Addition and Subtraction of Fractions

To calculate the overall value of a number, the process of addition and subtraction of fractions involves checking if the fractions have common denominators. For example, Donald drinks 1½ liters of water in the morning and 1½ liters of water in the evening. To calculate how much water Donald drinks in a day, we use addition and subtraction of fractions.

In a fraction, the top number indicates how many parts are under consideration. The bottom number shows how many equal pieces the whole is divided into. For example, in the fraction 1/2, the numerator shows one part, while the denominator represents that the whole is divided into two equal parts.

The process of adding and subtracting fractions involves joining and removing parts of a whole, as defined by fractions. To perform these operations effectively, some rules should be followed.

Rules for Adding Fractions 

Confirm the denominators are equal: Check the bottom numbers in two fractions are the same. For example, 5⁄10 + 4⁄10 = 9⁄10. Here, the denominators are the same, 10. So, the calculation will be like this:
 5⁄10 + 4⁄10 = 5 + 4/10 =  9⁄10.

If denominators are different, find the common denominator: In the given fractions, if the denominators are not the same, then identify the least common denominator. To find the least common denominator, we have to list the multiples of the given denominators. For instance, 1⁄4 + 1⁄6. Here, both the denominators are different. So we have to list the multiples of 4 and 6. 

The multiples of 4 include 4, 8, 12, 16, 20, 24, …

The multiples of 6 include 6, 12, 18, 24, 30, …

Among the lists of multiples, 12 is the least common multiple. So 12 is the denominator. Now, we need to match the LCD with the fractions. 

1⁄4 = 1×3/4×3 = 3⁄12

1⁄6 = 1×2/6×2 = 2⁄12. Now we can add both fractions easily.
 
 3⁄12 + 2⁄12 = 5⁄12.

Combine mixed numbers: Convert mixed numbers into improper fractions. After that follow the addition method. For instance,
 
1 1⁄3 +2 2⁄3 

It becomes 4⁄3 + 8⁄3 = 12⁄3 = 4

Rules for Subtracting 

Subtract the numerators: If the given fractions have the same denominators, then subtract the numerators. For instance, the given fractions are 8⁄3 and 4⁄3.
8⁄3 - 4⁄3 = 4⁄3

Use the biggest numerators to subtract fractions: We get a negative result when the numerator is larger than the other fraction. For example,

4⁄3 - 8⁄3 = -4⁄3 

Here, 8⁄3 is the larger fraction.

Subtract the mixed numbers in a fraction: Change the mixed numbers into improper fractions and then follow the remaining steps. 

First, multiply the whole number with the denominator. Then add the numerator we will get the improper fraction. 
For instance, 

3 1⁄2 - 1 2⁄3 

(3 × 2) + 1 = 7/2 and 

(1 × 3) + 2 = 5/3

Subtract these two fractions:

7/2 - 5/3 

Next, we have to find the least common denominator of 2 and 3. The result is 6. Now we have to match the LCD (least common denominator) with the fractions. It becomes:

21⁄6 - 10⁄6 = 11⁄6 = 1 5⁄6 .

Addition of Fractions 

The addition of fractions is a simple operation in mathematics. It teaches us to sum the fractions that have the same or different denominators. If the denominators are same, we only need to add the numerators. If the denominators are different, we have to find the least common denominator. 

Take a look at this:

We can add 1⁄4 and 2⁄4:

1⁄4 + 2⁄4 = 3⁄4

Here, the denominators are the same. Next, we can move on to the next set of fractions.

 3⁄4 + 4⁄4 = 7⁄4.

This sequence illustrates how fractions with the same denominator increase progressively, starting from 1⁄4, 2⁄4, 3⁄4, 4⁄4, and so on. 

Subtraction of Fractions 

Subtraction of fractions involves the subtraction of two fractional values. With this, we can find the difference between two fractions. The common denominators will remain unchanged and the numerators will be subtracted. 

For example, 

5⁄8 - 3⁄8 = 2⁄8

We can simplify 2⁄8 as 1⁄4. Take a look at this too:

 3⁄4 - 2⁄4 = 1⁄4 or 

3⁄4 - 1⁄4 = 2⁄4

2/4 = 1/2 

Performing addition and subtraction of fractions is sometimes tricky. Here are some of the tips and tricks to calculate the fractions using addition or subtraction:

Identify the least common denominator: If we get fractions that have different denominators, we have to figure out the LCD. It will help to make the process more simple and easier. LCD can be found by listing the multiples of denominators. 

Convert mixed numbers into improper fractions: It will help to reduce mistakes and the process more easier. While using improper fractions over mixed numbers, we can easily complete the task.

Simplify the fractions: If we get 4⁄8, it can be simplified into 1⁄2. It provides consistency and accuracy in calculations. Also, it avoids complications and helps to compare the values.

Be careful about the negative results: We get a negative result when the numerator is larger than the other fraction. Carefully handle the signs to avoid wrong results.

• Fraction: It is a part of a whole number. A fraction has a denominator and a numerator. For example, 5⁄6 is a fraction.

• Numerator: It is a part of a fraction. The numerator is the top number. It represents how many parts we have. For instance, 7⁄30 where 7 is the numerator and defines 7 parts is considered out of 30.

• Denominator: It refers to total parts in a whole number. In a fraction, a denominator is the bottom number. For instance, 7⁄30 where 30 is the denominator and defines the whole is counted into 30 parts. 

• Least common denominator: LCD refers to the least common denominator of a fraction. If the given fractions have different denominators we will find the LCD. After that rewrite the fractions then add or subtract them.