1/2 and 2/4 land on exactly the same point. They are the same amount.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Why it works
Cut every piece in two. You now have twice as many pieces, each half the size.
Both numbers change together
Twice as many pieces means twice the top number and twice the bottom number.
More pieces is not more cake
Cutting a cake into more slices does not give you more cake.
Cutting every piece into the same number of parts
Take 2/3 and cut each third into 4 pieces. Now there are 12 pieces and you have 8 of them: 2/3 = 8/12. Both numbers were multiplied by 4 because both the number of pieces you have and the number in the whole were multiplied by 4.
Why the amount does not change
Cutting pieces smaller does not add or remove any of the shape. You end up with more pieces, each proportionally smaller, and the shaded amount is exactly what it was. That is why equivalent fractions are equal rather than merely similar.
Going the other way: simplifying
Dividing top and bottom by the same number groups pieces back together: 8/12 divided by 4 gives 2/3. You can do this whenever top and bottom share a factor. When they share none, the fraction is in its simplest form.
The rule, stated carefully
Multiplying or dividing both the top and the bottom by the same non-zero number gives an equivalent fraction. Both. Doing it to only one changes the value entirely, which is the mistake this rule is most often used to make.
Step 2: Try It Yourself
Tap and try it out.
1/2
2/4
1/2 is equal to 2/4.
Compare how much of the whole each one covers.
Step 3: Watch an Example
One step at a time.
Watch Leo Turn 2/3 into Sixths
Leo wants 2/3 written in sixths.
- Step 1
He cuts each third into 2 pieces, making sixths.
Step 4: Your Turn
Practice makes it stick.
The Same Amount
Problem 1 of 2
3/4 written in eighths has what top number?
The Cake
Problem 2 of 2
1/3 written in twelfths has what top number?
Find the Match
1 of 4
1/2 = ?/10. What is the top number?
2 of 4
2/5 = ?/10. What is the top number?
3 of 4
3/4 = 9/?. What is the bottom number?
4 of 4
Does cutting a cake into more slices give more cake?
Step 5: Quick Check
Show what you know.
Question 1 of 2
2/3 = ?/9. What is the top number?
Question 2 of 2
Why do both numbers change together?
What You Learned
- Equivalent fractions are the same amount written differently.
- Cutting every piece the same way changes both numbers together.
- The amount on the line never moves.