Which Is Bigger: 3/4 or 2/3?
You've probably been here before. Plus, a recipe says three-quarters of a cup, but you only have a two-thirds measuring cup. Or maybe a kid asks you a homework question, and you pause for half a second — which one is actually bigger?
Here's the short version: 3/4 is bigger than 2/3. The difference isn't huge, but it's real. And there's a clean way to figure this out every single time, even when the numbers get trickier. Let me walk you through it.
What We're Actually Comparing
Both 3/4 and 2/3 are fractions* — numbers that represent parts of a whole. Which means the bottom number (the denominator*) tells you how many equal pieces something is split into. The top number (the numerator*) tells you how many of those pieces you've got.
So 3/4 means you've got 3 pieces out of 4 total. 2/3 means you've got 2 pieces out of 3 total. Practically speaking, on the surface, 3 feels like more than 2, and 4 feels like more than 3 — but that comparison doesn't really tell you anything, because the denominators are different. You're not comparing the same size of pieces.
That's the whole trick to fractions. Different denominators mean different piece sizes, and you can't just eyeball the top numbers and call it a day.
The Quick Trick: Cross-Multiplication
This is the method teachers love because it works every single time, no matter what fractions you throw at it.
You take the numerator of the first fraction and multiply it by the denominator of the second. In real terms, then you do the reverse — numerator of the second times denominator of the first. Whichever product is bigger, that fraction is bigger.
For 3/4 vs. 2/3:
- 3 × 3 = 9
- 2 × 4 = 8
9 is bigger than 8, so 3/4 wins. Done.
This works because you're really asking, "What's the smallest number where both denominators line up evenly?" — a common denominator — without having to find it. You're just doing a shortcut version of the same comparison.
Doing It the "Long Way" — Common Denominators
If you want the old-school version, you find the lowest common denominator* and convert both fractions so they share the same bottom number. For 4 and 3, the smallest shared number is 12.
- 3/4 = 9/12 (multiply top and bottom by 3)
- 2/3 = 8/12 (multiply top and bottom by 4)
Now it's easy. 9 out of 12 is more than 8 out of 12. Same answer.
Honestly, both methods work fine. So the cross-multiplication trick is faster once you get used to it. The common denominator method is easier to visualize if you're a more visual learner.
A Visual Way to Think About It
Picture a pizza. Cut it into 4 equal slices, and take 3 of them. That's 3/4 — you've left just one little sliver behind.
Now picture another pizza. In real terms, cut it into 3 equal slices, and take 2 of them. That's 2/3 — you've left one bigger slice behind.
The slice you left behind in the 3/4 pizza is small. The slice you left behind in the 2/3 pizza is bigger. So yeah, 3/4 gives you more pizza. Same logic applies whether you're talking about pizza, cups of flour, hours of your day, or anything else that can be split into parts.
Why This Comes Up More Than You'd Think
You'd be surprised how often this comparison sneaks into real life. Even so, cooking and baking is a big one — recipes use fractions constantly, and they don't always agree with each other. Plus, one recipe calls for 3/4 cup, another calls for 2/3. Knowing which is more helps you scale things up or down without breaking the dish.
It shows up in construction too. And if you're measuring lumber, fabric, or anything that comes in fractional inches, the difference between 3/4" and 2/3" actually matters. A loose fit versus a snug one.
And honestly? Kids hit this stuff in third or fourth grade, and a lot of them freeze up because nobody taught them the trick. School. They just get told to "find a common denominator" and they nod along without really getting it.
Want to learn more? We recommend where can a chemical system be found and plasmonic excitation can be used for cooling heating for further reading.
Common Mistakes People Make
Comparing the Numerators Alone
This is the big one. 3 is more than 2, so 3/4 must be more than 2/3, right? Not necessarily. The denominator changes the size of each piece, so you can't just look at the top number. If you compared 1/2 to 1/100, both have a numerator of 1 — but 1/2 is way bigger. The denominator is doing more work than people realize.
Assuming Bigger Denominator Means Smaller Fraction
A lot of people assume that because 4 is bigger than 3, 3/4 must be smaller than 2/3. Here's the thing — they aren't here. The logic sort of makes sense in a fuzzy way — "more pieces means smaller pieces" — but it only works if the numerators are the same. So that shortcut breaks down.
Forgetting the Pieces Are Different Sizes
This is the underlying issue behind both mistakes. On the flip side, when denominators differ, the "pieces" aren't the same size. And once you really internalize that, the rest of it gets a lot easier.
Practical Tips for Comparing Fractions
When Both Denominators Are Small
Under 12 or so? Just find the common denominator and convert. It's fast, and you'll get a clear answer you can actually picture.
When Numbers Get Bigger
Say you're comparing 7/9 and 5/7. Think about it: finding a common denominator means you'd be working with 63 — which is annoying. Here's the thing — cross-multiply instead. 7 × 7 = 49, 5 × 9 = 45.49 is bigger, so 7/9 is bigger. Way less work.
Convert to Decimals
If fractions just aren't clicking for you, plug them into a calculator and compare the decimal forms. 3/4 = 0.75 and 2/3 ≈ 0.On top of that, 667. Done. This isn't cheating, and it's actually really handy in everyday situations.
Draw It Out
Seriously. If you're stuck, draw two bars. Also, split one into 4 equal parts and shade 3. Split the other into 3 equal parts and shade 2. In real terms, the shaded area tells the whole story. This is the method I'd teach a kid first, because once you see it, the numbers start making sense.
Use Benchmark Fractions
Memorize a few anchor points: 1/2 = 0.Consider this: 5, 1/4 = 0. Because of that, 25, 3/4 = 0. Day to day, 75, 1/3 ≈ 0. 33, 2/3 ≈ 0.67. If a fraction is way above or below those markers, you can usually estimate which is bigger without doing any real math.
FAQ
Is 3/4 greater than 2/3?
Yes. Which means 3/4 equals 0. So naturally, 75 and 2/3 equals roughly 0. 667. So 3/4 is bigger by about 0.083, or 1/12 if you want to be exact about it.
How much bigger is 3/4 than 2/3?
The difference is 1/12. 3% if you're thinking in percentages. That's about 8.Small, but noticeable depending on what you're measuring.
How do I compare fractions without a calculator?
Cross-multiplication is your best friend. Multiply the top of one fraction by the bottom of the other, then compare the two products. Bigger product equals bigger fraction. Works every time, no calculator needed.
What's the easiest way to explain this to a kid?
Draw two rectangles. Here's the thing — cut one into 4 equal slices and color in 3. Cut the other into 3 equal slices and color in 2. But ask which one has more color. They'll get it immediately.
Are there any cases where this gets confusing?
Only when fractions have the same numerator or the same denominator. If the bottoms are the same, the bigger top number wins.
