Convert Division to Fraction: Solving 3 ÷ 9 Step by Step

Division to Fraction with Simplification

What fraction results from dividing 3 by 9?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the fraction
00:04 Write division as a fraction
00:09 Let's reduce the fraction, make sure to divide both numerator and denominator
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What fraction results from dividing 3 by 9?

2

Step-by-step solution

Let's write the division exercise:

3:9 3:9

Now let's write it in the form of a simple fraction, remembering that the numerator is on top and the denominator is on the bottom:

39 \frac{3}{9}

We'll divide both the numerator and denominator by a number that divides into both of them, in this case, the number is 3:

3:39:3=13 \frac{3:3}{9:3}=\frac{1}{3}

3

Final Answer

13 \frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division 3 ÷ 9 becomes fraction 39 \frac{3}{9}
  • Technique: Simplify by dividing both numerator and denominator by 3
  • Check: Verify 13×9=3 \frac{1}{3} \times 9 = 3 gives original dividend ✓

Common Mistakes

Avoid these frequent errors
  • Flipping numerator and denominator
    Don't write 3 ÷ 9 as 93 \frac{9}{3} = 3! This reverses the division and gives the wrong result. The dividend (3) goes on top and divisor (9) goes on bottom. Always write a ÷ b as ab \frac{a}{b} .

Practice Quiz

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Write the fraction shown in the diagram as a number:

FAQ

Everything you need to know about this question

Why does 3 ÷ 9 become a fraction with 3 on top?

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In division, the first number (dividend) becomes the numerator and the second number (divisor) becomes the denominator. So 3 ÷ 9 = 39 \frac{3}{9} .

How do I know what number to divide by when simplifying?

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Find the greatest common factor (GCF) of both numbers. For 3 and 9, the GCF is 3 since both numbers are divisible by 3.

Can I leave my answer as 39 \frac{3}{9} ?

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While 39 \frac{3}{9} is correct, it's not in simplest form. Always simplify fractions to their lowest terms: 39=13 \frac{3}{9} = \frac{1}{3} .

What if the division doesn't simplify evenly?

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That's fine! Some fractions like 29 \frac{2}{9} can't be simplified further because 2 and 9 share no common factors except 1.

How can I check if my simplified fraction is correct?

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Multiply your simplified fraction by the original divisor: 13×9=3 \frac{1}{3} \times 9 = 3 . If you get the original dividend, you're right!

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