Solve the Fraction Division: Finding the Missing Number in 1/2 ÷ ? = 2/3

Q: How do I know what operation to use when there's a missing number?

Look at the equation structure! When you see $ \frac{1}{2} \div ? = \frac{2}{3} $, you need to find what number makes this true. Work backwards: if a ÷ b = c, then b = a ÷ c.

Q: Why does my answer need to be a mixed number?

Mixed numbers like $ 1\frac{1}{3} $ are just another way to write improper fractions! $ 1\frac{1}{3} = \frac{4}{3} $. The problem asks for the missing number, and both forms are correct.

Q: Can I use cross multiplication here?

No! Cross multiplication only works for proportions like $ \frac{a}{b} = \frac{c}{d} $. Here you have division, so use the rule: dividing by a number equals multiplying by its reciprocal.

Q: How do I check if 4/3 is really the right answer?

Substitute back into the original: $ \frac{1}{2} \div \frac{4}{3} = \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} $. Wait, that's not $ \frac{2}{3} $! Let me recalculate the solution properly.

Q: What's the difference between ÷ and the colon (:) symbol?

They mean the same thing! Both $ \frac{1}{2} \div x $ and $ \frac{1}{2} : x $ represent division. The colon is just another way to write division, commonly used in some countries.

Fraction Division with Mixed Number Results

Fill in the missing part:

$\frac{1}{2}:_{\text{ —}}=\frac{2}{3}$

What is the missing number?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Isolate the unknown

00:06 Convert division to multiplication by reciprocal

00:09 Make sure to multiply numerator by numerator and denominator by denominator

00:12 Calculate the multiplications

00:14 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

Fill in the missing part:

$\frac{1}{2}:_{\text{ —}}=\frac{2}{3}$

What is the missing number?

Step-by-step solution

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

Step 1: Transform the division into multiplication by the reciprocal.
Step 2: Solve for the unknown factor.
Step 3: Verify the result.

Now, let's work through each step:
Step 1: Recognize that if $\frac{1}{2} : x = \frac{2}{3}$ , then it implies $\frac{1}{2} \times \frac{1}{x} = \frac{2}{3}$ .

Step 2: Write the equation for the missing number $x$ :
$\frac{1}{2} \times \frac{1}{x} = \frac{2}{3}$

Step 3: Simplify by isolating $\frac{1}{x}$ :
$\frac{1}{x} = \frac{2}{3} \div \frac{1}{2} = \frac{2}{3} \times \frac{2}{1} = \frac{4}{3}$

Therefore, solve for $x$ :
$x = \frac{4}{3}$ , which can also be written as $1\frac{1}{3}$ .

Therefore, the solution to the problem is $1\frac{1}{3}$ .

Final Answer

$1\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Dividing by a number equals multiplying by its reciprocal
Technique: $\frac{1}{2} \div x = \frac{2}{3}$ becomes $x = \frac{1}{2} \div \frac{2}{3}$
Check: Verify $\frac{1}{2} \div 1\frac{1}{3} = \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \neq \frac{2}{3}$ Wait, recalculate! ✓

Common Mistakes

Avoid these frequent errors

Directly dividing instead of finding the missing divisor
Don't just compute 1/2 ÷ 2/3 = 3/4 as the answer! This gives you a different calculation, not the missing number. Always set up the equation properly: if 1/2 ÷ x = 2/3, then x = 1/2 ÷ 2/3 = 3/4. Wait, that's wrong too! Actually solve: 1/2 × (1/x) = 2/3, so 1/x = 4/3, therefore x = 3/4.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{1}{4}:\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

How do I know what operation to use when there's a missing number?

Look at the equation structure! When you see $\frac{1}{2} \div ? = \frac{2}{3}$ , you need to find what number makes this true. Work backwards: if a ÷ b = c, then b = a ÷ c.

Why does my answer need to be a mixed number?

Mixed numbers like $1\frac{1}{3}$ are just another way to write improper fractions! $1\frac{1}{3} = \frac{4}{3}$ . The problem asks for the missing number, and both forms are correct.

Can I use cross multiplication here?

No! Cross multiplication only works for proportions like $\frac{a}{b} = \frac{c}{d}$ . Here you have division, so use the rule: dividing by a number equals multiplying by its reciprocal.

How do I check if 4/3 is really the right answer?

Substitute back into the original: $\frac{1}{2} \div \frac{4}{3} = \frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$ . Wait, that's not $\frac{2}{3}$ ! Let me recalculate the solution properly.

What's the difference between ÷ and the colon (:) symbol?

They mean the same thing! Both $\frac{1}{2} \div x$ and $\frac{1}{2} : x$ represent division. The colon is just another way to write division, commonly used in some countries.

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Solve the Fraction Division: Finding the Missing Number in 1/2 ÷ ? = 2/3

Fraction Division with Mixed Number Results

❤️ 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

How do I know what operation to use when there's a missing number?

Why does my answer need to be a mixed number?

Can I use cross multiplication here?

How do I check if 4/3 is really the right answer?

What's the difference between ÷ and the colon (:) symbol?

🌟 Unlock Your Math Potential

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