Solve the Fraction Problem: 1/2 Divided by 2

Q: What does it mean to divide by a whole number?

Dividing by a whole number like 2 means splitting something into 2 equal parts. So $ \frac{1}{2} ÷ 2 $ means taking half of something and splitting it in half again!

Q: How do I find the reciprocal of a whole number?

The reciprocal of any whole number is 1 over that number. So the reciprocal of 2 is $ \frac{1}{2} $, reciprocal of 5 is $ \frac{1}{5} $, etc.

Q: Why does dividing make the answer smaller?

When you divide a positive number by something greater than 1, you're breaking it into smaller pieces. Since $ \frac{1}{2} $ is already small, dividing by 2 makes it even smaller: $ \frac{1}{4} $.

Q: Can I just multiply the denominators when dividing fractions?

No! That only works for multiplication. For division, you must flip the second fraction and then multiply: $ \frac{1}{2} ÷ 2 = \frac{1}{2} × \frac{1}{2} $.

Fraction Division with Reciprocal Multiplication

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Any number divided by 1 is always equal to itself

00:11 Let's convert division to multiplication by reciprocal

00:23 Make sure to multiply numerator by numerator and denominator by denominator

00:30 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

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

Step-by-step solution

To solve $\frac{1}{2} : 2$ , we need to rewrite the division as multiplication by the reciprocal of 2. The reciprocal of 2 is $\frac{1}{2}$ .

Thus, the expression becomes:

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

Calculating the multiplication, we have:

$\frac{1}{4}$

Therefore, the solution to the problem is $\frac{1}{4}$ , which corresponds to choice 3.

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Dividing by a number means multiplying by its reciprocal
Technique: Convert $\frac{1}{2} ÷ 2$ to $\frac{1}{2} × \frac{1}{2} = \frac{1}{4}$
Check: Multiply answer by divisor: $\frac{1}{4} × 2 = \frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying instead of dividing by the whole number
Don't multiply $\frac{1}{2} × 2 = 1$ when you see division! This gives the wrong operation and answer. Always remember division means multiply by the reciprocal: $\frac{1}{2} ÷ 2 = \frac{1}{2} × \frac{1}{2}$ .

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{2}:3=$ $$ $$ $$

FAQ

Everything you need to know about this question

What does it mean to divide by a whole number?

Dividing by a whole number like 2 means splitting something into 2 equal parts. So $\frac{1}{2} ÷ 2$ means taking half of something and splitting it in half again!

How do I find the reciprocal of a whole number?

The reciprocal of any whole number is 1 over that number. So the reciprocal of 2 is $\frac{1}{2}$ , reciprocal of 5 is $\frac{1}{5}$ , etc.

Why does dividing make the answer smaller?

When you divide a positive number by something greater than 1, you're breaking it into smaller pieces. Since $\frac{1}{2}$ is already small, dividing by 2 makes it even smaller: $\frac{1}{4}$ .

Can I just multiply the denominators when dividing fractions?

No! That only works for multiplication. For division, you must flip the second fraction and then multiply: $\frac{1}{2} ÷ 2 = \frac{1}{2} × \frac{1}{2}$ .

How can I check my division answer?

Multiply your answer by what you divided by. If you get back to your starting number, you're correct! $\frac{1}{4} × 2 = \frac{1}{2}$ ✓

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