To subtract fractions, follow these three main steps:
- Make the denominators the same
If the fractions have different denominators, find the lowest common denominator (LCD). Convert each fraction to an equivalent fraction with this common denominator by multiplying the numerator and denominator appropriately. This ensures the fractions represent parts of the same whole
- Subtract the numerators
Once the denominators are the same, subtract the numerator of the second fraction from the numerator of the first fraction. Keep the denominator the same. For example, 34−14=3−14=24\frac{3}{4}-\frac{1}{4}=\frac{3-1}{4}=\frac{2}{4}43−41=43−1=42
- Simplify the result if possible
Reduce the resulting fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. For example, 24\frac{2}{4}42 simplifies to 12\frac{1}{2}21
Example with unlike denominators:
Subtract 12−16\frac{1}{2}-\frac{1}{6}21−61:
- Find LCD of 2 and 6, which is 6.
- Convert 12\frac{1}{2}21 to 36\frac{3}{6}63 (multiply numerator and denominator by 3).
- Now subtract: 36−16=26\frac{3}{6}-\frac{1}{6}=\frac{2}{6}63−61=62.
- Simplify 26\frac{2}{6}62 to 13\frac{1}{3}31
Alternative formula method:
You can also use the formula:
ab−cd=ad−bcbd\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}ba−dc=bdad−bc
Multiply numerator of the first fraction by denominator of the second and vice versa, subtract, and put over the product of the denominators. Then simplify if needed
. This method works well especially when denominators are different. In summary, subtracting fractions involves equalizing denominators, subtracting numerators, and simplifying the result
