Convert Fraction 19/2 to Mixed Number: Step-by-Step Solution

Improper Fractions with Division Method

Write the fraction as a mixed number:

192= \frac{19}{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
00:03 Break down 19 into 18 plus 1
00:08 Break down into whole number and remainder
00:16 Convert from whole fraction to whole number, and add to 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:

192= \frac{19}{2}=

2

Step-by-step solution

To convert 192 \frac{19}{2} into a mixed number, let's follow these steps:

  • Step 1: Divide the numerator by the denominator.
    Perform 19÷2 19 \div 2 . The quotient is 9 and the remainder is 1.
  • Step 2: Express the result as a mixed number.
    The quotient 9 will be the whole number part, and the remainder 1 will be the numerator of the fractional part, over the original denominator 2. Therefore, we express the result as 912 9\frac{1}{2} .

Hence, the fraction 192 \frac{19}{2} as a mixed number is 912 9\frac{1}{2} .

3

Final Answer

912 9\frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Divide numerator by denominator to find whole and remainder
  • Technique: 19÷2=9 19 \div 2 = 9 remainder 1 gives 912 9\frac{1}{2}
  • Check: Convert back: 9×2+1=19 9 \times 2 + 1 = 19 over 2 ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong remainder position
    Don't put the quotient as the numerator and remainder as whole number = 192 1\frac{9}{2} ! This reverses the division result completely. Always put the quotient as the whole number and remainder over the original denominator.

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's the difference between improper fractions and mixed numbers?

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An improper fraction has a numerator larger than the denominator (like 192 \frac{19}{2} ). A mixed number combines a whole number with a proper fraction (like 912 9\frac{1}{2} ).

Why do I divide the numerator by the denominator?

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Division tells us how many whole groups fit into the numerator! 19÷2 19 \div 2 means "how many 2s fit into 19?" The answer is 9 whole groups with 1 left over.

What if there's no remainder when I divide?

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If there's no remainder, you get a whole number with no fractional part! For example, 102=5 \frac{10}{2} = 5 with no remainder means the answer is just 5.

How do I check if my mixed number is correct?

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Multiply the whole number by the denominator, add the numerator, then put over the original denominator. If you get your starting fraction, you're right!

Can I simplify the fractional part of a mixed number?

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Yes! Always simplify the fraction part to lowest terms. For example, if you get 346 3\frac{4}{6} , simplify to 323 3\frac{2}{3} .

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