Subtraction of Fractions

Subtraction of fractions is an arithmetic operation to be performed to find the difference between two fractions. To subtract two like fractions we have to subtract their numerators and write the difference over the common denominator, while to subtract two unlike fractions, we have to first convert them into like fractions by taking the LCM of the denominators. We can subtract a whole number and fraction too by writing the whole number in fractional form, for example, 3 = 3/1. Let us learn more about subtracting fractions in detail in this article.

Fractions are referred to as a part of a whole. A group of fractions can be classified as like fractions and unlike fractions based on the denominator value. Like fractions are those that have the same denominator. For example, 3/4 and 5/4. While unlike fractions are those that have different denominators, for example, 2/3 and 4/7. We can find the difference between two like fractions, unlike fractions and fractions and whole numbers. The steps for subtracting fractions are listed below:

• Step 1: Identify whether the given fractions have the same denominator or different denominators.
• Step 2: In the case of like fractions, subtract the numerators and write their difference over the common denominator. For example, 5/7 - 2/7 = (5 - 2)/7 = 3/7. On the other hand, with unlike fractions, find the LCM of the denominators.
• Step 3: Multiply the numerator and denominator of each fraction with a whole number to get the LCM in the denominator. It is done to convert unlike fractions to like fractions.
• Step 4: Subtract their numerators and write the difference over the common denominator.

This is how we subtract two fractions. There are two cases that come up while learning subtraction of fractions and those are subtracting like fractions and unlike fractions. Let's learn about each in detail.

The fractions with like denominators can be easily subtracted by subtracting their numerators. The steps to subtract the fractions with like denominators are given below:

• Subtract the numerators.
• Write the common denominator as the denominator of the resultant fraction.
• Now, the obtained answer can be reduced to its lowest form, if needed.

Let us subtract the fractions 4/5 and 2/5 using a rectangular model. We represent 4/5 in this model by shading 4 out of 5 parts. We will further shade 2 parts from our shaded parts of the model to represent removing 2/5.

We are now left with 2 parts in the shaded parts of the model. Thus the subtraction of the fractions is given as (4/5 - 2/5) = 2/5.

Two fractions with different or unlike denominators can be subtracted by following the steps written below:

1. First, take the LCM of the denominators.
2. We convert the given fractions to like fractions with the denominator as the LCM.
3. Now, subtract the numerators and write their difference over the common denominator.
4. Simplify, if needed.

Let us understand how to subtract unlike fractions using the area model: (2/5 - 1/3). This indicates that we have to remove (1/3)^rd part from 2/5. We can represent it as below.

As our model is divided into 15 parts, this is our denominator. This is the LCM of the denominators of the given fractions. The first rectangle shows the portion represented by 2/5 (in rows) and 1/3 (in columns) in the given model. Now, shift the portion of 1/3 to 2/5 so that we can deduct 1/3 from 2/5. We see that there is only 1 part left which is not shaded out. Thus, the answer is given as, 2/5 - 1/3 = 1/15. Numerically, it can be expressed as,

2/5 - 1/3

⇒ (2 × 3)/(5 × 3) - (1 × 5)/(3 × 5) [As the LCM of 5 and 3 is 15]

⇒ 6/15 - 5/15

⇒ 1/15

Hence, 2/5 - 1/3 = 1/15.

Use our free online subtracting fractions calculator to verify your answers.

Similar to subtracting two fractions, we can also subtract a fraction from a whole number and vice-versa. Every whole number can be written in the fractional form by writing 1 as the denominator, for example, we can write 7 as 7/1. So, for subtracting a fraction and a whole number we first make them write in fractional form, then we can easily find the difference by applying the same rules as subtracting two unlike fractions. To subtract a fraction from a whole number, consider the following example: 2 - 1/4.

• We convert the whole number to a fractional form as, 2 = 2/1.
• Now, subtract them like unlike fractions.

So, to subtract 2/1 - 1/4, the LCM of 1 and 4 is 4. Multiply the numerator and denominator of 2/1 by 4 to get 4 in the denominator.

2/1 - 1/4 = (2 × 4)/(1 × 4) - 1/4

= 8/4 - 1/4

= 7/4

= \(1\frac {3}{4}\)

Hence, 2 - 1/4 = 7/4. This is how we subtract fractions with whole numbers.

Tips and Tricks:

• Steps of subtracting fractions with different denominators:

  a) Convert the given fractions to like fractions by taking the LCM of the denominators.
  b) Find the equivalent fractions of the given fractions whose denominator is the LCM.
  c) Subtract the numerators and retain the same denominator.

• For unlike fractions, never subtract the numerators and denominators directly.
  (3/5 - 2/3) ≠ (1/2)
• When subtracting unlike fractions, it is not necessary to find the LCM of the denominators. Any common multiple will do. So, simply multiplying the two denominators gives us a common multiple. This may lead to larger looking numbers, but it can be reduced to its lowest form.

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• Adding Fractions

What is Addition and Subtraction of Fractions?

Addition and subtraction of fractions are the two arithmetic operations performed to add or subtract fractions. The rules of adding or subtracting fractions are the same. Like fractions can be added/subtracted by adding/subtracting their numerators and retaining the common denominator, while unlike fractions can be added/subtracted by converting them to like fractions first.

How to Subtract Fractions?

We can subtract like fractions and unlike fractions using the steps given below:

• For like fractions, subtract the numerators and retain the same denominator.
• For subtracting unlike fractions, take the LCM of the denominators and convert the fractions to like fractions and subtract them.
• Reduce to its lowest term if needed.

What is the Rule of Subtracting Fractions?

The basic rule to subtract fractions is to first make sure that they have a common denominator. If they have different denominators, then we first convert those into like fractions.

How to Subtract Fractions with Whole Numbers?

We can use the steps given below to subtract fractions from whole numbers:

• We write the whole number as a fraction by writing 1 in the denominator.
• Once it is done, we obtain two unlike fractions.
• Now, we subtract both unlike fractions and the answer is obtained.
• The obtained value can be reduced to its lowest term if needed.

Let us see an example:

2 - 1/5 = 2/1 - 1/5
(2/1 × 5/5) - (1/5) = 10/5 - 1/5 = 9/5
= \(1\frac{4}{5}\)

How to Subtract Fractions with Different Denominators?

Follow the steps below to subtract fractions with different denominators:

• Find the LCM of denominators.
• Multiply the numerator and denominator of each fraction by a whole number to obtain LCM in the denominator.
• Subtract them as like fractions.
• Reduce the final answer if required.

How to Solve Subtracting Fractions?

We can simplify subtracting fractions in the below ways:

• In case of like fractions, the fractions can be subtracted by subtracting their numerators and the output can be simplified easily.
• For unlike fractions, the denominators are first made common and only then the fractions are subtracted. Once subtracted, the output can be simplified easily.

Let us see an example of it.
2/4 - 2/5 = (2/4 × 5/5) - (2/5 × 4/4)

= 10/20 - 8/20

= 2/20

= 1/10

How do you Subtract Improper Fractions?

The improper fractions are subtracted similarly as in case of proper fractions:

• For like fractions, subtract the numerators and retain the same denominator.
• For subtracting unlike fractions, take the LCM of the denominators and convert the fractions to equivalent fractions and subtract them as like fractions.

Once the subtraction is done, if the answer obtained is an improper fraction, we convert the fraction to a mixed number to write it in simplest form.