Subtracting Fractions: Common Denominator Method

Subtracting Fractions

Common Denominator Method

Subtracting fractions involves two main steps: identifying the type of fractions and performing the subtraction. When dealing with like fractions, the common denominator method is used, which involves subtracting the numerators and writing the difference over the common denominator. For example, if we have the fractions 5/7 and 3/7, we can subtract them as follows: 5/7 - 3/7 = 2/7. This is because the numerators are subtracted (5 - 3 = 2), and the result is written over the common denominator (7).

Simplifying the Result

In some cases, the result of subtracting fractions may be simplified by finding the greatest common factor (GCF) of the numerator and denominator. If the GCF is a factor of both, it can be divided by both to simplify the fraction. For example, if we have the fraction 12/18, we can simplify it by dividing both the numerator and denominator by 6, resulting in the simplified fraction 2/3.

Word Problems Involving Subtracting Fractions

Word problems often involve subtracting fractions in real-life scenarios. For instance, if you are running a certain distance and have already covered a portion of it, you can subtract the covered distance from the total distance to determine the remaining distance. Similarly, in cooking, you might need to subtract the amount of a particular ingredient you've already added to determine how much more you need to add.

Finding the Least Common Denominator (LCD)

When dealing with unlike fractions, the LCD method is used. The LCD is the smallest number that can be divided evenly by both denominators. For example, if we have the fractions 2/5 and 3/4, the LCD is 12, as it can be divided by both 5 and 4. To subtract unlike fractions, we convert them to equivalent fractions with the LCD as the denominator, then subtract the numerators. For example, to subtract 2/5 from 3/4, we would convert them to equivalent fractions with a denominator of 12 (2/5 becomes 12/24, and 3/4 becomes 12/12). The subtraction would then be 12/24 - 12/24 = 0/24, which simplifies to 0.