Subtraction of Fractions

Q: How do you subtract fractions with the same denominator?

Subtract the numerators and keep the denominator the same. For example, 5/7 − 2/7 = 3/7.

Q: How do you subtract fractions with different denominators?

Find the LCM of the denominators. Convert both fractions to equivalent fractions with the LCM as the denominator. Then subtract the numerators.

Q: What is borrowing in mixed number subtraction?

When the fraction part of the first number is smaller than the second, borrow 1 from the whole number. Convert that 1 into a fraction with the same denominator and add it to the existing fraction. Then subtract.

Q: Can the answer be negative?

In Class 6, you usually subtract the smaller fraction from the larger one. But mathematically, subtracting a larger fraction from a smaller one gives a negative result. For example, 1/4 − 3/4 = −2/4 = −1/2.

Q: Do you subtract the denominators?

No. Never subtract (or add) the denominators. The denominator tells you the size of each part. Only the numerators change.

Q: Should you always simplify the answer?

Yes. Always simplify the fraction to its lowest terms. For example, 4/8 should be written as 1/2.

Class 6Class 7Fractions

If a cake is cut into 8 equal pieces and you eat 3 pieces, you have eaten 3/8 of the cake. If your friend then eats 2 more pieces, the remaining cake is 8/8 − 3/8 − 2/8 = 3/8. This is subtraction of fractions.

Subtracting fractions works just like adding them — if the denominators are the same, subtract the numerators. If they are different, first make them the same using the LCM.

In Class 6 NCERT Maths, you will learn to subtract like fractions, unlike fractions, and mixed numbers.

What is Subtraction of Fractions - Grade 6 Maths (Fractions)?

Subtraction of like fractions:

a/c − b/c = (a − b)/c

Keep the denominator the same. Subtract the numerators.

Subtraction of unlike fractions:

Find the LCM of the denominators.
Convert each fraction to an equivalent fraction with the LCM as denominator.
Subtract the numerators. Keep the common denominator.
Simplify if possible.

Subtraction of Fractions Formula

Formula for subtracting two fractions:

a/b − c/d = (a×d − c×b) / (b×d)

The LCM method gives a simpler denominator than cross-multiplication.

Subtracting mixed numbers:

Subtract the whole number parts.
Subtract the fraction parts (convert to like fractions if needed).
If the fraction part of the first number is smaller, borrow 1 from the whole number.

Types and Properties

Cases in subtraction of fractions:

Like fractions: Subtract numerators directly. Example: 5/7 − 2/7 = 3/7.
Unlike fractions: Find LCM, convert, then subtract. Example: 3/4 − 1/3 = 9/12 − 4/12 = 5/12.
Whole number − fraction: Write the whole number as a fraction. Example: 3 − 1/5 = 15/5 − 1/5 = 14/5 = 2 4/5.
Mixed numbers: Subtract whole parts and fraction parts separately. Borrow if needed.

Solved Examples

Example 1: Subtracting Like Fractions

Problem: Subtract 7/9 − 4/9.

Solution:

Same denominator (9). Subtract numerators: 7 − 4 = 3.

7/9 − 4/9 = 3/9 = 1/3.

Answer: 1/3

Example 2: Subtracting Unlike Fractions

Problem: Subtract 3/4 − 1/6.

Solution:

Step 1: LCM of 4 and 6 = 12.

Step 2: 3/4 = 9/12 and 1/6 = 2/12.

Step 3: 9/12 − 2/12 = 7/12.

Answer: 7/12

Example 3: Subtracting from 1

Problem: Subtract: 1 − 3/8.

Solution:

1 = 8/8.

8/8 − 3/8 = 5/8.

Answer: 5/8

Example 4: Subtracting from a Whole Number

Problem: Subtract: 5 − 2/3.

Solution:

5 = 15/3.

15/3 − 2/3 = 13/3 = 4 1/3.

Answer: 4 1/3

Example 5: Subtracting Mixed Numbers (Easy)

Problem: Subtract: 5 3/4 − 2 1/4.

Solution:

Whole parts: 5 − 2 = 3.

Fraction parts: 3/4 − 1/4 = 2/4 = 1/2.

Answer: 3 1/2

Example 6: Subtracting Mixed Numbers (Borrowing)

Problem: Subtract: 4 1/6 − 1 5/6.

Solution:

Fraction part: 1/6 − 5/6. Since 1/6 < 5/6, we borrow 1 from the whole number.

4 1/6 = 3 + 1 + 1/6 = 3 + 6/6 + 1/6 = 3 7/6.

Now: 3 7/6 − 1 5/6.

Whole parts: 3 − 1 = 2.

Fraction parts: 7/6 − 5/6 = 2/6 = 1/3.

Answer: 2 1/3

Example 7: Subtracting Unlike Mixed Numbers

Problem: Subtract: 3 1/2 − 1 1/3.

Solution:

Whole parts: 3 − 1 = 2.

Fraction parts: 1/2 − 1/3. LCM of 2 and 3 = 6.

1/2 = 3/6, 1/3 = 2/6. So 3/6 − 2/6 = 1/6.

Answer: 2 1/6

Example 8: Word Problem

Problem: A rope is 7/8 m long. A piece of 3/8 m is cut off. What is the remaining length?

Solution:

7/8 − 3/8 = 4/8 = 1/2 m.

Answer: The remaining rope is 1/2 m long.

Example 9: Result that Needs Simplifying

Problem: Subtract: 5/6 − 1/3.

Solution:

LCM of 6 and 3 = 6. 1/3 = 2/6.

5/6 − 2/6 = 3/6 = 1/2.

Answer: 1/2

Example 10: Subtracting Three Fractions

Problem: Subtract: 1 − 1/4 − 1/2.

Solution:

LCM of 1, 4, 2 = 4. 1 = 4/4, 1/2 = 2/4.

4/4 − 1/4 − 2/4 = 1/4.

Answer: 1/4

Real-World Applications

Where subtraction of fractions is used:

Cooking: If a recipe needs 3/4 cup of flour and you have already added 1/2 cup, you need 3/4 − 1/2 = 1/4 cup more.
Time: If a film is 2 hours long and you have watched 1 1/4 hours, you have 3/4 hour left.
Shopping: If you have Rs. 5 1/2 and spend Rs. 3 1/4, you have Rs. 2 1/4 left.
Measurement: Cutting a piece from a length of cloth involves subtracting fractions.

Key Points to Remember

For like fractions: subtract numerators, keep the denominator.
For unlike fractions: find the LCM, convert to like fractions, then subtract.
Always simplify the answer to its lowest terms.
If the result is an improper fraction, convert it to a mixed number.
For mixed numbers: subtract whole parts and fraction parts separately.
If the fraction being subtracted is larger, borrow 1 from the whole number.
Never subtract denominators — they stay the same.

Practice Problems

Subtract: 5/6 − 1/6.
Subtract: 3/4 − 2/5.
Subtract: 1 − 5/9.
Subtract: 4 − 1/3.
Subtract: 6 2/3 − 3 1/3.
Subtract: 5 1/4 − 2 3/4. (Hint: you need to borrow.)

Frequently Asked Questions

Q1. How do you subtract fractions with the same denominator?

Subtract the numerators and keep the denominator the same. For example, 5/7 − 2/7 = 3/7.

Q2. How do you subtract fractions with different denominators?

Find the LCM of the denominators. Convert both fractions to equivalent fractions with the LCM as the denominator. Then subtract the numerators.

Q3. What is borrowing in mixed number subtraction?

When the fraction part of the first number is smaller than the second, borrow 1 from the whole number. Convert that 1 into a fraction with the same denominator and add it to the existing fraction. Then subtract.

Q4. Can the answer be negative?

In Class 6, you usually subtract the smaller fraction from the larger one. But mathematically, subtracting a larger fraction from a smaller one gives a negative result. For example, 1/4 − 3/4 = −2/4 = −1/2.

Q5. Do you subtract the denominators?

No. Never subtract (or add) the denominators. The denominator tells you the size of each part. Only the numerators change.

Q6. Should you always simplify the answer?

Yes. Always simplify the fraction to its lowest terms. For example, 4/8 should be written as 1/2.

Subtraction of Fractions

What is Subtraction of Fractions - Grade 6 Maths (Fractions)?

Subtraction of Fractions Formula

Types and Properties

Solved Examples

Example 1: Subtracting Like Fractions

Example 2: Subtracting Unlike Fractions

Example 3: Subtracting from 1

Example 4: Subtracting from a Whole Number

Example 5: Subtracting Mixed Numbers (Easy)

Example 6: Subtracting Mixed Numbers (Borrowing)

Example 7: Subtracting Unlike Mixed Numbers

Example 8: Word Problem

Example 9: Result that Needs Simplifying

Example 10: Subtracting Three Fractions

Real-World Applications

Key Points to Remember

Practice Problems

Frequently Asked Questions

Q1. How do you subtract fractions with the same denominator?

Q2. How do you subtract fractions with different denominators?

Q3. What is borrowing in mixed number subtraction?

Q4. Can the answer be negative?

Q5. Do you subtract the denominators?

Q6. Should you always simplify the answer?

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