Convert Fraction 12/5 to Mixed Number: Step-by-Step Solution

Improper Fractions with Division Method

Write the fraction as a mixed number:

125= \frac{12}{5}=

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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
00:03 Break down 12 into 10 plus 2
00:07 Break into whole number and remainder
00:18 Convert from whole fraction to whole number, and combine with mixed fraction
00:24 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:

125= \frac{12}{5}=

2

Step-by-step solution

To convert the improper fraction 125 \frac{12}{5} into a mixed number, we need to understand how to express the fraction as a combination of a whole number and a proper fraction.

  • Step 1: Divide the numerator by the denominator. We have 12÷5 12 \div 5 .
  • Step 2: Perform the division.
    When dividing 12 by 5, the quotient is 2, since 5×2=10 5 \times 2 = 10 . This gives us the whole number part of the mixed number.
  • Step 3: Determine the remainder.
    The remainder is 1210=2 12 - 10 = 2 . This remainder becomes the numerator of the fractional part.
  • Step 4: Write the mixed number.
    Using the quotient and remainder, we express the fraction as a mixed number: 225 2\frac{2}{5} .

Therefore, the fraction 125 \frac{12}{5} as a mixed number is 225 2\frac{2}{5} .

3

Final Answer

225 2\frac{2}{5}

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: 12 ÷ 5 = 2 R2
  • Check: Convert back: 2 × 5 + 2 = 12, so 225=125 2\frac{2}{5} = \frac{12}{5}

Common Mistakes

Avoid these frequent errors
  • Using the wrong remainder as numerator
    Don't just subtract any multiple from 12 = wrong fractional part! Students often use 12 - 5 = 7 instead of 12 - 10 = 2. Always subtract the largest multiple of the denominator that fits into the 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

How do I know when a fraction is improper?

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A fraction is improper when the numerator is larger than or equal to the denominator. Since 12 > 5, the fraction 125 \frac{12}{5} is improper and can be converted to a mixed number.

Why do I need to find how many times 5 goes into 12?

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This division tells you the whole number part of your mixed number! 5 goes into 12 exactly 2 times with some left over, so 2 becomes your whole number.

What if there's no remainder when I divide?

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If there's no remainder, then your fraction equals a whole number! For example, 105=2 \frac{10}{5} = 2 with no fractional part needed.

Can I convert a mixed number back to an improper fraction?

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Yes! Multiply the whole number by the denominator, add the numerator: 225=(2×5)+25=125 2\frac{2}{5} = \frac{(2×5)+2}{5} = \frac{12}{5}

What's the easiest way to check my work?

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Convert your mixed number back to an improper fraction using the formula above. If you get the original fraction, you're correct!

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