Solve: Division Problem 1/2 ÷ 3 Using Ratio Notation

Q: Why do I flip the 3 to 1/3?

Because dividing by 3 is the same as multiplying by one-third! Think of it this way: if you have half a pizza and divide it among 3 people, each person gets $ \frac{1}{6} $ of the whole pizza.

Q: How do I remember which number to flip?

Always flip the second number (the one you're dividing by). In $ \frac{1}{2} ÷ 3 $, you flip the 3 to get $ \frac{1}{3} $, then multiply.

Q: Why is 1/6 smaller than 1/2?

When you divide something, you make it smaller! Dividing $ \frac{1}{2} $ by 3 means splitting it into 3 equal parts, so each part is $ \frac{1}{6} $.

Q: Do I need to simplify my answer?

Always check if you can simplify! In this case, $ \frac{1}{6} $ cannot be simplified further since 1 and 6 share no common factors other than 1.

Fraction Division with Reciprocal Method

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

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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

00:09 We'll convert division to multiplication by reciprocal

00:22 We'll make sure to multiply numerator by numerator and denominator by denominator

00:27 Let's calculate the multiplications

00:30 And this is the solution to the question

Step-by-step written solution

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Understand the problem

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

Step-by-step solution

To solve this problem of dividing a fraction by a whole number, we'll follow these steps:

Step 1: Change the whole number to a reciprocal fraction.
Step 2: Multiply the original fraction by the reciprocal.
Step 3: Simplify the resulting fraction, if necessary.

Now, let's apply these steps:
Step 1: The whole number $3$ is converted to the reciprocal fraction $\frac{1}{3}$ .
Step 2: Multiply the fraction $\frac{1}{2}$ by $\frac{1}{3}$ :

$\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}$

Step 3: The resulting fraction $\frac{1}{6}$ is already in its simplest form.

Therefore, when $\frac{1}{2}$ is divided by $3$ , the resulting answer is $\frac{1}{6}$ .

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by whole number equals multiplication by reciprocal
Technique: Convert $\frac{1}{2} ÷ 3$ to $\frac{1}{2} × \frac{1}{3} = \frac{1}{6}$
Check: Verify $\frac{1}{6} × 3 = \frac{1}{2}$ to confirm division worked ✓

Common Mistakes

Avoid these frequent errors

Multiplying by the whole number instead of its reciprocal
Don't multiply $\frac{1}{2} × 3 = \frac{3}{2}$ ! This gives you the opposite operation and makes your answer 9 times too big. Always flip the whole number to its reciprocal first: 3 becomes $\frac{1}{3}$ .

Practice Quiz

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

FAQ

Everything you need to know about this question

Why do I flip the 3 to 1/3?

Because dividing by 3 is the same as multiplying by one-third! Think of it this way: if you have half a pizza and divide it among 3 people, each person gets $\frac{1}{6}$ of the whole pizza.

How do I remember which number to flip?

Always flip the second number (the one you're dividing by). In $\frac{1}{2} ÷ 3$ , you flip the 3 to get $\frac{1}{3}$ , then multiply.

What if I'm dividing by a fraction instead?

Same rule! Flip the fraction you're dividing by. For example: $\frac{1}{2} ÷ \frac{2}{3}$ becomes $\frac{1}{2} × \frac{3}{2}$ .

Why is 1/6 smaller than 1/2?

When you divide something, you make it smaller! Dividing $\frac{1}{2}$ by 3 means splitting it into 3 equal parts, so each part is $\frac{1}{6}$ .

Do I need to simplify my answer?

Always check if you can simplify! In this case, $\frac{1}{6}$ cannot be simplified further since 1 and 6 share no common factors other than 1.

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