Solve Division: 1/2 ÷ 9½ Step-by-Step Solution

Q: Why do I need to convert the mixed number first?

Mixed numbers like $ 9\frac{1}{2} $ are harder to work with in division. Converting to improper fractions like $ \frac{19}{2} $ makes the division process much clearer and prevents errors.

Q: How do I remember to flip and multiply?

Think of it as "Keep, Change, Flip": Keep the first fraction, change division to multiplication, flip the second fraction. So $ \frac{1}{2} ÷ \frac{19}{2} $ becomes $ \frac{1}{2} × \frac{2}{19} $.

Q: Why does the 2 cancel out in this problem?

We have $ \frac{1}{2} × \frac{2}{19} $, and the 2 in the denominator of the first fraction cancels with the 2 in the numerator of the second fraction, leaving us with $ \frac{1}{19} $.

Q: How can I check if my answer is correct?

Multiply your answer by the original divisor: $ \frac{1}{19} × 9\frac{1}{2} $ should equal $ \frac{1}{2} $. If it does, your division is correct!

Q: Is the answer always smaller when dividing fractions?

Not always! When you divide by a fraction less than 1, the result gets bigger. But when dividing by a number greater than 1 (like $ 9\frac{1}{2} $), the result gets smaller, which is why $ \frac{1}{19} $ is much smaller than $ \frac{1}{2} $.

Fraction Division with Mixed Numbers

$(+\frac{1}{2}):(+9\frac{1}{2})=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Positive divided by positive is always positive

00:12 Convert mixed fraction to fraction

00:29 Write division as multiplication by reciprocal

00:32 Swap numerator and denominator

00:35 Reduce what's possible

00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(+\frac{1}{2}):(+9\frac{1}{2})=\text{ ?}$

Step-by-step solution

Since we are dividing two positive numbers, the result must be a positive number:

$+:+=+$

First, let's convert the mixed fraction into an improper fraction as follows:

$9\frac{1}{2}=\frac{9\times2+1}{2}=\frac{18+1}{2}=\frac{19}{2}$

Now we have the exercise:

$\frac{1}{2}:\frac{19}{2}=$

Then we can convert the division into multiplication, remembering to switch the numerator and denominator:

$\frac{1}{2}\times\frac{2}{19}=$

Finally, we can cancel out the 2s to get:

$\frac{1}{19}$

Final Answer

$\frac{1}{19}$

Key Points to Remember

Essential concepts to master this topic

Rule: When dividing fractions, multiply by the reciprocal of the divisor
Technique: Convert $9\frac{1}{2}$ to $\frac{19}{2}$ before dividing
Check: $\frac{1}{19} \times \frac{19}{2} = \frac{1}{2}$ matches original dividend ✓

Common Mistakes

Avoid these frequent errors

Trying to divide mixed numbers directly without converting
Don't divide $\frac{1}{2} ÷ 9\frac{1}{2}$ directly = confusing and wrong results! Mixed numbers must be converted first because division rules only work properly with improper fractions. Always convert mixed numbers to improper fractions before dividing.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number first?

Mixed numbers like $9\frac{1}{2}$ are harder to work with in division. Converting to improper fractions like $\frac{19}{2}$ makes the division process much clearer and prevents errors.

How do I remember to flip and multiply?

Think of it as "Keep, Change, Flip": Keep the first fraction, change division to multiplication, flip the second fraction. So $\frac{1}{2} ÷ \frac{19}{2}$ becomes $\frac{1}{2} × \frac{2}{19}$ .

Why does the 2 cancel out in this problem?

We have $\frac{1}{2} × \frac{2}{19}$ , and the 2 in the denominator of the first fraction cancels with the 2 in the numerator of the second fraction, leaving us with $\frac{1}{19}$ .

How can I check if my answer is correct?

Multiply your answer by the original divisor: $\frac{1}{19} × 9\frac{1}{2}$ should equal $\frac{1}{2}$ . If it does, your division is correct!

Is the answer always smaller when dividing fractions?

Not always! When you divide by a fraction less than 1, the result gets bigger. But when dividing by a number greater than 1 (like $9\frac{1}{2}$ ), the result gets smaller, which is why $\frac{1}{19}$ is much smaller than $\frac{1}{2}$ .

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