How to Subtract Fractions: A Complete Guide for Beginners

Subtracting fractions can be daunting for some pupils, but it is a fundamental math skill they must master. If you think how to subtract fractions sounds difficult, then this guide can help you.

Read on to learn how to add and subtract fractions, how to subtract mixed fractions, how to subtract fractions with like denominators and unlike denominators from whole numbers, and more about subtracting fractions!

What are Fractions?

Fractions are numerical values that represent parts of a whole. Fractions consist of two parts, the numerator and the denominator. The top part of the fraction is called the numerator and the bottom part is called the denominator.

For example, 2/3 is a fraction. Here, 2 is the numerator and 3 is the denominator.

Types of fractions

Based on the numerator and the denominator, there are different types of fractions:

Proper Fraction: In a proper fraction, the numerator is smaller than the denominator. For example: 3/7, 2/7, etc.

Improper Fraction: In improper fractions, the numerator is greater than the denominator. For example: 9/7, 11/9, etc.

Mixed Fraction: A mixed fraction is a combination of a positive fraction and a whole number. For example: 2 ⅘、4 ⅔.

Like Fractions: Fractions with the same denominator are called similar fractions. For example, 9/2, 5/2, 7/2, etc.

Unlike Fractions: Fractions with different denominators are called unlike fractions. Examples: 2/7, 2/9, 3/11, and so on.

Unit Fraction: In a unit fraction, the numerator should be equal to 1. For example, 1/3, 1/4, 1/5.

Equivalent Fractions: Equivalent fractions are fractions that represent the same value. If we multiply or divide the numerator and denominator by the same value, we get equivalent fractions, such as 2/4, 4/8, 8/16, etc.

Related fractional terms definitions

Before we jump into further steps for subtracting fractions, adding fractions, etc., let’s first cover some basic terms that you’ll come across.

Common denominator: When two or more fractions have the same denominator, they are common denominator.

Common factor: Factors are numbers we multiply together to get another number. When we find the factors of two or more numbers and then find some factors are “common”, then they are called common factors.

Least common multiple (LCM): The least common multiple is the smallest number that is divisible by both denominators.

Greatest common divisor (GCD): The greatest common divisor is the greatest number that will divide a given set of numbers equally.

Simplify: In mathematics, simplifying or simplification is when you reduce the expression, fraction, problem, or result to its simplest form.

What is Subtracting Fractions?

Before we formally learn how to subtract fractions, let’s think about this question: What is Meant by Subtracting Fractions?

In Mathematics, subtracting fractions means the process of the subtraction of two fractional values. We have learned to subtract the whole numbers. For example, the subtraction of 5 from 7 results in 2. (i.e. 7 – 5 = 2). Similarly, we can perform subtraction operations on fractions. Subtracting fractions includes:

• Subtracting Fractions with Like Denominators
• Subtracting Fractions with Unlike Denominators
• Subtracting Mixed Fractions
• Subtracting Fractions with Whole Numbers

Now, let’s discuss all these fraction subtractions in detail with examples and learn the steps on how to subtract fractions.

How to Subtract Fractions with Like Denominators

Subtraction of fractions with the same denominator is the subtraction of fractions with the same denominator value. Here are the detailed steps for subtracting fractions with the same denominator.

• Step 1: Keep the denominator values as it is and subtract the numerator value, which will give the result.
• Step 2: If required, simplify the fraction.

Example: Subtract 5/12 from 9/12.

Solution: Given: (9/12) – (5/12)

Here, the denominator values are the same, and keep the value as it is. Now, subtract the numerator values:

(9/12) – (5/12) = (9-5)/12

(9/12) – (5/12) = 4/12

Simplify the fraction, and we get,

(9/12) – (5/12) = 1/3

Therefore, (9/12) – (5/12) = 1/3.

How to Subtract Fractions with Different Denominators

Subtracting fractions with unlike denominators means the subtraction of fractions with different denominator values. To subtract fractions with different denominators:

1. Find the lowest common multiple (LCM) of the denominators.
2. Convert the denominator to the LCM value by multiplying the numerator and denominator using the same number.
3. Subtract the numerators, once the fractions have the same denominator values.
4. Simplify the fraction, if required
5. Complete the subtraction.

Example: Subtract 2/3 from 3/5.

Solution: (3/5) – (2/3)

Find the LCM of 3 and 5. The LCM of 3 and 5 is 15. To make the denominators equal, convert the denominators to the LCM value.

Thus, (3/5) – (2/3) = (9/15) – (10/15)

Now, the denominators are equal and we can subtract the numerator values:

(3/5) – (2/3) = (9/15) – (10/15)

= (9-10)/15 = -1/15

So, (3/5) – (2/3) = -1/15.

How to Subtract Mixed Fractions

Here are the steps to subtract mixed fractions:

1. Convert mixed fractions into the improper fraction.
2. Let’s check the denominator values:
   

   If the fractions are like fractions, follow the procedure of subtracting fractions with like denominators.If the fractions are unlike fractions, follow the procedure of subtracting fractions with unlike denominators.

Example: Subtract 8 ⅚ from 15 ¾.

Solution: (15 ¾) – (8 ⅚ )

Now, convert mixed fractions into improper fractions.

(15 ¾) – (8 ⅚ ) = (63/4)- (53/6)

Let’s find the LCM of 4 and 6 and make the denominators equal.

LCM of 4 and 6 is 12

(63/4)- (53/6) = (189/12) – (106/12)

(63/4)- (53/6) = 83/12

Therefore, (15 ¾) – (8 ⅚ ) = 83/12

Note: We can also convert improper fractions to mixed numbers if needed.

How to Subtract Fractions with Whole Numbers

Follow the below steps while subtracting the fractions with whole numbers:

• Step 1: Convert the whole number into the fractional form. For example, if 5 is a whole number, convert it into a fraction as 5/1
• Step 2: Now, follow the procedure of subtracting fractions with unlike denominators.
• Step 3: Simplify the fraction, if required.

Example: Subtract: 2 – (1/2)

Solution:

First, convert the whole number “2” into the fractional form as “2/1”.

2 – (1/2) = (2/1)- (1/2)

Now, take the LCM of 1 and 2.

The LCM of 1 and 2 is 2.

(2/1) – (1/2) = (4/2) – (1/2)

= (4-1)/2 = 3/2

Thus, 2 – (1/2) = 3/2.

How to Add and Subtract fractions

Similar to adding and subtracting whole numbers, fractions can be added and subtracted. First, remember the different types of fractions we mentioned above: like, unlike, and equivalent fractions. An important rule is that we can only add and subtract like fractions.

The reason is simple, that is, you can’t add 2 apples and 3 bananas to get 5 apples, because they are not all apples. The same is true for fractions, you can’t add unlike fractions because they have different “denominators” or units. The same goes for subtraction. You can’t subtract unlike units from one another. Let’s take a look at the steps to add and subtract fractions!

Step 1: Make the fractions like fractions

If you are working with fractions with the same denominator (such as 1/3 and 2/3), then the denominators are already the same, so you can go straight to step 2. However, when you are faced with two fractions with different denominators, you must convert the fractions to the same denominator.

There are two ways to solve this problem:

• If one denominator is a multiple of the other denominator

For instance, (2/4) + (3/8) =?

In this example, the denominators are different: 4 and 8. However, 8 is a multiple of 4. This means that we can multiply 4 x 2 to get 8. By doing this, the denominators are the same, making them act like fractions. However, 2/8 is not an equivalent fraction of 2/4 – leaving it as 2/8 would make it a completely different fraction.

Therefore, we must also multiply the numerator (2) by the same number that we multiplied the denominator by (2). This changes 2/4 to 4/8. 2/4 and 4/8 are equivalent fractions, and 4/8 and 3/8 act like fractions, so now we can add the fractions together. The problem now: (4/8) + (3/8) = 7/8

• If both the denominators have no common factor

Let’s use this problem as an example: (2/5) – (1/4) =?

We can see that the denominators are different: 5 and 4. Also, 4 is not a multiple of 5, and 5 is not a multiple of 4. The simplest thing to do here is to multiply the two denominators together to find a common factor. So: 5 x 4 = 20. Then 20 becomes our new denominator for both fractions.

Remember that you must also multiply the numerators to convert each equation to an equivalent fraction so that the equation remains the same. Thus:

The final result is: 8/20 – 5/20 = 3/20

Step 2: Add and subtract the numerators

Once you have the same fraction, you can add or subtract the numerator. The sum or difference will become the new numerator, and the common denominator discussed in Step 1 will remain the same. (The answers to the above two questions are already given in Step 1.)

Frequently Asked Questions

1. What is the common denominator of ½ and ⅕?

The common denominator is 10.

• We know that 2 and 5 are the denominators, and they do not share any common factors.
• We must multiply 2 x 5 to find the common denominator. The common denominator is 10.
• 2 x 5 = 10

2. What is the simplified fraction of 20/60?

The simplified fraction is 1/3.

• 60 is a multiple of 20.
• 20 goes into itself one time, giving us a numerator of 1.
• 20 goes into 60 three times, giving us a denominator of 3.

Conclusion

Now that you have an understanding of how to subtract fractions, this knowledge will be of great benefit to you whether you are solving math problems or applying fractions in real life.

If you are looking for more in-depth lessons and exercises, you can also check out WuKong online math courses, which are designed to make math fun and accessible to everyone. Let’s explore math together!