How to subtract fractions? Theory & Practice

To subtract fractions, similar to the process how to add fractions, follow further explained steps:

$how to subtract fractions$

Check the Denominators

Same Denominator: If the fractions have the same denominator, you can simply subtract the numerators (the top numbers) and keep the denominator the same.
Different Denominator: If the fractions have different denominators, you need to find a common denominator before you can subtract them.

Find a Common Denominator (if needed)

To find a common denominator:

Least Common Denominator (LCD): This is the smallest number that both denominators can divide into evenly. It’s the least common multiple (LCM) of the denominators.
Make Equivalent Fractions: Once you have the LCD, convert each fraction to an equivalent fraction with the LCD as the new denominator. To do this, divide the LCD by the original denominator of each fraction, and multiply both the numerator and denominator of the fraction by the resulting quotient.

$how to subtract fractions$

Subtract the Numerators

Once the fractions have the same denominator, subtract the numerator of the second fraction from the numerator of the first fraction. Place this result over the common denominator.

Simplify the Fraction (if possible)

After subtracting, if the numerator is larger than the denominator or if both are divisible by the same number, you may need to simplify the fraction.
- Reduce the Fraction: Divide both the numerator and the denominator by their greatest common divisor (GCD).
- Convert to Mixed Number (if necessary): If the numerator is larger than the denominator after subtraction, you might want to convert the improper fraction to a mixed number.

Let’s subtract

34 – 12

Different Denominators: The denominators are 4 and 2
Common Denominator: The LCD of 4 and 2 is 4
Make Equivalent Fractions: 34 is already with a denominator of 4. Convert 12 to an equivalent fraction with a denominator of 4 by multiplying both the numerator and denominator by 2, resulting in 24
Subtract the Numerators: 34 – 24
Simplify: the fraction 14 is already in its simplest form