Solve Fraction Division: 2/3 ÷ 2 Step by Step

Q: Why do I multiply by the reciprocal instead of just dividing?

Division and multiplication by reciprocals are the same operation! When you divide by 2, you're really multiplying by $ \frac{1}{2} $. This method makes the calculation much easier with fractions.

Q: What's the reciprocal of a whole number like 2?

The reciprocal of any whole number is 1 over that number. So the reciprocal of 2 is $ \frac{1}{2} $, reciprocal of 5 is $ \frac{1}{5} $, and so on.

Q: Do I always need to simplify my final answer?

Yes, always! Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. $ \frac{2}{6} $ becomes $ \frac{1}{3} $ when you divide both by 2.

Q: What if the whole number is larger than the numerator?

The process is exactly the same! For example, $ \frac{2}{3} \div 5 = \frac{2}{3} \times \frac{1}{5} = \frac{2}{15} $. You'll just get a smaller fraction as your answer.

Fraction Division with Whole Numbers

Solve the following exercise:

$\frac{2}{3}:2=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Let's write the number as a fraction

00:09 Any number divided by 1 is always equal to itself

00:13 Make sure to divide numerator by numerator and denominator by denominator

00:16 Let's calculate the quotients

00:20 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

Solve the following exercise:

$\frac{2}{3}:2=\text{?}$

Step-by-step solution

To solve this problem, we need to divide the fraction $\frac{2}{3}$ by the whole number 2.

We'll follow these steps:

Step 1: Express the division operation with reciprocal multiplication.
Step 2: Simplify the expression if possible.

Step 1: To divide $\frac{2}{3}$ by 2, we multiply $\frac{2}{3}$ by the reciprocal of 2. The reciprocal of 2 is $\frac{1}{2}$ . Thus, we have:

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

Step 2: Perform the multiplication:

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

Simplify $\frac{2}{6}$ by dividing the numerator and the denominator by their greatest common divisor, which is 2:

$\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}$

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

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Dividing by a number means multiplying by its reciprocal
Technique: Convert $\frac{2}{3} \div 2$ to $\frac{2}{3} \times \frac{1}{2} = \frac{2}{6}$
Check: Simplify final answer by finding GCD: $\frac{2}{6} = \frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing the denominator by the whole number
Don't change $\frac{2}{3} \div 2$ to $\frac{2}{3 \div 2} = \frac{2}{1.5}$ ! This gives a wrong answer because you're making the fraction bigger instead of smaller. Always multiply by the reciprocal of the divisor.

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

Why do I multiply by the reciprocal instead of just dividing?

Division and multiplication by reciprocals are the same operation! When you divide by 2, you're really multiplying by $\frac{1}{2}$ . This method makes the calculation much easier with fractions.

What's the reciprocal of a whole number like 2?

The reciprocal of any whole number is 1 over that number. So the reciprocal of 2 is $\frac{1}{2}$ , reciprocal of 5 is $\frac{1}{5}$ , and so on.

Do I always need to simplify my final answer?

Yes, always! Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. $\frac{2}{6}$ becomes $\frac{1}{3}$ when you divide both by 2.

How can I check if my answer is correct?

Multiply your answer by the original divisor - you should get back to the original fraction! Check: $\frac{1}{3} \times 2 = \frac{2}{3}$ ✓

What if the whole number is larger than the numerator?

The process is exactly the same! For example, $\frac{2}{3} \div 5 = \frac{2}{3} \times \frac{1}{5} = \frac{2}{15}$ . You'll just get a smaller fraction as your answer.

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