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fractions

Adding fractions with related denominators

Use equivalent fractions for denominators such as halves and quarters.

Quick answer

You can add fractions with related denominators by making the bottom numbers (denominators) the same, then adding the top numbers (numerators).

Learning outcome

By the end of this page, you will be able to add two fractions that have related denominators, such as 1/2 + 1/4, by finding a common denominator and adding the numerators. Success signs:
  • You can identify when two fractions have related denominators
  • You can find a common denominator for two fractions
  • You can add the numerators after making the denominators the same
  • You can simplify your answer if needed

Why this matters

Adding fractions with related denominators is useful in many everyday situations. When you're cooking and need to add 1/2 cup of sugar to 1/4 cup of sugar, you need to know how much you have in total. When you're sharing a pizza with friends and you eat 1/3 of it while your friend eats 1/6 of it, you need to add those parts together. Understanding how to add fractions helps you solve real problems involving sharing, measuring, and comparing parts of a whole.

How it works

Adding fractions with related denominators is a bit like sharing toys. If you have 1/2 of a cake and your friend has 1/4 of the same cake, you want to know how much cake you have altogether. Here's how to do it step by step:
  1. Look at the denominators (bottom numbers) of both fractions
  2. Check if one denominator is a multiple of the other
  3. If yes, multiply the numerator (top number) and denominator of the smaller fraction by the same number to make the denominators the same
  4. Add the numerators together
  5. Keep the same denominator

Examples you can see

Let's look at a few examples to understand how this works. Example 1: Add 1/2 + 1/4 Step 1: Look at the denominators. We have 2 and 4. Step 2: Check if one is a multiple of the other. 4 is 2 × 2, so yes. Step 3: Make the denominators the same by multiplying 1/2 by 2/2 (which is 1, so it doesn't change the value). 1/2 × 2/2 = 2/4 Now we have 2/4 + 1/4 Step 4: Add the numerators: 2 + 1 = 3 Step 5: Keep the denominator the same: 3/4 Example 2: Add 2/3 + 1/6 Step 1: Look at the denominators. We have 3 and 6. Step 2: Check if one is a multiple of the other. 6 is 3 × 2, so yes. Step 3: Make the denominators the same by multiplying 2/3 by 2/2. 2/3 × 2/2 = 4/6 Now we have 4/6 + 1/6 Step 4: Add the numerators: 4 + 1 = 5 Step 5: Keep the denominator the same: 5/6 Example 3: Add 3/4 + 1/8 Step 1: Look at the denominators. We have 4 and 8. Step 2: Check if one is a multiple of the other. 8 is 4 × 2, so yes. Step 3: Make the denominators the same by multiplying 3/4 by 2/2. 3/4 × 2/2 = 6/8 Now we have 6/8 + 1/8 Step 4: Add the numerators: 6 + 1 = 7 Step 5: Keep the denominator the same: 7/8

Try it as a mini adventure

Adventure: The Pizza Party You're planning a pizza party for your class. You ordered 1/2 of a large pizza for the children and 1/4 of a small pizza for the teachers. 1st time: You need to work out how much pizza you have in total. What fractions are you adding? 2nd time: What denominators do you see? Are they related? 3rd time: How many quarters make up 1/2? What do you multiply 1/2 by to get quarters? 4th time: What is 1/2 + 1/4? 5th time: What is the total amount of pizza in quarters? 6th time: If each slice is 1/8 of a pizza, how many slices are there altogether?

Common mistakes

  • Mistake: Adding the denominators too. Why it happens: Children might think that since you're adding fractions, you add everything. Fix: Remember, only add the numerators (top numbers). Keep the denominator (bottom number) the same after making them equal.
  • Mistake: Not finding a common denominator. Why it happens: Children might think they can just add 1/3 + 1/6 by adding 1 + 1 = 2 and 3 + 6 = 9, making 2/9. Fix: Always check if one denominator is a multiple of the other. If not, find a common denominator.
  • Mistake: Forgetting to simplify the answer. Why it happens: Children might not know how to simplify fractions. Fix: Look for common factors in the numerator and denominator. Divide both by the same number to make the fraction smaller but equal.

Parent and carer guide

This is a key skill for children to learn, as it builds the foundation for more advanced fraction work. Here's how you can help:
  • Use real-life examples like sharing pizza or cake to show how fractions work
  • Encourage your child to explain their thinking when adding fractions
  • Ask questions like: "How did you make the denominators the same?" or "Why did you multiply by 2/2?"
  • Practice with different related fractions, like 1/3 + 1/6 or 3/5 + 1/10
  • Don't worry if your child makes mistakes – they're part of learning!
  • Use visual aids like fraction circles or bars to help your child see the relationships
  • Remember to praise effort, not just correct answers

Practice questions

  1. What is 1/2 + 1/4?
  2. What is 2/3 + 1/6?
  3. What is 3/4 + 1/8?
  4. What is 1/5 + 2/10?
  5. What is 2/7 + 1/14?
  6. What is 3/8 + 1/4?
  7. What is 1/3 + 1/9?
  8. What is 4/5 + 2/10?
Answers:
  1. 3/4
  2. 5/6
  3. 7/8
  4. 4/10 or 2/5
  5. 5/14
  6. 5/8
  7. 4/9
  8. 10/10 or 1

FAQ

What does "related denominators" mean?

Related denominators are denominators where one number is a multiple of the other. For example, 2 and 4 are related because 4 is 2 × 2. So are 3 and 6, because 6 is 3 × 2.

Can I add fractions with unrelated denominators?

Yes, but you need to find a common denominator that works for both fractions. This is a bit more complex than related denominators and will be covered in a future lesson.

Why do I need to make the denominators the same?

Just like you can't add 3 apples and 4 oranges, you can't add 1/3 and 1/4 because they represent different parts of a whole. Making the denominators the same means they're parts of the same whole, so you can add them.

How do I know which fraction to multiply by?

You multiply the fraction with the smaller denominator by a number that makes its denominator equal to the larger one. For example, to make 1/4 into 2/8, you multiply by 2/2.

What if I get a fraction that can be simplified?

If the numerator and denominator have a common factor, you can divide both by that number to make the fraction simpler. For example, 4/8 can be simplified to 1/2.