Subtraction of Fractions

A fraction represents a part of a whole or a division of a quantity. Fractions consist of two numbers: the numerator, and the denominator. The numerator, also called the top number, represents how many parts we have. The denominator is another part of the fraction, the denominator represents the total number of equal parts that make up a whole.

For example, ¾. This means 3 out of 4 equal parts of something. There are many types of fractions. The most common types are mentioned below:
 

• Proper Fractions: In proper fractions, the numerator is smaller than the denominator. The fractions are less than one. For example, ½, ¼, ¾.
   
• Mixed Fractions: Mixed fractions are a combination of a whole number and a proper fraction. A mixed fraction can be converted into an improper fraction. For example, \(3{1\over3}\), \(1{2\over3}\), \(3{3\over4}\).
   
• Like Fractions: Like fractions are the fractions with the same denominator. For example, \(3\over 4\), \(1\over 4\), \(7\over4\).
   
• Unlike Fractions: Unlike fractions are the fractions with different denominators. For example, ½, ¼, ¾.

Some key features of subtraction of fractions are as follows:
 

• Fractions can be subtracted from only when they have the same denominator. The difference between fractions is found by subtracting the numerators.
   
• When fractions have different denominators, we find the LCM or the least common denominator, then convert them to have the same denominator with the help of the LCM.
   
• Improper fractions can be subtracted as they are. To find the difference between mixed numbers, change the mixed fraction to an improper fraction and then do the subtraction.
   
• To find the difference between mixed fractions where the second fraction is less than the first fraction, subtract the integer parts and fractional parts separately.
   

To subtract fractions, and get the answer right, we have to follow the following steps mentioned below:

Step 1: First, we have to check the denominators, whether they are the like or unlike.

Step 2: If the denominators are different, then we must find the LCM (Least Common Multiple). Then convert the fractions to equivalent fractions using the LCM.

Step 3: Once the denominators are the same, we have to subtract the numerators while keeping the denominator unchanged.

Step 4: Finally, we have to simplify the final answer if the answer can be simplified.

The three types of fractions that can be subtracted are as follows:
 

• Subtracting Fractions with Unlike Denominators
   
• Subtracting Fractions With Whole Numbers

As we have discussed in the above steps, if we follow the above steps, we can subtract fractions with unlike denominators. For example, subtract 3/4 - 1/6.

Step 1: Identify the denominators: 
The denominators are unlike or not the same.

Step 2: Find the LCM:
The LCM of 4 and 6 is 12.

Convert the Fractions:

3/4 = (3 × 3) / (4 × 3) = 9/12

1/6 = (1 × 2) / (6 × 2) = 2/12

Subtract the numerators:

9/12 - 2/12 = 7/12

We can easily subtract a fraction with whole numbers. It is like subtracting fractions. Let us consider an example to understand it better.

Subtract 7 from 19/2

Step 1: As 7 is a whole number, we have to convert 7 into a fraction. To do that, we have to keep 1 as the denominator of 7. So 7 becomes 7/1.

Step 2: Now subtracting fractions as usual:

⇒ \({19 \over 2} - {7 \over 1}\)

= \({19 \over 2} - {7 \times 2 \over 1\times 2}\)

= \({19 \over 2} - {14 \over 2}\)

= \({19-14 \over 2} \)

= \(5\over2\).

The subtraction of fractions has numerous applications across various fields. Let us explore how the subtraction of fractions is used in different areas:
 

• Cooking and Baking: We use subtraction of fractions in cooking and baking, where recipes often require subtracting fractional amounts of ingredients. For example, if a recipe calls for ¾ cup of sugar, but you have already added ½ cup, you will need to subtract ½ from ¾ to determine how much more to add.
   
• Finance:  People use fraction subtraction when dealing with money, discounts, and budgeting. For example, If someone has \(5{3\over 4}\) dollars and spends \(2{1\over2}\) dollars, they subtract the fractions to find what remains.
   
• Sports: Subtraction of fractions is also useful in sports and fitness. Athletes track time and distances, often leading to subtraction of fractions to analyze performance improvements. For example, a runner who previously completed a lap in \(13\over5\) minutes and now finishes in \(12\over5\) minutes must subtract to find their improvement.