Solve the Fraction Equation: 2/3 × ? = 1/3

Q: Why do I flip the fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal! The reciprocal of $ \frac{2}{3} $ is $ \frac{3}{2} $ because flipping the numerator and denominator gives you the opposite operation.

Q: How do I remember which fraction to flip?

Flip the fraction you're dividing by! In $ \frac{1}{3} \div \frac{2}{3} $, you flip $ \frac{2}{3} $ to get $ \frac{3}{2} $, then multiply.

Q: Can I solve this without using reciprocals?

You could use cross-multiplication if you rewrite it as $ \frac{2}{3} \times x = \frac{1}{3} $, but the reciprocal method is usually faster and clearer for this type of problem.

Q: What if my answer doesn't simplify to a nice fraction?

That's okay! Always check if your fraction can be simplified by finding common factors in the numerator and denominator. In this case, $ \frac{3}{6} = \frac{1}{2} $.

Q: How do I check my work?

Substitute your answer back into the original equation: $ \frac{2}{3} \times \frac{1}{2} $. Multiply to get $ \frac{2}{6} = \frac{1}{3} $. If it matches the right side, you're correct!

Fraction Division with Reciprocal Method

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

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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 Write division as multiplication by the reciprocal, and calculate the products

00:09 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

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

Step-by-step solution

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

Step 1: Identify the equation $\frac{2}{3} \times x = \frac{1}{3}$ .
Step 2: To isolate $x$ , we'll divide both sides by $\frac{2}{3}$ .
Step 3: Perform the division by $\frac{2}{3}$ by multiplying by its reciprocal.

Let's work through each step:

Step 1: We start with the equation $\frac{2}{3} \times x = \frac{1}{3}$ .

Step 2: To solve for $x$ , divide both sides by $\frac{2}{3}$ :

$x = \frac{1}{3} \div \frac{2}{3}$

Step 3: Dividing by a fraction is equivalent to multiplying by the reciprocal:

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

Calculate the multiplication:

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

$x = \frac{1}{2}$

Therefore, the solution to the problem is $\frac{1}{2}$ , which corresponds to choice .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide by a fraction means multiply by its reciprocal
Technique: $\frac{1}{3} \div \frac{2}{3} = \frac{1}{3} \times \frac{3}{2}$
Check: Substitute: $\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Attempting to subtract fractions instead of dividing
Don't try to solve $\frac{2}{3} \times ? = \frac{1}{3}$ by subtracting $\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$ ! This gives the wrong operation and ignores the multiplication. Always isolate the unknown by dividing both sides by $\frac{2}{3}$ .

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 fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal! The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$ because flipping the numerator and denominator gives you the opposite operation.

How do I remember which fraction to flip?

Flip the fraction you're dividing by! In $\frac{1}{3} \div \frac{2}{3}$ , you flip $\frac{2}{3}$ to get $\frac{3}{2}$ , then multiply.

Can I solve this without using reciprocals?

You could use cross-multiplication if you rewrite it as $\frac{2}{3} \times x = \frac{1}{3}$ , but the reciprocal method is usually faster and clearer for this type of problem.

What if my answer doesn't simplify to a nice fraction?

That's okay! Always check if your fraction can be simplified by finding common factors in the numerator and denominator. In this case, $\frac{3}{6} = \frac{1}{2}$ .

How do I check my work?

Substitute your answer back into the original equation: $\frac{2}{3} \times \frac{1}{2}$ . Multiply to get $\frac{2}{6} = \frac{1}{3}$ . If it matches the right side, you're correct!

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