Subtraction of Fractions with Practice Problems

What is Subtraction of Fractions?

Subtraction of fractions means finding the difference between two fractions. This is similar to subtraction with whole numbers, but we need to be careful with the denominators.

For example: If you eat 2/5 of a chocolate bar and give away 1/5, the remaining part is:

2/5 − 1/5 = 1/5

In this case, the denominators are the same, which makes the subtraction easy.

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What is a Fraction?

A fraction is a number that represents a part of a whole. It has two parts:

• Numerator (top number): How many parts you have.

• Denominator (bottom number): Total equal parts the whole is divided into.

For example, in the fraction 3/4, the number 3 is the numerator and 4 is the denominator.

Read More: Numerator and Denominator

How to Subtract Fractions?

To learn how to subtract fractions, you first need to check if the denominators are the same or different. There are three main cases:

1. Subtracting fractions with like denominators

2. Subtraction of fractions with unlike denominators

3. Subtracting mixed numbers and subtracting fractions with whole numbers

Let’s go through each one in detail with examples.

Read More: Like Fractions And Unlike Fractions 

Subtracting Fractions with Like Denominators

Like denominators mean both fractions have the same bottom number. This makes subtraction easy because the size of each part is already the same. Here are steps to subtract fractions having same denominators:

Step 1: Check that both fractions have the same denominator (bottom number). This means they are like denominators.

Step 2: Keep the denominator the same in your answer. You do not need to change it.

Step 3: Subtract the numerators (top numbers) to find the new numerator.

Step 4: Write the result as a new fraction using the same denominator and the subtracted numerator.

Step 5: Simplify the fraction if possible by dividing both the top and bottom numbers by a common factor.

Example:

Subtract 5/9 from 7/9.

Solution: Both denominators are 9.

7/9 − 5/9 = (7 − 5)/9 = 2/9

So, the answer is 2/9.

This is the easiest type of subtraction of fractions. You only need to subtract the numerators.

Read More: Adding Fractions

Subtraction of Fractions with Unlike Denominators

When two fractions have different denominators, they are called unlike fractions. You cannot subtract them right away because the sizes of the parts are not the same. To subtract them correctly, you must first make the denominators the same. Here are steps to subtract fractions having different denominators:

Step 1: Find the LCM (Least Common Multiple) of the two denominators. This helps you create a common denominator that both fractions can use.

Step 2: Convert both fractions so they have the same denominator. To do this, multiply the numerator and denominator of each fraction by whatever number is needed to make the denominators equal to the LCM.

Step 3: Subtract the numerators while keeping the new common denominator the same.

Step 4: Simplify the final fraction if possible by dividing both the numerator and the denominator by a common factor.

Example:

Subtract 2/3 from 3/5.

Step 1: LCM of 3 and 5 is 15.

Step 2: Convert both fractions:

• 3/5 = 9/15
  
  

• 2/3 = 10/15

Step 3: Subtract:

9/15 − 10/15 = −1/15

Answer: −1/15

Even though the result is negative, that’s okay. It means you took away more than you had.

Read More: Multiple of fractions 

Subtracting Fractions with Whole Numbers

Sometimes, you may need to subtract a fraction from a whole number. For example, 2 − 1/4. Since they are different types of numbers, we first convert the whole number into a fraction. Here are steps to subtract fractions with whole numbers::

Step 1: Convert the whole number into a fraction. For example, 2 becomes 2/1.

Step 2: Find the least common denominator (LCM) of the two denominators.

Step 3: Rewrite both fractions using this common denominator.

Step 4: Subtract the numerators and keep the denominator the same.

Step 5: Simplify the result if needed.

Example: Subtract 1/2 from 2.

Step 1: Convert 2 to a fraction → 2 = 2/1

Step 2: Find the LCM of 1 and 2 → LCM = 2

Step 3: Convert the fractions:

• 2/1 = 4/2

• 1/2 stays the same
  
  

Step 4: Subtract the numerators:

4/2 − 1/2 = 3/2

3/2, or 1 1/2 when written as a mixed number.

Subtracting Mixed Numbers

A mixed number has a whole number part and a fraction part, like 3 1/2. There are two common ways to subtract mixed numbers.

• Convert to improper fractions

• Subtract the whole and fractional parts separately

Let’s try both methods.

Read More: Proper Fraction

Method 1: Convert to Improper Fractions

Example: Subtract 2 ¾ from 5 ½

Step 1: Convert mixed numbers to improper fractions

• 5 ½ = (5 × 2) + 1 = 11⁄2

• 2 ¾ = (2 × 4) + 3 = 11⁄4

Step 2: Find the Least Common Denominator (LCD)

• Denominators are 2 and 4

• The Least Common Denominator of 2 and 4 is 4

Step 3: Convert both fractions to have the same denominator

• 11⁄2 = (11 × 2)/(2 × 2) = 22⁄4

• 11⁄4 stays the same

Step 4: Subtract the fractions

22⁄4 − 11⁄4 = (22 − 11)/4 = 11⁄4

Step 5: Convert the improper fraction back to a mixed number

11⁄4 = 2 R3 → 2 ¾

Method 2: Subtract Whole and Fractional Parts Separately

Example: Subtract 3 1⁄5 from 6 2⁄5

Step 1: Subtract the whole numbers:
6 − 3 = 3

Step 2: Subtract the fractions:
2⁄5 − 1⁄5 = 1⁄5

Final Answer: 3 1⁄5

This method works well when the fraction in the first number is greater than or equal to the fraction in the second number. If the fraction in the second number is larger, you will need to use regrouping to subtract properly.

Read More: Mixed Fraction

Regrouping in Subtracting Mixed Numbers

Sometimes, you cannot subtract the fractional parts of mixed numbers directly because the fraction in the second number is larger than the fraction in the first. In such cases, you need to regroup or borrow from the whole number.

Example: Subtract 2 ¾ from 5 ¼

We are solving:

 5 ¼ − 2 ¾

Step 1: Subtract the whole numbers:

5 − 2 = 3

Step 2: Subtract the fractions:

 ¼ − ¾ is not possible, because ¼ is smaller than ¾.

So, we regroup by borrowing 1 from the whole number 3.Change 3 to 2, and add 4⁄4 (which equals 1) to ¼:

¼ + 4⁄4 = 5⁄4

Now subtract the fractions:

 5⁄4 − 3⁄4 = 2⁄4, which simplifies to ½

Now bring back the whole number:

Final answer: 2 ½

This is how you subtract mixed numbers using regrouping when the fractional part in the first number is smaller than in the second.

Subtraction of Fractions Practice Questions

Practice is the best way to improve your understanding of subtraction of fractions. The questions below include all types: like denominators, unlike denominators, subtraction from whole numbers, and subtracting mixed numbers. Try solving them step by step, and simplify your answers wherever possible.

1. 7⁄10 − 2⁄10 = ?

2. 5⁄6 − 1⁄3 = ?

3. 4 − 3⁄4 = ?
   6 1⁄2 − 2 1⁄2 = ?

4. 3⁄4 − 2⁄3 = ?

5. 8 − 5⁄6 = ?

6. 5 1⁄4 − 2 3⁄4 = ?

7. 9 2⁄5 − 6 4⁄5 = ?

8. 2⁄3 − 1⁄6 = ?

9. 7 3⁄8 − 3 7⁄8 = ?

Important Tips for Subtraction of Fractions

Here are some helpful tips to remember when working on subtraction of fractions problems:

• Always check if the denominators are the same before you subtract.

• If the fractions have different denominators, find the Least Common Denominator (LCM) to make them the same.

• When working with subtracting mixed numbers, convert them to improper fractions if needed.

• After performing any subtraction of fractions, always simplify your answer to its lowest form.

Also Read: Division of Fractions 

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