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!