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

Q: Why do we use the reciprocal when dividing fractions?

Division is the opposite of multiplication. When we divide by 3, we're asking "what times 3 equals $ \frac{1}{3} $?" Using the reciprocal $ \frac{1}{3} $ makes this calculation straightforward!

Q: What's the reciprocal of a whole number like 3?

The reciprocal of any whole number is 1 divided by that number. So the reciprocal of 3 is $ \frac{1}{3} $. Remember: number × reciprocal = 1.

Q: How do I multiply fractions like in step 3?

Multiply fractions by multiplying numerator × numerator and denominator × denominator:$ \frac{1}{3} × \frac{1}{3} = \frac{1×1}{3×3} = \frac{1}{9} $

Q: Can I check my answer using multiplication?

Yes! If $ \frac{1}{3} ÷ 3 = \frac{1}{9} $ is correct, then $ \frac{1}{9} × 3 $ should equal $ \frac{1}{3} $. Let's verify: $ \frac{1}{9} × 3 = \frac{3}{9} = \frac{1}{3} $ ✓

Q: Is there a shortcut for dividing by whole numbers?

Yes! When dividing a fraction by a whole number, you can simply multiply the denominator by that number. So $ \frac{1}{3} ÷ 3 = \frac{1}{3×3} = \frac{1}{9} $.

Fraction Division with Reciprocal Method

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

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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

00:10 Let's convert division to multiplication by reciprocal

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

00:28 Let's calculate the multiplications

00:31 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

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

Step-by-step solution

To solve the problem $\frac{1}{3} : 3$ , we will follow these clear steps:

Step 1: Understand that dividing by 3 is equivalent to multiplying by the reciprocal of 3, which is $\frac{1}{3}$ .
Step 2: Convert the division problem $\frac{1}{3} : 3$ into a multiplication problem $\frac{1}{3} \times \frac{1}{3}$ .
Step 3: Perform the multiplication of fractions:

Using the formula $\frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$ , we have:

$\frac{1}{3} \times \frac{1}{3} = \frac{1 \cdot 1}{3 \cdot 3} = \frac{1}{9}$ .

Therefore, the solution to the problem is $\frac{1}{9}$ .

Final Answer

$\frac{1}{9}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Dividing by a number equals multiplying by its reciprocal
Technique: Convert $\frac{1}{3} ÷ 3$ to $\frac{1}{3} × \frac{1}{3} = \frac{1}{9}$
Check: Verify that $\frac{1}{9} × 3 = \frac{1}{3}$ gives original dividend ✓

Common Mistakes

Avoid these frequent errors

Directly dividing numerators and denominators separately
Don't divide 1÷3 and 3÷1 separately = wrong answer like $\frac{1}{3}$ ! This ignores proper fraction division rules and gives the original fraction instead of the quotient. Always convert division to multiplication by the reciprocal first.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do we use the reciprocal when dividing fractions?

Division is the opposite of multiplication. When we divide by 3, we're asking "what times 3 equals $\frac{1}{3}$ ?" Using the reciprocal $\frac{1}{3}$ makes this calculation straightforward!

What's the reciprocal of a whole number like 3?

The reciprocal of any whole number is 1 divided by that number. So the reciprocal of 3 is $\frac{1}{3}$ . Remember: number × reciprocal = 1.

How do I multiply fractions like in step 3?

Multiply fractions by multiplying numerator × numerator and denominator × denominator:

$\frac{1}{3} × \frac{1}{3} = \frac{1×1}{3×3} = \frac{1}{9}$

Can I check my answer using multiplication?

Yes! If $\frac{1}{3} ÷ 3 = \frac{1}{9}$ is correct, then $\frac{1}{9} × 3$ should equal $\frac{1}{3}$ . Let's verify: $\frac{1}{9} × 3 = \frac{3}{9} = \frac{1}{3}$ ✓

Is there a shortcut for dividing by whole numbers?

Yes! When dividing a fraction by a whole number, you can simply multiply the denominator by that number. So $\frac{1}{3} ÷ 3 = \frac{1}{3×3} = \frac{1}{9}$ .

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