Question
what must you do when adding and subtracting fractions
Answers
GPT-4o mini
When adding or subtracting fractions, follow these steps:
1. **Find a Common Denominator**:
- If the fractions have the same denominator, you can proceed to the next step.
- If they have different denominators, find the least common denominator (LCD). This is the smallest multiple that both denominators share.
2. **Rewrite the Fractions**:
- Convert each fraction to an equivalent fraction with the common denominator. You do this by multiplying the numerator and the denominator of each fraction by whatever value is necessary to achieve the common denominator.
3. **Add or Subtract the Numerators**:
- After ensuring both fractions have the same denominator, perform the addition or subtraction on the numerators. Keep the common denominator the same.
4. **Simplify the Result**:
- If possible, reduce the resulting fraction to its simplest form by dividing the numerator and the denominator by their greatest common factor (GCF).
5. **Convert Improper Fractions (if needed)**:
- If the final fraction is an improper fraction (where the numerator is greater than the denominator), you may want to convert it to a mixed number.
### Example:
To add \( \frac{1}{4} + \frac{1}{6} \):
1. **Find the LCD**: The least common denominator of 4 and 6 is 12.
2. **Rewrite the fractions**:
- \( \frac{1}{4} = \frac{3}{12} \) (multiply numerator and denominator by 3)
- \( \frac{1}{6} = \frac{2}{12} \) (multiply numerator and denominator by 2)
3. **Add the numerators**: \( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \)
4. **Simplify**: \( \frac{5}{12} \) is already in simplest form.
So, \( \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \).
1. **Find a Common Denominator**:
- If the fractions have the same denominator, you can proceed to the next step.
- If they have different denominators, find the least common denominator (LCD). This is the smallest multiple that both denominators share.
2. **Rewrite the Fractions**:
- Convert each fraction to an equivalent fraction with the common denominator. You do this by multiplying the numerator and the denominator of each fraction by whatever value is necessary to achieve the common denominator.
3. **Add or Subtract the Numerators**:
- After ensuring both fractions have the same denominator, perform the addition or subtraction on the numerators. Keep the common denominator the same.
4. **Simplify the Result**:
- If possible, reduce the resulting fraction to its simplest form by dividing the numerator and the denominator by their greatest common factor (GCF).
5. **Convert Improper Fractions (if needed)**:
- If the final fraction is an improper fraction (where the numerator is greater than the denominator), you may want to convert it to a mixed number.
### Example:
To add \( \frac{1}{4} + \frac{1}{6} \):
1. **Find the LCD**: The least common denominator of 4 and 6 is 12.
2. **Rewrite the fractions**:
- \( \frac{1}{4} = \frac{3}{12} \) (multiply numerator and denominator by 3)
- \( \frac{1}{6} = \frac{2}{12} \) (multiply numerator and denominator by 2)
3. **Add the numerators**: \( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \)
4. **Simplify**: \( \frac{5}{12} \) is already in simplest form.
So, \( \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \).