Convert Fraction 7/2 to Mixed Number: Step-by-Step Solution

Improper Fractions with Division Method

Write the fraction as a mixed number:

72= \frac{7}{2}=

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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
00:04 Break down 7 into 6 plus 1
00:09 Divide into whole fraction and remainder
00:18 Convert from whole fraction to whole number, and combine into mixed fraction
00:23 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:

72= \frac{7}{2}=

2

Step-by-step solution

To convert the fraction 72 \frac{7}{2} into a mixed number, follow these steps:

  • Step 1: Divide the numerator by the denominator. Perform the division 7÷2 7 \div 2 .
  • Step 2: Determine the quotient and remainder. The division 7÷2 7 \div 2 gives a quotient of 3 and a remainder of 1.
  • Step 3: The quotient becomes the whole number part of the mixed number.
  • Step 4: Write the remainder over the original denominator to form the fractional part. So, the remainder 1 over 2 gives the fraction 12\frac{1}{2}.

Therefore, the mixed number is 312 3\frac{1}{2} .

This corresponds to choice 2.

3

Final Answer

312 3\frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Divide numerator by denominator to find whole part
  • Technique: For 72 \frac{7}{2} , calculate 7 ÷ 2 = 3 remainder 1
  • Check: Convert back: 312=72 3\frac{1}{2} = \frac{7}{2} because 3×2+1=7 ✓

Common Mistakes

Avoid these frequent errors
  • Using the wrong number as the whole part
    Don't use the numerator (7) as the whole number = 712 7\frac{1}{2} ! This ignores the division step completely. Always divide first: 7 ÷ 2 = 3 remainder 1, so the whole part is 3.

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 remember which number goes where in the mixed number?

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Think of it like this: quotient becomes the whole number, remainder becomes the new numerator, and the original denominator stays the same. So for 72 \frac{7}{2} : quotient=3, remainder=1, denominator=2 gives 312 3\frac{1}{2} .

What if there's no remainder when I divide?

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Great! That means your fraction was actually a whole number all along. For example, 82=4 \frac{8}{2} = 4 with no fractional part needed.

Can I convert a mixed number back to check my work?

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Absolutely! To convert 312 3\frac{1}{2} back: multiply the whole number by the denominator (3×2=6), then add the numerator (6+1=7). Put this over the original denominator: 72 \frac{7}{2}

Why can't I just guess and check the answer choices?

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While you could convert each choice back to an improper fraction, learning the division method helps you solve any fraction conversion problem, not just multiple choice ones!

What does 'remainder' mean in division?

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The remainder is what's left over after division. When you divide 7 by 2, you get 3 groups of 2 (which equals 6), plus 1 left over. That leftover 1 is your remainder!

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