Subtract 3 4 From 2 3
Ever stare at a math problem written as a fraction stacked on top of another fraction and feel your brain do a little hiccup? That's why most of us learned subtracting fractions the "easy" way back in school, but throw a mixed number or a different denominator into the mix and suddenly the whole thing feels like a trap. Yeah. Let's walk through it — slowly enough that it actually sticks this time.
The problem here: subtract 3/4 from 2/3. Now, it's a small-looking problem, but it's a really good one for showing how fraction subtraction actually works. Once you get this, you can do most of them.
What the Problem Actually Says
When someone writes "subtract 3/4 from 2/3," they mean exactly one thing: take the fraction 3/4 away from 2/3. So order matters here, by the way. "Subtract A from B" means B minus A, not A minus B.
2/3 − 3/4 = ?
Both fractions are smaller than 1, and 3/4 is actually bigger than 2/3, which is the first little wrinkle. It's not wrong. Because of that, when you subtract a bigger number from a smaller one, the answer ends up negative. That's fine. It's just a sign that you should expect a negative result going in.
Quick visual check: 2/3 is a little over half, and 3/4 is three quarters. So yes — 3/4 is larger. The difference will be negative.
Why This One Trips People Up
There are really two traps here, and they catch different people for different reasons.
Trap one: the denominators are different. Most of us were taught that you can only subtract fractions directly when the bottom numbers match. 2/3 and 3/4 don't match. So the instinct to just subtract across the top and bottom (and get something like −1/1) is wrong. It feels like it should work, but it doesn't, because the pieces aren't the same size.
Trap two: the answer will be negative. A lot of students see a "minus" sign and expect a positive answer. When the math gives them a negative one, they assume they made an error. They didn't. Negative answers are valid in fraction subtraction — they're just less common in the early practice problems most textbooks give you.
How to Actually Solve It
Here's the method, step by step, the way you'd want to explain it to a friend who's forgotten fifth-grade math.
Find a Common Denominator
You need the bottom numbers to match before you can subtract the tops. The usual move is to find the least common denominator, which is just the smallest number that both denominators divide into evenly.
For 3 and 4, the least common multiple is 12. So we're going to rewrite both fractions as twelfths.
- 2/3 → multiply top and bottom by 4 → 8/12
- 3/4 → multiply top and bottom by 3 → 9/12
Nothing about the value of either fraction has changed. We just cut the wholes into smaller, equal pieces so the two fractions now use the same piece size.
Subtract the Numerators
Now the subtraction is straightforward:
8/12 − 9/12 = −1/12
The denominators stay at 12. Just subtract straight across the tops: 8 minus 9 is negative 1.
Simplify If You Can
−1/12 is already in its simplest form. 1 and 12 don't share any factors other than 1, so there's nothing to reduce. That's your final answer.
A Slightly Faster Way
Once you've done this a few times, you might notice you can skip the rewriting step with a trick called the "butterfly method" or cross-multiplication. It looks like this:
- Multiply the top of the first fraction by the bottom of the second: 2 × 4 = 8
- Multiply the top of the second fraction by the bottom of the first: 3 × 3 = 9
- Subtract: 8 − 9 = −1
- Multiply the two bottoms: 3 × 4 = 12
- Combine: −1/12
Same answer, less writing. Now, useful on a test, worth knowing. This leads to it works because it's secretly doing the common-denominator method in one move. But for understanding what's actually happening, the step-by-step version is better.
Common Mistakes People Make
Forgetting to flip the order. "Subtract 3/4 from 2/3" is not the same as "subtract 2/3 from 3/4." The first is 2/3 − 3/4. The second is 3/4 − 2/3, which gives a positive 1/12. Read the problem carefully.
Subtracting the denominators too. A really common error looks like: 2/3 − 3/4 = −1/1, or worse, −1/0. The denominator never gets subtracted. It only changes when you rewrite both fractions with a new common one.
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Dropping the negative sign. If the answer is negative, write it as negative. Don't just write 1/12 and hope nobody notices. The sign is part of the answer.
Trying to simplify before you subtract. Some students look at 2/3 and 3/4 and try to reduce one of them. But both are already in lowest terms. Nothing to simplify until after you've combined them.
When the Problem Looks Different
This same logic applies to a whole family of problems, not just 2/3 minus 3/4. If you ever see something like "subtract 5/6 from 7/8," the process is identical: find a common denominator, rewrite both fractions, subtract the tops, simplify.
The only real complication comes in when one of the numbers is a mixed number, like "subtract 3/4 from 2 1/3.Here's the thing — " In that case, you'd first turn 2 1/3 into an improper fraction (7/3), then proceed as usual. Negative answers are still on the table, depending on the size of the numbers.
FAQ
What's the answer to 2/3 minus 3/4?
The answer is −1/12. Since 3/4 is the larger fraction, subtracting it from 2/3 leaves a small negative result.
Why do I need a common denominator to subtract fractions?
Fractions with different denominators are using different "sizes" of pieces. You can't reliably subtract pieces of different sizes until you've translated them into a common size. That's what the common denominator does — it makes the pieces comparable.
Can the answer to a fraction subtraction problem be negative?
Absolutely. That said, fractions are no exception. Here's the thing — anytime you subtract a larger value from a smaller one, the result is negative. Negative fraction answers are completely valid.
Do I always have to simplify the answer?
Mathematically, simplified answers are usually preferred, but technically 2/24 and 1/12 are the same number. If you're submitting work for a grade, simplify. If you're sketching something on a napkin, don't sweat it.
Is there a way to check my work?
Yes. Convert both fractions to decimals. And 667 − 0. 083. 0.667, and 3/4 is 0.And −1/12 is about −0.Which means 75 = −0. 2/3 is about 0.Also, 75. 083. The numbers match, so the answer checks out.
So the whole thing boils down to: same denominator, subtract the tops, don't lose the sign. Plus, it's a tiny problem, but the thinking behind it is the same thinking that handles bigger, messier fraction work later on. Get comfortable with it here, and the harder stuff stops feeling hard.
Common Mistakes to Avoid
Even when you know the steps, it's easy to slip up. Here are the most common errors:
Forgetting to find a common denominator. Some students try to subtract 2/3 - 3/4 as 2-3 over 3-4, which gives -1/-1 or 1. This is completely wrong. You cannot subtract denominators.
Subtracting the denominators instead of finding a common one. The mistake above is part of a larger pattern: treating fraction operations like integer operations. Fractions need special handling.
Losing track of the negative sign. When you get -1/12, writing just 1/12 is like saying you owe someone a dollar but only paying them 12 cents. The negative sign matters.
Not simplifying when possible. While 2/24 and 1/12 are mathematically equivalent, 1/12 is the expected answer. Simplification shows you've completed the problem fully.
Adding instead of subtracting. It happens more than you'd think. Double-check that you're performing the correct operation.
Practice Makes Perfect
Fraction subtraction seems simple, but it's foundational for algebra, calculus, and beyond. Spend time with problems like these:
- 1/2 - 1/3
- 3/5 - 2/7
- 5/6 - 7/8
- 1/4 - 5/6
Work through them slowly at first, focusing on each step. As you gain confidence, you can work more quickly while maintaining accuracy.
Remember: mathematics isn't about memorizing procedures—it's about understanding relationships. When you see 2/3 - 3/4, you're really asking "how much smaller is 2/3 compared to 3/4?" The answer, -1/12, tells you that 2/3 falls short of 3/4 by exactly one twelfth.
That's the power of fractions: they let us measure and compare parts precisely, even when those parts don't divide evenly into whole units. Master this skill now, and you'll find complex mathematical concepts become much more approachable later.
