Solve the Fraction Equation: 2/3 × Unknown = 1/6

Q: Why do I flip the second fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal. Think of it this way: dividing by $ \frac{2}{3} $ means "how many $ \frac{2}{3} $'s fit into the number?" This is equivalent to multiplying by $ \frac{3}{2} $.

Q: How do I find the reciprocal of a fraction?

Simply flip the numerator and denominator! The reciprocal of $ \frac{2}{3} $ is $ \frac{3}{2} $. For whole numbers like 5, write it as $ \frac{5}{1} $ first, then flip to get $ \frac{1}{5} $.

Q: Can I solve this by cross-multiplying?

Not directly! Cross-multiplication works when you have $ \frac{a}{b} = \frac{c}{d} $. Here you have $ \frac{2}{3} \times x = \frac{1}{6} $, so you need to isolate x by dividing both sides by $ \frac{2}{3} $.

Q: How do I simplify the final fraction?

Find the greatest common factor (GCF) of the numerator and denominator. For $ \frac{3}{12} $, the GCF of 3 and 12 is 3, so divide both by 3 to get $ \frac{1}{4} $.

Fraction Division with Reciprocal Multiplication

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the unknown value.

00:07 First, we need to isolate the unknown.

00:10 Next, change division into multiplication by the reciprocal, and calculate.

00:15 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

To solve the equation $\frac{2}{3} \times x = \frac{1}{6}$ , we need to find the value of $x$ by isolating it.

Step 1: Set the equation to solve for $x$ :
$\frac{2}{3} \times x = \frac{1}{6}$ .
Step 2: Isolate $x$ by dividing both sides by $\frac{2}{3}$ :
$x = \frac{1}{6} \div \frac{2}{3}$ .
Step 3: Performing the division by multiplying with the reciprocal:
$x = \frac{1}{6} \times \frac{3}{2}$ .
Step 4: Simplify the expression:
$\frac{1 \times 3}{6 \times 2} = \frac{3}{12} = \frac{1}{4}$ .

Thus, the number that satisfies the equation is $\frac{1}{4}$ .

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: To divide by a fraction, multiply by its reciprocal
Technique: $\frac{1}{6} \div \frac{2}{3} = \frac{1}{6} \times \frac{3}{2}$
Check: Substitute back: $\frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing fractions incorrectly
Don't divide $\frac{1}{6} \div \frac{2}{3}$ by dividing numerators and denominators separately = $\frac{1÷2}{6÷3} = \frac{0.5}{2}$ ! This gives a completely wrong method and answer. Always flip the second fraction and multiply: $\frac{1}{6} \times \frac{3}{2}$ .

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{3}\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

Why do I flip the second fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal. Think of it this way: dividing by $\frac{2}{3}$ means "how many $\frac{2}{3}$ 's fit into the number?" This is equivalent to multiplying by $\frac{3}{2}$ .

How do I find the reciprocal of a fraction?

Simply flip the numerator and denominator! The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$ . For whole numbers like 5, write it as $\frac{5}{1}$ first, then flip to get $\frac{1}{5}$ .

Can I solve this by cross-multiplying?

Not directly! Cross-multiplication works when you have $\frac{a}{b} = \frac{c}{d}$ . Here you have $\frac{2}{3} \times x = \frac{1}{6}$ , so you need to isolate x by dividing both sides by $\frac{2}{3}$ .

Why does my answer come out as a decimal?

If you're getting decimals, you might be using a calculator incorrectly. Keep everything in fraction form throughout the problem: $\frac{1}{6} \times \frac{3}{2} = \frac{3}{12} = \frac{1}{4}$ . This avoids rounding errors!

How do I simplify the final fraction?

Find the greatest common factor (GCF) of the numerator and denominator. For $\frac{3}{12}$ , the GCF of 3 and 12 is 3, so divide both by 3 to get $\frac{1}{4}$ .

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