X Tables
fractions

Subtracting fractions with related denominators

Convert to common parts before subtracting.

Quick answer

To subtract fractions with related denominators, you need to make the bottom numbers (denominators) the same, then subtract the top numbers (numerators).

Learning outcome

By the end of this page, you will be able to subtract fractions that have related denominators by finding a common denominator and then subtracting the numerators. Success signs:
  • You can find a common denominator for two fractions
  • You can subtract the numerators after making the denominators the same
  • You can simplify your answer if needed
  • You can check your answer by adding it back to the fraction you subtracted from

Why this matters

Subtracting fractions with related denominators is useful in many everyday situations. For example, when you are sharing a pizza or cake, you might need to take away a piece and figure out how much is left. When you are measuring ingredients for a recipe, you might need to take away a certain amount. In sports, like football or rugby, you might need to work out how many points are left to score. Understanding how to subtract fractions helps you solve these real-life problems with confidence.

How it works

Let's look at how to subtract fractions with related denominators step by step:
  1. Check the denominators: See if the bottom numbers are the same or related (like 2 and 4, or 3 and 6).
  2. Find a common denominator: If the denominators are different, find a number that both can be divided by. For example, if you have halves and quarters, you can use fourths as the common denominator.
  3. Convert the fractions: Change each fraction so they both have the same denominator.
  4. Subtract the numerators: Take away the top numbers (numerators) and keep the denominator the same.
  5. Simplify if needed: If the answer can be simplified (like 4/8 becomes 1/2), do it.

Examples you can see

Let's try a few examples together. Example 1: You have 3/4 of a pizza and you eat 1/4 of it. How much pizza is left? Step 1: The denominators are the same (4), so we don't need to change them. Step 2: Subtract the numerators: 3 - 1 = 2. Step 3: The answer is 2/4. Step 4: Simplify 2/4 to 1/2. So, you have 1/2 of the pizza left. Example 2: You have 5/6 of a chocolate bar and you give away 2/6 of it. How much is left? Step 1: The denominators are the same (6), so we don't need to change them. Step 2: Subtract the numerators: 5 - 2 = 3. Step 3: The answer is 3/6. Step 4: Simplify 3/6 to 1/2. So, you have 1/2 of the chocolate bar left. Example 3: You have 3/5 of a cake and you eat 1/10 of it. How much cake is left? Step 1: The denominators are 5 and 10. These are related because 10 is a multiple of 5. Step 2: We will use 10 as the common denominator. Step 3: Convert 3/5 to tenths: 3/5 = 6/10 (because 3 × 2 = 6 and 5 × 2 = 10). Step 4: Now we have 6/10 - 1/10. Step 5: Subtract the numerators: 6 - 1 = 5. Step 6: The answer is 5/10. Step 7: Simplify 5/10 to 1/2. So, you have 1/2 of the cake left.

Try it as a mini adventure

The Great Fraction Bakery Challenge You are the head baker at a magical bakery that makes fractional cakes! Your job is to make sure you always have the right amount of ingredients for your cakes. You are making a special cake that needs 7/8 of a cup of sugar, but you already used 3/8 of a cup. How much sugar do you still need to add? Step 1: What do we need to do? We need to subtract 3/8 from 7/8. Step 2: The denominators are the same (8), so we can go straight to subtracting. Step 3: 7 - 3 = 4. Step 4: So, you need 4/8 of a cup more sugar. Step 5: Simplify 4/8 to 1/2. You need 1/2 a cup of sugar more. Now, you have another challenge: You have 9/12 of a batch of cookies and you eat 3/12 of them. How many cookies are left? Step 1: Subtract 3/12 from 9/12. Step 2: The denominators are the same (12). Step 3: 9 - 3 = 6. Step 4: The answer is 6/12. Step 5: Simplify 6/12 to 1/2. You have 1/2 of the batch of cookies left.

Common mistakes

  • Mistake: Forgetting to make the denominators the same before subtracting. Why it happens: The child may not understand that fractions with different denominators cannot be directly subtracted. Fix: Always check if the denominators are the same. If not, find a common denominator first.
  • Mistake: Subtracting the denominators instead of the numerators. Why it happens: Confusion between the roles of numerators and denominators. Fix: Remember that numerators are the top numbers (what we subtract) and denominators are the bottom numbers (what stays the same).
  • Mistake: Forgetting to simplify the final answer. Why it happens: Children may not know how to simplify or think it's not necessary. Fix: Always check if the fraction can be simplified by finding a common factor in the numerator and denominator.

Parent and carer guide

Helping your child with subtracting fractions with related denominators can be fun and easy! Here are some tips:
  • Use real-life examples: Think about sharing food, like pizza or cake, to make the concept more tangible.
  • Visual aids: Draw circles or rectangles and divide them to show fractions. This helps children see what's happening.
  • Practice with games: Use fraction cards or online games to make practice more engaging.
  • Encourage checking: After solving, ask your child to add the answer back to the fraction they subtracted from to see if they get the original fraction.
  • Be patient: It's normal for children to make mistakes at first. Use them as learning opportunities.

Practice questions

  1. What is 5/6 - 2/6? Answer: 3/6 or 1/2
  2. What is 7/10 - 3/10? Answer: 4/10 or 2/5
  3. What is 9/12 - 5/12? Answer: 4/12 or 1/3
  4. What is 4/5 - 1/5? Answer: 3/5
  5. What is 11/15 - 6/15? Answer: 5/15 or 1/3
  6. What is 8/9 - 3/9? Answer: 5/9
  7. What is 6/8 - 2/8? Answer: 4/8 or 1/2
  8. What is 10/11 - 4/11? Answer: 6/11
  9. What is 3/7 - 1/7? Answer: 2/7
  10. What is 13/14 - 9/14? Answer: 4/14 or 2/7

FAQ

What does "related denominators" mean?

Related denominators are denominators that are connected, like 2 and 4, or 3 and 6. One can be divided by the other, or they can both be divided by the same number to make them the same.

Do I always need to simplify my answer?

Yes, if the fraction can be simplified (if the numerator and denominator have a common factor), you should simplify it to its lowest form.

Can I subtract fractions with different denominators?

Yes, but first you must find a common denominator. This is done by finding a number that both denominators can divide into evenly.

Why is it important to find a common denominator?

It's important because you can only subtract fractions that have the same size parts. If the parts are different sizes, you can't directly take away one from the other.

What if I can't simplify the fraction?

If the numerator and denominator have no common factors other than 1, then the fraction is already in its simplest form and does not need to be simplified.