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Year 6 Maths

Adding & Subtracting Fractions

Master adding and subtracting fractions with unlike denominators and learn to work with mixed numbers.

Same Denominator (Quick Review)

When fractions have the same denominator, simply add or subtract the numerators and keep the denominator the same.

2⁄7 + 3⁄7 = 5⁄7

5⁄9 − 2⁄9 = 3⁄9 = 1⁄3

Unlike Denominators

When the denominators are different, you must first find a common denominator before adding or subtracting.

Step-by-Step Method

  1. Find the lowest common denominator (LCD) of both fractions.
  2. Convert each fraction to an equivalent fraction with the LCD.
  3. Add or subtract the numerators.
  4. Simplify if possible.

Example: 1⁄3 + 1⁄4

Step 1: LCD of 3 and 4 = 12

Step 2: 1⁄3 = 4⁄12 and 1⁄4 = 3⁄12

Step 3: 4⁄12 + 3⁄12 = 7⁄12

Answer: 7⁄12

Adding & Subtracting Mixed Numbers

A mixed number has a whole part and a fraction part (e.g. 23⁄4). To add or subtract mixed numbers, you can either work with the whole and fraction parts separately, or convert to improper fractions first.

Example: 12⁄3 + 21⁄4

Step 1: Add whole numbers: 1 + 2 = 3

Step 2: Add fractions: 2⁄3 + 1⁄4 (LCD = 12)

Step 3: 8⁄12 + 3⁄12 = 11⁄12

Answer: 3 + 11⁄12 = 311⁄12

Regrouping When Subtracting

Sometimes when subtracting mixed numbers, the fraction part of the first number is smaller than the fraction part of the second. You need to regroup (borrow 1 from the whole number).

Tip: If you prefer, convert both mixed numbers to improper fractions first, then subtract. This avoids regrouping entirely!

Key Vocabulary

Common Denominator

A shared denominator that two or more fractions can both be converted to.

Mixed Number

A number with a whole part and a fraction part (e.g. 31⁄2).

Improper Fraction

A fraction where the numerator is larger than the denominator (e.g. 7⁄4).

Regroup

To borrow 1 from the whole number and convert it into a fraction to make subtraction possible.

Worked Examples

1

2⁄5 + 1⁄3

Step 1: LCD of 5 and 3 = 15

Step 2: 2⁄5 = 6⁄15, 1⁄3 = 5⁄15

Answer: 6⁄15 + 5⁄15 = 11⁄15

2

3⁄4 − 1⁄6

Step 1: LCD of 4 and 6 = 12

Step 2: 3⁄4 = 9⁄12, 1⁄6 = 2⁄12

Answer: 9⁄12 − 2⁄12 = 7⁄12

3

31⁄2 − 13⁄4

Step 1: Convert to improper: 7⁄2 − 7⁄4

Step 2: LCD = 4: 14⁄4 − 7⁄4 = 7⁄4

Answer: 7⁄4 = 13⁄4

Knowledge Check

Select the correct answer for each question.

Question 1

1⁄4 + 1⁄6 = ?

Question 2

5⁄6 − 1⁄3 = ?

Question 3

2⁄3 + 3⁄5 = ?

Question 4

21⁄3 + 11⁄2 = ?

Question 5

7⁄8 − 1⁄4 = ?

Key Concepts Summary

Year 6: Equivalent Fractions