Hey there! In today’s post, we will review the key concepts for adding and subtracting fractions. This is a helpful refresher for those entering Year 5 who have already covered this topic in Year 4.

### Understanding Denominators

When adding or subtracting fractions, it’s crucial that the denominators are the same. If they are not, we must convert the fractions to equivalent fractions with common denominators before proceeding.

### Adding Fractions with Different Denominators

Let’s look at an example:

$$\frac{2}{5} + \frac{1}{15}$$

**Step 1: Identify the Denominators**

We have two fractions with different denominators: 5 and 15.

**Step 2: Find a Common Denominator**

The smallest common multiple of 5 and 15 is 15. This will be our common denominator.

**Step 3: Convert to Equivalent Fractions**

We’ll convert (\frac{2}{5}) to an equivalent fraction with a denominator of 15 by multiplying the numerator and denominator by 3 (since 5 x 3 = 15):

$$\frac{2}{5} = \frac{6}{15}$$

**Step 4: Perform the Addition**

Now our fractions have the same denominator, so we can simply add the numerators:

$$\frac{6}{15} + \frac{1}{15} = \frac{7}{15}$$

**Summary:**

$$\frac{2}{5} + \frac{1}{15} = \frac{6}{15} + \frac{1}{15} = \frac{7}{15}$$

Let’s try another:

**Example 2: Adding Three Eighths and One Third**

**Step 1: Identify the Denominators**

We have:

$$\frac{3}{8} + \frac{1}{3}$$

**Step 2: Find a Common Denominator**

The smallest common multiple of 8 and 3 is 24.

**Step 3: Convert to Equivalent Fractions**

To convert (\frac{3}{8}):

$$\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}$$

To convert (\frac{1}{3}):

$$\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}$$

**Step 4: Perform the Addition**

Now with the same denominator, we simply add the numerators:

$$\frac{9}{24} + \frac{8}{24} = \frac{17}{24}$$

**Summary:**

$$\frac{3}{8} + \frac{1}{3} = \frac{9}{24} + \frac{8}{24} = \frac{17}{24}$$

### Subtracting Fractions with Different Denominators

Subtraction follows the same process, except we subtract the numerators rather than adding them.

**Example 3: Subtracting Three Quarters and One Sixth**

**Step 1: Identify the Denominators**

We have:

$$\frac{3}{4} – \frac{1}{6}$$

**Step 2: Find a Common Denominator**

The smallest common multiple of 4 and 6 is 12.

**Step 3: Convert to Equivalent Fractions**

To convert (\frac{3}{4}):

$$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$

To convert (\frac{1}{6}):

$$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$$

**Step 4: Perform the Subtraction**

Now we can subtract the numerators:

$$\frac{9}{12} – \frac{2}{12} = \frac{7}{12}$$

**Summary:**

$$\frac{3}{4} – \frac{1}{6} = \frac{9}{12} – \frac{2}{12} = \frac{7}{12}$$

Let’s try one more subtraction example:

**Example 4: Subtracting Two Fifths and One Eighth**

**Step 1: Identify the Denominators**

We have:

$$\frac{2}{5} – \frac{1}{8}$$

**Step 2: Find a Common Denominator**

The smallest common multiple of 5 and 8 is 40.

**Step 3: Convert to Equivalent Fractions**

To convert (\frac{2}{5}):

$$\frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40}$$

To convert (\frac{1}{8}):

$$\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}$$

**Step 4: Perform the Subtraction**

Now we simply subtract the numerators:

$$\frac{16}{40} – \frac{5}{40} = \frac{11}{40}$$

**Summary:**

$$\frac{2}{5} – \frac{1}{8} = \frac{16}{40} – \frac{5}{40} = \frac{11}{40}$$

### Try It Yourself

Now you should feel equipped to practice adding and subtracting fractions on your own. Remember, the key steps are:

- Identify the denominators
- Find a common denominator
- Convert to equivalent fractions
- Perform the addition/subtraction

I hope this has served as a helpful refresher on adding and subtracting fractions. Wishing you all the best as you continue developing your maths skills. Please reach out with any other questions!