that now have like denominators.
4. **Simplify** the result if necessary.
**Example:**
Let's say we want to add \( \frac{2}{3} + \frac{1}{4} \).
1. The denominators are 3 and 4. The least common denominator (LCD) is 12.
2. Convert each fraction:
- \( \frac{2}{3} \) can be converted to \( \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \)
- \( \frac{1}{4} \) can be converted to \( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
3. Now add them:
\[ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \]
So, while you can't add or subtract fractions with unlike denominators without changing them, you can convert them to like fractions and then perform the operation.
Here's how you can do it:
1. **Find the least common denominator (LCD)** of the fractions. This is the smallest number that both denominators can evenly divide into.
2. **Convert each fraction** to an equivalent fraction with the common denominator by multiplying the numerator and denominator by the appropriate value.
3. **Perform the addition or subtraction** with the new fractions that now have like denominators.
4. **Simplify** the result if necessary.
**Example:**
Let's say we want to add \( \frac{2}{3} + \frac{1}{4} \).
1. The denominators are 3 and 4. The least common denominator (LCD) is 12.
2. Convert each fraction:
- \( \frac{2}{3} \) can be converted to \( \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \)
- \( \frac{1}{4} \) can be converted to \( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
3. Now add them:
\[ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \]
So, while you can't add or subtract fractions with unlike denominators without changing them, you can convert them to like fractions and then perform the operation.