Solve Mixed Number Division: 2⅓ ÷ ½ Step-by-Step

Q: How do I remember to flip the second fraction?

Think of it as "dividing by a fraction means multiplying by its flip!" So $ \div \frac{1}{2} $ becomes $ \times 2 $. Division and multiplication are opposite operations.

Q: What if I forget to convert back to a mixed number at the end?

Your answer would still be mathematically correct! $ \frac{14}{3} $ and $ 4\frac{2}{3} $ are the same value. However, mixed numbers are often easier to understand and visualize.

Q: Can I just multiply 2⅓ by 2 directly?

No! You must use the reciprocal method for division. Multiplying by 2 would give you $ 4\frac{2}{3} $, which happens to be correct here, but only because $ \frac{1}{2} $'s reciprocal is 2.

Q: How do I check if my final answer is correct?

Multiply your answer by the divisor: $ 4\frac{2}{3} \times \frac{1}{2} $. Convert to improper fractions: $ \frac{14}{3} \times \frac{1}{2} = \frac{14}{6} = \frac{7}{3} = 2\frac{1}{3} $ ✓

Mixed Number Division with Improper Fractions

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve the problem together.

00:07 First, convert the mixed number into an improper fraction.

00:11 Calculate the numerator carefully, then write it back in our exercise.

00:20 Now, change the division sign to multiplication by using the reciprocal.

00:28 Remember, multiply numerator by numerator and denominator by denominator.

00:34 Great! Let's do the multiplications.

00:41 Next, convert the result back into a mixed number.

00:45 Break down 14 into 12 plus 2.

00:50 Separate into a whole number part and a fractional remainder.

00:56 Turn the whole fraction into a whole number and form the mixed number.

01:03 And that's how you find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the mixed number $2\frac{1}{3}$ to an improper fraction.
Step 2: Take the reciprocal of $\frac{1}{2}$ .
Step 3: Multiply the improper fraction by the reciprocal.
Step 4: Simplify the resulting fraction if necessary, and convert back to a mixed number.

Now, let's work through each step:
Step 1: Convert the mixed number $2\frac{1}{3}$ to an improper fraction.
$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}$ .
Step 2: The reciprocal of $\frac{1}{2}$ is $2$ .
Step 3: Multiply $\frac{7}{3}$ by $2$ :
$\frac{7}{3} \times 2 = \frac{7 \times 2}{3} = \frac{14}{3}$ .
Step 4: Convert the improper fraction $\frac{14}{3}$ to a mixed number.
Divide 14 by 3, which is 4 with a remainder of 2, so we have $4\frac{2}{3}$ .

Therefore, the solution to the problem is $4\frac{2}{3}$ .

Final Answer

$4\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Change division to multiplication by the reciprocal
Conversion: Transform $2\frac{1}{3}$ to $\frac{7}{3}$ before calculating
Verification: Check that $4\frac{2}{3} \times \frac{1}{2} = 2\frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing mixed numbers without converting to improper fractions first
Don't try to divide $2\frac{1}{3}$ directly by $\frac{1}{2}$ = confusing steps and wrong answer! Working with mixed numbers makes the reciprocal method unclear. Always convert mixed numbers to improper fractions first, then apply division as multiplication by reciprocal.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number to an improper fraction?

Converting to improper fractions makes division much easier! You can't easily find the reciprocal of a mixed number like $2\frac{1}{3}$ , but you can easily work with $\frac{7}{3}$ .

How do I remember to flip the second fraction?

Think of it as "dividing by a fraction means multiplying by its flip!" So $\div \frac{1}{2}$ becomes $\times 2$ . Division and multiplication are opposite operations.

What if I forget to convert back to a mixed number at the end?

Your answer would still be mathematically correct! $\frac{14}{3}$ and $4\frac{2}{3}$ are the same value. However, mixed numbers are often easier to understand and visualize.

Can I just multiply 2⅓ by 2 directly?

No! You must use the reciprocal method for division. Multiplying by 2 would give you $4\frac{2}{3}$ , which happens to be correct here, but only because $\frac{1}{2}$ 's reciprocal is 2.

How do I check if my final answer is correct?

Multiply your answer by the divisor: $4\frac{2}{3} \times \frac{1}{2}$ . Convert to improper fractions: $\frac{14}{3} \times \frac{1}{2} = \frac{14}{6} = \frac{7}{3} = 2\frac{1}{3}$ ✓

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Solve Mixed Number Division: 2⅓ ÷ ½ Step-by-Step

Mixed Number Division with Improper Fractions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to convert the mixed number to an improper fraction?

How do I remember to flip the second fraction?

What if I forget to convert back to a mixed number at the end?

Can I just multiply 2⅓ by 2 directly?

How do I check if my final answer is correct?

🌟 Unlock Your Math Potential

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