Scroll to keep cutting the same whole
Step 1 of 5
Start with one chocolate bar
Cut it into 2 equal parts and take 1 part. The shaded amount is one half.
GRADE 4 · A FRACTION SECRET
Why can different fractions be equal?
The numbers look different, so how can they name the same amount? Do not memorize a rule yet. We will cut the same chocolate bar a few more times and let the answer appear.
12
=
24
The shaded length is exactly the same
First, remove a common mistake
“A larger denominator means a larger fraction” is not true. The denominator tells us how many equal parts the whole was cut into. In the same whole, eighths are smaller than halves. You cannot compare fractions by looking only at the denominator.
TURN THE DISCOVERY INTO A RULE
The piece count changed.
The amount did not.
When every piece is cut into the same number of smaller equal pieces, the total number of pieces and the number of shaded pieces grow by the same factor. There are more small pieces, but together the shaded pieces still cover the original half.
12
=
1 × 22 × 2
=
24
The key: cut every part into 2 smaller equal parts, so both the total piece count and the shaded piece count double. Cutting each part into 3 or 4 works the same way, as long as the whole stays the same.
CHECK IT YOURSELF
Keep dividing each half
Choose how many smaller pieces to cut from each part. Watch the numerator and denominator change together while the shaded length stays put.
1/2 = 2/4
There are 4 small parts and 2 are shaded. The shaded amount is still one half of the whole.
The pieces have different names.
They cover the same amount.
1/2 = 2/4 = 4/8, not because we memorized a rule, but because cutting the same whole into smaller pieces cannot add or remove any of it.
A Disassemble course · everywhy.ai