Convert Fraction 8/3 to Mixed Number: Step-by-Step Solution

Improper Fractions with Division Method

Write the fraction as a mixed number:

83= \frac{8}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Write as a mixed fraction
00:07 Break down 8 into 6 plus 2
00:10 Break into whole number and remainder
00:17 Convert from whole fraction to whole number, and add to mixed fraction
00:27 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

Write the fraction as a mixed number:

83= \frac{8}{3}=

2

Step-by-step solution

To convert the improper fraction 83 \frac{8}{3} into a mixed number, we begin by performing long division on 8 by 3.

  • Step 1: Divide 8 by 3. The division gives us 2 as the whole number because 3 fits into 8 two times.
  • Step 2: Calculate the remainder: 8(3×2)=2 8 - (3 \times 2) = 2 .
  • Step 3: Construct the fractional part with the remainder. The remainder over the original denominator gives us 23 \frac{2}{3} .

Therefore, putting it together, 83 \frac{8}{3} as a mixed number is 223 2\frac{2}{3} .

The correct answer is choice 3: 223 2\frac{2}{3} .

3

Final Answer

223 2\frac{2}{3}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Divide numerator by denominator to find whole number part
  • Technique: Use remainder as new numerator: 8 ÷ 3 = 2 remainder 2
  • Check: Convert back: 223=83 2\frac{2}{3} = \frac{8}{3}

Common Mistakes

Avoid these frequent errors
  • Using wrong remainder in fractional part
    Don't write the quotient as the fractional part = backwards answer! Many students write 22 \frac{2}{2} instead of 23 \frac{2}{3} . Always keep the original denominator and use only the remainder as the new numerator.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction as a mixed number:

\( \frac{10}{7}= \)

FAQ

Everything you need to know about this question

What makes a fraction 'improper'?

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A fraction is improper when the numerator is larger than the denominator, like 83 \frac{8}{3} . This means the fraction represents more than one whole unit!

Why do I need to convert to a mixed number?

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Mixed numbers are easier to visualize! 223 2\frac{2}{3} clearly shows you have 2 whole pieces plus 23 \frac{2}{3} of another piece.

What if there's no remainder when I divide?

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Perfect! That means your improper fraction is actually a whole number. For example, 93=3 \frac{9}{3} = 3 with no fractional part needed.

How do I check if my mixed number is correct?

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Convert it back to an improper fraction! Multiply the whole number by the denominator, add the numerator: 2×3+2=8 2 \times 3 + 2 = 8 , so 223=83 2\frac{2}{3} = \frac{8}{3}

Can I simplify the fractional part of a mixed number?

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Always simplify if possible! If your remainder and denominator have common factors, reduce the fraction to its lowest terms before writing your final answer.

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