What Is 1/3 Divided by 4/5? | Fraction Division Made Clear

The result is 5/12, found by multiplying 1/3 by the reciprocal of 4/5.

You typed “What Is 1/3 Divided by 4/5?” because fraction division can feel slippery. One minute you’re dividing, the next minute you’re flipping things, and it’s easy to lose the thread. This page gives you a clean way to do it, plus a couple of fast checks so you can trust your answer.

We’ll solve the exact problem, show what each move means, and then lock it in with a couple of sanity checks you can run on any similar question. No fluff. Just the math you need, in the order you need it.

What Is 1/3 Divided by 4/5? Step-by-step method

Start with the division problem:

1/3 ÷ 4/5

Step 1: Keep the first fraction

The first fraction (1/3) stays as it is. In fraction division, the first fraction is the amount you start with.

Step 2: Change division to multiplication

Rewrite the division sign as a multiplication sign:

1/3 × (something)

Step 3: Flip the second fraction

The second fraction (4/5) flips to its reciprocal (5/4). A reciprocal is what you get when the top and bottom swap places.

So the problem becomes:

1/3 × 5/4

Step 4: Multiply across

Multiply the numerators (tops), then multiply the denominators (bottoms):

(1 × 5) / (3 × 4) = 5/12

Step 5: Simplify if possible

5/12 is already in lowest terms. The number 5 has factors 1 and 5. The number 12 has factors 1, 2, 3, 4, 6, 12. No shared factor beyond 1, so the fraction stays 5/12.

That’s the full solution: 1/3 ÷ 4/5 = 5/12.

1/3 ÷ 4/5 With Fractions: The Clean Setup

If you want a fast setup that stays readable, write fraction division in one line like this:

a/b ÷ c/d = a/b × d/c

Now plug in your numbers:

1/3 ÷ 4/5 = 1/3 × 5/4

Then multiply:

1 × 5 = 5

3 × 4 = 12

Answer: 5/12

This “multiply by the reciprocal” rule is standard in school math and matches what you’ll see in reputable lessons like OpenStax and Khan Academy. If you want a quick refresher from a trusted text, OpenStax walks through multiplying and dividing fractions in a clear sequence: OpenStax section on multiplying and dividing fractions.

Why flipping the second fraction works

Fraction division is tied to the idea of “how many groups.” When you divide A by B, you’re asking how many Bs fit into A.

Try the same thought with whole numbers first. If you have 12 cookies and pack them into bags of 3, you do 12 ÷ 3. You’re counting how many groups of 3 fit into 12.

With fractions, it’s the same style of question, just with smaller group sizes. When you do 1/3 ÷ 4/5, you’re asking:

• How many groups of size 4/5 fit into 1/3?

Since 4/5 is bigger than 1/3, you already know the answer must be less than 1. That one sentence is a handy mental check. If your final answer comes out bigger than 1, something went off the rails.

The “flip and multiply” step is a shortcut that comes from inverse operations. Multiplication and division undo each other. The reciprocal is the number that undoes a fraction under multiplication, since a fraction times its reciprocal equals 1. Khan Academy explains this idea in plain language and uses the same rule you used above: Khan Academy dividing fractions review.

Two quick checks that catch most mistakes

You don’t need extra pages open to check your work. Two fast checks keep you honest.

Size check

Since 1/3 is smaller than 4/5, dividing 1/3 by 4/5 must give a number smaller than 1. Your result, 5/12, is smaller than 1. Good sign.

Reverse check

If 1/3 ÷ 4/5 = 5/12, then multiplying the result by 4/5 should bring you back to 1/3.

Compute it:

5/12 × 4/5 = (5 × 4) / (12 × 5) = 20/60

Simplify 20/60 by dividing top and bottom by 20:

20/60 = 1/3

You landed back at 1/3, so the division result checks out.

How to avoid the classic slip-ups

Most wrong answers come from one of a few habits. If you can spot them, you can fix them fast.

Flipping the wrong fraction

Only the second fraction (the divisor) gets flipped. In 1/3 ÷ 4/5, only 4/5 turns into 5/4. If you flip 1/3 by mistake, you change the whole question.

Forgetting to change division to multiplication

After you flip the second fraction, you multiply. If you keep the division sign, your next step won’t match the reciprocal rule, and your arithmetic will drift.

Multiplying across incorrectly

When you have 1/3 × 5/4, you multiply top with top and bottom with bottom. A common mix-up is cross-multiplying like you might do when comparing fractions. Cross-multiplying is a different move for a different task.

Simplifying the wrong way

When you simplify, you divide the numerator and denominator by the same number. You can’t subtract the same number from both, and you can’t cancel terms that are added. Cancelling works with multiplication, not addition.

Mid-article practice table for pattern spotting

Once you’ve solved one problem, the next win is seeing the pattern. The table below gives a set of fraction-division problems, the reciprocal rewrite, and the simplified result. Use it to train your eyes to spot when an answer should land under 1, equal 1, or rise above 1.

Division problem	Rewrite as multiplication	Simplified result
1/3 ÷ 4/5	1/3 × 5/4	5/12
2/3 ÷ 5/6	2/3 × 6/5	4/5
3/4 ÷ 1/2	3/4 × 2/1	3/2
5/8 ÷ 5/8	5/8 × 8/5	1
7/10 ÷ 7/5	7/10 × 5/7	1/2
9/11 ÷ 3/11	9/11 × 11/3	3
4/9 ÷ 2/3	4/9 × 3/2	2/3
1/5 ÷ 2/25	1/5 × 25/2	5/2

A visual way to think about 1/3 ÷ 4/5

Some learners like a picture-based meaning. Here’s a clean way to frame it without drawing anything.

Ask: “How many 4/5-sized chunks fit into 1/3?” Since 1/3 is smaller than 4/5, you won’t fit a full chunk. You’ll fit a fraction of a chunk.

That fraction of a chunk is the answer, 5/12. It says: you have five-twelfths of one full 4/5 chunk.

If you want to sanity-check with a rough decimal sense (without turning this into a calculator exercise), note that 1/3 is close to 0.333… and 4/5 is 0.8. A number near 0.333 divided by 0.8 should land near 0.416. The fraction 5/12 equals 0.4166…, so it matches that sense check.

How to do it fast in your head with small numbers

With small numerators and denominators, you can make the work lighter by cancelling before you multiply. This keeps numbers from ballooning.

Cancel before multiplying

Start from the rewrite:

1/3 × 5/4

Look for shared factors across a numerator and the opposite denominator. Here, 1 shares no factor with 4, and 5 shares no factor with 3. So there’s nothing to cancel early, and you multiply straight across to get 5/12.

On other problems, early cancelling can save time. In the table above, 9/11 × 11/3 collapses fast because 11 cancels, leaving 9/3, then 3.

Where this shows up outside homework

Fraction division pops up in everyday tasks that involve “how many groups” thinking.

• Cooking: You have 1/3 cup of something and a recipe calls for 4/5 cup per batch. Fraction division tells you what fraction of a batch you can make.
• Measuring fabric: You have 1/3 yard left and each piece needs 4/5 yard. The quotient tells you what portion of a full piece you can cut.
• Rates: If a unit is “per 4/5 of an hour” and you only have 1/3 of an hour, division compares the time you have with the time unit.

In all cases, the answer under 1 makes sense, since your available amount is smaller than the needed amount.

Second table: Mistakes, what they cause, and the fix

This table is built as a quick error detector. If your answer feels off, scan the left column, match what you did, then apply the fix.

Mistake	What it causes	Fix
Flip the first fraction	Solves a different problem	Keep the first fraction unchanged
Flip both fractions	Answer drifts, often far	Flip only the divisor (second fraction)
Keep the division sign after flipping	Steps stop matching the reciprocal rule	Change “÷” to “×” after the rewrite
Cross-multiply as if comparing fractions	Random-looking result	Multiply top with top and bottom with bottom
Cancel across addition	Invalid simplification	Cancel only across multiplication
Forget the size check	Wrong answer slips through	Ask “Should it be under 1 or over 1?”

A tight recap you can reuse

When you divide by a fraction, you multiply by its reciprocal. For this problem, the reciprocal of 4/5 is 5/4. Multiply 1/3 × 5/4 to get 5/12. Then run the reverse check: 5/12 × 4/5 returns 1/3.

If you can do those two checks, you won’t just get the answer. You’ll know it’s right.