Fractions and times tables
Use multiplication facts to simplify and find equivalent fractions.
Quick answer
You can use times tables to help you find equivalent fractions and simplify fractions. When you multiply or divide both the top and bottom numbers (the numerator and denominator) by the same number, you get an equivalent fraction.
Learning outcome
By the end of this page, you will understand how to use your times tables to find equivalent fractions and simplify fractions. You will be able to:
- Find equivalent fractions by multiplying or dividing both parts by the same number
- Simplify fractions by dividing both parts by a common times table number
- Use your knowledge of multiplication to solve fraction problems
- Apply this to real-life situations like sharing food or dividing up playtime
Why this matters
Fractions and times tables work together to help you solve problems in everyday life. When you share a pizza with friends, you use fractions. When you play games or divide up your toys, you use times tables. Understanding how they connect helps you:
- Work out how to share things fairly
- Compare different amounts
- Measure ingredients for recipes
- Understand scores in sports
- Make better decisions about money and time
These skills are important for school maths and for understanding how the world works around you!
How it works
Let's learn how to use multiplication and division to work with fractions:
- Find equivalent fractions: Multiply both the top and bottom numbers by the same number
- Simplify fractions: Divide both the top and bottom numbers by the same number
- Use times tables: Think about which multiplication facts help you find the right number to multiply or divide by
Remember: When you multiply or divide both parts of a fraction by the same number, you get an equivalent fraction that looks different but means the same thing!
Examples you can see
Let's look at how times tables help us with fractions:
Example 1: Finding equivalent fractions
Imagine you have 1/2 of a pizza. You want to know how many slices that is if the pizza is cut into 8 pieces instead of 4.
What times table can help? 2 × 4 = 8
So we multiply both top and bottom by 4:
| Original fraction | Multiply by 4 | New fraction |
|---|---|---|
| 1/2 | 1 × 4 / 2 × 4 | 4/8 |
So 1/2 = 4/8 - they are the same amount!
Example 2: Simplifying fractions
Imagine you have 6/12 of a cake. You want to know what fraction that is in its simplest form.
What times table can help? 6 × 2 = 12 and 6 ÷ 6 = 1
So we divide both top and bottom by 6:
| Original fraction | Divide by 6 | Simplified fraction |
|---|---|---|
| 6/12 | 6 ÷ 6 / 12 ÷ 6 | 1/2 |
So 6/12 = 1/2 - they are the same amount!
Example 3: Real-world problem
Sammy has 15 stickers and wants to share them equally between 3 friends. What fraction of the stickers does each friend get?
First, we need to know: 15 ÷ 3 = 5
So each friend gets 5 stickers out of 15 total stickers.
That's 5/15 of the stickers.
Now we can simplify this fraction using times tables:
What times table helps us simplify 5/15?
5 × 3 = 15 and 5 ÷ 5 = 1
| Original fraction | Divide by 5 | Simplified fraction |
|---|---|---|
| 5/15 | 5 ÷ 5 / 15 ÷ 5 | 1/3 |
Each friend gets 1/3 of the stickers!
Try it as a mini adventure
Adventure: The Fraction Bakery
You are a baker in a magical bakery where fractions come to life! Your task is to make equivalent cakes using different sized ingredients.
First challenge: You have a recipe that uses 2 cups of flour to make 1 cake. You want to make 4 cakes. How much flour do you need?
Step 1: What times table helps? 2 × 2 = 4
Step 2: Multiply both parts of 2/1 by 2
Step 3: 2 × 2 / 1 × 2 = 4/2
Step 4: This means you need 4 cups of flour for 2 cakes
Second challenge: You made 8 cakes but only used 4 cups of flour. What fraction of flour did you use for each cake?
Step 1: 4 ÷ 8 = 1/2
Step 2: Each cake used 1/2 cup of flour
Step 3: You can also think of it as 4/8 = 1/2
Step 4: 1/2 cup per cake
Common mistakes
- Mistake: Only multiply or divide one part of the fraction, not both
Why it happens: Confusing fraction rules with addition or subtraction
Fix: Always multiply or divide both top and bottom by the same number - Mistake: Using the wrong times table to simplify fractions
Why it happens: Not knowing which number divides both parts evenly
Fix: Find the biggest number that goes into both parts (highest common factor) - Mistake: Thinking 2/4 = 1/2 because 2 is half of 4
Why it happens: Confusing the concept of "half" with fraction simplification
Fix: Remember to divide both parts by the same number - 2/4 = 1/2 because 2÷2 = 1 and 4÷2 = 2 - Mistake: Forgetting that equivalent fractions are the same size
Why it happens: Not visualizing fractions as parts of the same whole
Fix: Use drawings or physical objects to see that 1/2 and 2/4 are the same amount
Parent and carer guide
Helping your child with fractions and times tables is easier than you think:
- Start with real objects: Use pizza slices, cookies, or blocks to show how fractions work
- Ask questions: "If we have 12 cookies and 3 friends, how many does each get?"
- Use times tables: Point out that 3 × 4 = 12, so 12 ÷ 3 = 4
- Play games: Use fraction cards or online games that involve multiplication
- Be patient: It's normal to get confused at first - practice makes progress!
- Watch for frustration: If they're getting upset, take a break and come back later
- Connect to daily life: Cooking, sharing snacks, or dividing up toys all use fractions
- Encourage mistakes: "Let's see what happens when we try that"
- Practice regularly: 5-10 minutes daily is better than one long session
- Be positive: Celebrate small wins and progress, not just perfect answers
Practice questions
- What fraction is equivalent to 3/4 when multiplied by 2?
Answer: 6/8 - What is 8/12 simplified using times tables?
Answer: 2/3 - Find an equivalent fraction to 5/10 by multiplying by 3.
Answer: 15/30 - What is 10/15 simplified?
Answer: 2/3 - What fraction is equivalent to 1/3 when multiplied by 5?
Answer: 5/15 - Find the simplest form of 9/18.
Answer: 1/2 - What fraction is equivalent to 2/5 when multiplied by 4?
Answer: 8/20 - What is 6/24 simplified?
Answer: 1/4 - Find an equivalent fraction to 4/6 by multiplying by 2.
Answer: 8/12 - What is 12/16 simplified using times tables?
Answer: 3/4
FAQ
What is the connection between fractions and times tables?
Fractions and times tables are connected because you can use multiplication facts to find equivalent fractions and division facts to simplify fractions. When you multiply or divide both the top and bottom of a fraction by the same number, you get an equivalent fraction.
How do I know which times table to use?
Look for the biggest number that goes into both the numerator and denominator. For example, with 6/12, you can use 6 because 6 × 2 = 12 and 6 ÷ 6 = 1. The largest number that divides both is 6, so you divide by 6 to simplify.
Can I use any number to multiply or divide fractions?
No, you must multiply or divide both the top and bottom by the same number. If you only change one part, the fraction changes its value. For example, 2/3 × 2 = 4/3 (not 4/6).
Why do we need to simplify fractions?
Simplifying fractions makes them easier to understand and work with. It's like having 2/4 of a pizza instead of 8/16 - they're the same amount, but 2/4 is simpler to think about.
How can I practice at home?
Practice with everyday activities like sharing food, dividing up toys, or cooking. Ask questions like "If we have 12 cookies and 4 people, what fraction does each person get?" or "What's the same as 3/6?" Use times tables to help find the answers.