Fill the missing numerator: 3/4 = ?/20.
Give me a hint
How many times larger is the new denominator?
Compare a worked response
15
20 ÷ 4 = 5, so 3 × 5 = 15.
Equivalent fractions & simplest form
Change the name of the parts without changing the amount.
Your learning goal
Generate equivalent fractions and simplify by common factors, with a model to justify each change.
Understand the idea
Split every part in the same way
If each third is split into two equal pieces, thirds become sixths. Two thirds now contains four sixths. The whole stays fixed, so 2/3 = 4/6. The extra lines change the partition, not the amount.
Words worth knowing
- Equivalent fractions
- Fractions that name the same number.
- Common factor
- A non-zero integer that divides both integers exactly.
- Simplest form
- A fraction whose numerator and denominator have no common factor greater than 1.
- Greatest common factor
- The greatest positive integer that divides both integers exactly.
Make it visible
Same amount. A different partition.
Predict a result, change a value, and use the diagram to explain your reasoning.
Predict before changing a value. Every whole in a bar diagram uses the same size. The models use non-negative amounts up to two wholes per input.
Multiply by a form of one
For any non-zero factor k, k/k = 1. Multiplying numerator and denominator by k leaves the value unchanged: 3/5 = 9/15. Multiplying only the numerator or only the denominator changes the value.
Simplify by grouping equal parts
To simplify 12/18, divide both integers by a common factor. Dividing by 6 gives 2/3. You can also divide by 2 and then by 3. The steps differ, but the number does not. Simplest form is useful for communicating an answer clearly.
Choose a useful name for the next task
The simplest form is not always the form you need during a calculation. To add 2/3 to 1/6, writing 2/3 as 4/6 makes equal units visible. Keep equivalent forms available, then simplify the final result.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
Rewrite 5/12 with denominator 36
- 12 × 3 = 36, so use the same factor for the numerator.
- 5 × 3 = 15. Therefore 5/12 = 15/36.
- Check by simplifying 15/36: dividing both integers by 3 returns 5/12.
Simplify 18/24
- A common factor is 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
- 18/24 = 3/4. No positive integer greater than 1 divides both 3 and 4.
- The number is still three quarters, even though the parts have been regrouped.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Is 6/9 in simplest form? Explain and simplify.
Give me a hint
Look for a factor shared by 6 and 9.
Compare a worked response
No; 6/9 = 2/3.
Both integers are divisible by 3. Dividing both by 3 keeps the value unchanged.
Independent practice
Build a strategy you can explain.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Check the concepts, too.
What does the answer mean?
Resizing a recipe keeps the ratio between ingredients constant. Equivalent fractions give you different names for the same proportion.