A fraction is referred to as a part of a whole. Subtraction on the other hand refers to the operation of removing a number from a group. Fractions can be subtracted in three simple steps. The first method applies only when the denominators of the fractions to be involved in subtraction are the same. It goes like:
- Make sure that the denominators (the bottom numbers) are the same.
- Subtract the numerators (top numbers). Put the answer that you get over the same denominator.
- Lastly, simplify the fraction if need be.
Example: 3/4 - 1/4 =?
Solution:
- The denominators for the both the fractions are the same, 2. Proceed straight to the second step.
- Subtract the numerators and put the result over the same denominator. In the fractions ¾ and ¼, the numerators are 3 and 1. The subtraction will be 3 – 1 as explained above in step 2. The result is 2. When placed above the same denominator it becomes 2/4.
- Simplify the fraction. The answer 2/4 is not completely simplified. You do this by dividing both the numerator and the denominator by a common number. In this case the common number is 2. The simplification results into the final answer which is ½.
In some cases, the denominators may be different. For example, you can be told to work out \(\frac{1}{2} - \frac{1}{6}\). The denominators, 2 and 6 are not the same. In this case, you:
- For purposes of making the bottom number the same, find the least common divisor of the denominators. The LCM of 2 and 6 is 6. Divide the LCM by each denominator and multiply the answer with that fraction. For example, in ½, 6 ÷ 2= 3. Therefore, ½ x 3 = 3/6. For the second fraction 1/6, 6 ÷ 6 = 1. Therefore 1/6 × 1 = 1/6. We now have similar denominators and can therefore proceed to step 2.
- 3/6 – 1/6. Subtract the numerators. 3 – 1 = 2. Place the answer above the denominator. 2/6.
- Lastly, simplify. Simplifying 2/6 will give us 1/3 as the final answer.
SUBTRACTING MIXED FRACTIONS.
A mixed fraction refers to a fraction having a whole number and a fraction. Example: 1½. For easier subtraction, start by converting these mixed fractions into improper fractions. An improper fraction is that which has the numerator being larger than the denominator. For example, 20/3.
Example: solve the following, \(2 \frac{1}{3}\) – \(1 \frac{1}{2}\)=?
- Convert the fractions into improper fractions. \(2 \frac{1}{3}\) becomes 7/3 and 1½ becomes 3/2. The least common divisor of the two denominators 3 and 2 is 6. Divide 6 by both the denominators and multiply the answer with the fraction. In the fraction 7/3, 6 ÷ 3 = 2 then 2 × 7/3 = 14/6. In the fraction 3/2, 6 ÷ 2 = 3 then 3/2 × 3 = 9/6.
- Subtract the numerators then place the answer above the denominator. 14 – 9 = 5 therefore, the answer becomes 5/6.
