3/5 and 2/3 cannot be compared by counting, because fifths and thirds are different sizes.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Rewrite both in the same unit
In fifteenths, 3/5 is 9/15 and 2/3 is 10/15. Now they can be counted.
A quicker check
4/9 is less than a half, and 5/8 is more. That settles it without rewriting.
The wholes must match
Half of a small pizza is not more than a third of a huge one. Compare only equal wholes.
Why unlike fractions cannot be compared directly
Comparing 2/3 and 3/5 by looking at the numbers fails: 2 is less than 3, yet 2/3 is the larger fraction. The pieces are different sizes, so the counts are not comparable. You must first rewrite both with the same unit.
Finding a common denominator
Thirds and fifths can both be cut into fifteenths: 2/3 = 10/15 and 3/5 = 9/15. Now both count the same unit, so 10 beats 9 and 2/3 is larger. Fifteen is a common multiple of 3 and 5, which is where the multiples work pays off.
The half benchmark
Sometimes you can compare without any rewriting. 3/8 is less than half, because half of 8 is 4 and you have only 3. And 5/9 is more than half. If one fraction is under a half and the other over, you are done in a second.
Sanity check with a picture
If a comparison feels wrong, draw both fractions as bars of the same length. The picture never lies, and it will tell you immediately whether the arithmetic went astray. Fraction intuition is built by checking against pictures often enough.
Step 2: Try It Yourself
Tap and try it out.
3/5
2/3
3/5 is less than 2/3.
Compare how much of the whole each one covers.
Step 3: Watch an Example
One step at a time.
Watch Ana Compare 3/5 and 2/3
Ana works out which is bigger.
- Step 1
She looks for a unit both can be written in: fifteenths.
Step 4: Your Turn
Practice makes it stick.
The Two Jugs
Problem 1 of 2
One jug is 5/8 full, another 1/2. Which has more?
The Reading
Problem 2 of 2
Ana read 2/5 of her book, Leo 3/8 of his. Who read more, if the books are the same?
Which Is Bigger?
1 of 4
Is 3/4 bigger than 2/3?
2 of 4
3/5 written in tenths has what top number?
3 of 4
Is 4/9 more or less than a half?
4 of 4
Is 5/6 bigger than 7/12?
Step 5: Quick Check
Show what you know.
Question 1 of 2
2/3 written in twelfths has what top number?
Question 2 of 2
Why can you not compare 2/5 and 1/2 by counting?
What You Learned
- Rewrite both fractions in the same unit, then count.
- Comparing to a half is often quicker.
- Both fractions must be of the same whole.