What Is 1 Divided By 1 3

Okay, this one starts with a little honest confusion. "What is 1 divided by 1 3" is the kind of search query where the person typing it probably isn't even sure what they're asking. That's why are we dividing 1 by 13? Now, dividing 1 by 1, then by 3? Solving some weird expression with a missing symbol? All of the above, depending on how you read it.

So instead of picking one interpretation and pretending the others don't exist, let's walk through every reasonable way to read this — and end up at the answer that actually makes sense.

What "1 Divided by 1 3" Probably Means

Here's the thing — in most cases when someone types something like this, they're trying to figure out a math expression and got a little lost on the keyboard. The most likely intended question is one of these:

• What is 1 divided by 1/3? (one divided by one-third)
• What is 1 divided by 13? (one divided by thirteen)
• What is 1 ÷ 1 ÷ 3? (worked left to right)

Each one gives a totally different answer. So the real first step is figuring out which problem you're actually trying to solve.

If You Mean 1 ÷ (1/3)

This is the interpretation that trips up the most people, so let's start here.

One-third is a fraction. To divide by a fraction, you flip it upside down and multiply. That's the rule, and it works every time.

So:

1 ÷ (1/3) = 1 × (3/1) = 3

That feels weird to a lot of people at first. To figure out how many of those small slices fit into a whole pizza, you'd need three of them. But think about it this way: one-third of a pizza is a small slice. How can dividing 1 by something give you a bigger number? So 1 ÷ (1/3) = 3 makes perfect sense once you stop overthinking it.

This is also the version of the problem that comes up most in school math, especially when students first learn about dividing by fractions. Teachers love this one because the answer surprises almost everyone the first time.

If You Mean 1 ÷ 13

This one's straightforward — no tricks, no flipping required.

1 ÷ 13 = roughly 0.0769...

It repeats forever, actually. Because of that, the decimal expansion of 1/13 is 0. 076923076923..., with the pattern 076923 repeating. It's one of those quirky numbers that shows up in recreational math. Some people find that pattern oddly satisfying.

If you're doing this on a calculator, you'll usually get something like 0.Day to day, 0769230769 rounded off, but the true answer never ends. It just keeps cycling through the same six digits.

If You Mean (1 ÷ 1) ÷ 3

Read the problem strictly left to right, like you would in most programming languages and like the old PEMDAS-style order suggests for a chain of same-operation problems.

1 ÷ 1 = 1

Then 1 ÷ 3 = 1/3, or about 0.3333...

This one's the simplest of the bunch, and the answer is exactly what you'd guess going in. No surprises. Small thing, real impact.

If You Mean 1 ÷ (1 × 3)

Maybe the "1 3" was meant to be 1·3, and you forgot the multiplication sign. In that case:

1 × 3 = 3

Then 1 ÷ 3 = 1/3, or about 0.333...

Same answer as the version above, but for a different reason.

Why the Confusion Happens

Honestly? That's why in a textbook, everything is clear — fractions sit on top of each other, division uses a proper ÷ or a slash, parentheses are everywhere. Math notation is brutal when you're typing it out. On a phone keyboard or in a search bar, all of that collapses into a string of numbers and spaces, and suddenly "1 divided by 1/3" becomes "1 divided by 1 3" because the slash and the space got lost.

This is one of those tiny human moments where the tool (a search engine, a calculator, a homework helper) ends up doing the right thing only if it guesses what you meant. Consider this: most calculators will read "1/1/3" left to right and give you 1/3, not 3. So if you actually wanted the first interpretation we covered, you'd need to type it as 1/(1/3) or 1÷(1÷3).

Worth knowing if you've been getting answers that don't match what your teacher or textbook shows.

Want to learn more? We recommend how many days until january 17 and square footage calculator with feet and inches for further reading.

How to Tell Which One You Actually Want

Here's a quick gut-check. Ask yourself: does the answer feel like it should be a small number, or a big one?

• If you expect something small (a fraction less than 1), you're probably looking at 1 ÷ 13, 1 ÷ 3, or one of the left-to-right versions.
• If the answer is supposed to be 3 or thereabouts, you're definitely looking at 1 ÷ (1/3).

Most people searching this query are students running into the "divide by a fraction" lesson for the first time, and the expected answer is 3. Day to day, that's the version with the surprising, "wait, really? " reaction. The others are more routine.

Common Mistakes With This Kind of Problem

A few things go wrong consistently when people try to work out problems like this.

Mixing up the rule. The "flip and multiply" rule for dividing fractions is solid, but people sometimes flip the wrong number. If the problem is 1 ÷ (1/3), you flip the 1/3 to get 3/1. You do not flip the 1.

Reading left to right in the wrong context. In arithmetic, division and multiplication have the same priority and you go left to right. But in a written problem like 1 ÷ 1/3, the fraction bar groups things together, so it's really 1 ÷ (1/3), not (1 ÷ 1)/3. Context matters more than order of operations here.

Stopping at the first interpretation. If you typed the question in a hurry, you might get an answer and just go with it, even if it's not the answer that matches your homework. Double-check by reading the original problem out loud. "One divided by one-third" sounds very different from "one divided by one, divided by three."

What Actually Helps

If you're stuck on a problem like this and the search results aren't making sense, try rewriting it yourself before searching. Which means type the whole thing as code, like 1 / (1/3) or 1 / 13, and run it in a calculator app. That removes the guesswork.

If you're a student, write the original problem down on paper. Plus, the act of writing fractions as actual stacked fractions (numerator over denominator) tends to clear up ambiguity almost immediately. Your brain processes visual fractions differently from typed ones.

And if a teacher or textbook gave you the problem with the answer 3, the question is almost certainly the first one we covered: 1 ÷ (1/3) = 3.

FAQ

What is 1 divided by 1/3 as a fraction?

It's 3/1, which simplifies to just 3. When you divide by a fraction, you multiply by its reciprocal. The reciprocal of 1/3 is 3/1.

What is 1 divided by 13 in decimal form?

About 0.So a more precise way to write it is 0.So naturally, 076923076923... And 0769, but the digits 076923 actually repeat forever. , with the bar over the repeating part if you want to be formal about it.

Is 1 divided by 1/3 the same as 3 divided by 1?

Yes. They're literally the same problem written two different ways. If 1 ÷ (1/3) = 3, then 3 × (1/3) = 1, which checks out.

Why is dividing by a fraction the same as multiplying by its reciprocal?

Short version: it's a rule that comes out of how fractions work. Because of that, if you have 1 and you want to know how many 1/3-sized pieces fit inside, you need three of them. Mathematically, that's expressed as 1 × 3 = 3, which is the same as 1 ÷ (1/3).

usually enough for day-to-day use.

Wrapping Up

The answer to "what is 1 divided by 1 3" depends entirely on what was actually meant. Here's the thing — in nearly every case involving this exact phrasing, whether from a worksheet, a calculator display, or a standard math problem, it's asking for 1 ÷ (1/3), which equals 3. The alternative, (1 ÷ 1)/3, equals 1/3, and is rarely what's intended since it's a strange way to write such a simple problem.

If your search results are showing both answers, look at the source. Worth adding: homework sites and textbook PDFs almost always mean the first one. Random number-typing sites or encoding errors are more likely to produce the second.

When in doubt, rewrite the problem from scratch. Stack the fraction, use parentheses, or run it through a calculator with code-style input. The few extra seconds it takes will save you the confusion of sorting through conflicting answers later.