How to Break Fractions and Mixed Numbers Apart to Add or Subtract
When you're dealing with fractions and mixed numbers, it's often useful to break them apart to simplify the process of adding or subtracting.
A Step-by-step Guide to Breaking Fractions and Mixed Numbers Apart to Add or Subtract
Here’s a step-by-step guide to breaking down fractions and mixed numbers to add or subtract:
Step 1: Convert mixed numbers to improper fractions
A mixed number is a whole number combined with a fraction. To convert it into an improper fraction:
- Multiply the whole number by the denominator of the fraction.
- Add the numerator of the fraction to that product.
- The result is your new numerator, with the denominator staying the same.
For example, let’s convert the mixed number \(2 \frac{3}{4}\) to an improper fraction:
- Multiply 2 (the whole number) by 4 (the denominator): 2 * 4 = 8
- Add 3 (the numerator): \(8 + 3 = 11\)
- So, \(2 \frac{3}{4}\) as an improper fraction is \( \frac{11}{4}\).
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Step 2: Make sure the fractions have a common denominator
If the fractions have different denominators, you’ll need to find the least common denominator (LCD). Multiply the numerator and denominator of each fraction by whatever number will make the denominator equal to the LCD.
For example, if you’re adding \( \frac{1}{2}\) and \( \frac{2}{3}\), the LCD is 6. Multiply the numerator and denominator of \( \frac{1}{2}\) by 3 to get \( \frac{3}{6}\), and multiply the numerator and denominator of \( \frac{2}{3}\) by 2 to get \( \frac{4}{6}\).
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