Standard Form

To calculate a number’s overall value, we add or subtract fractions by ensuring they 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 considered. 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 differ, find the least common denominator (LCD) to proceed with addition: 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 

           1 1⁄3  = 4⁄3

           2 2⁄3  = 8⁄3

           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: A negative result occurs if you subtract a larger fraction from a smaller one. 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 (the 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 the 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 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.