Solve: 4/5 Divided by 2 - Fraction Division Problem

Q: What does 'reciprocal' mean exactly?

The reciprocal of a number is what you get when you flip it upside down! For whole numbers like 2, write it as $ \frac{2}{1} $ first, then flip to get $ \frac{1}{2} $.

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

Dividing by a number is exactly the same as multiplying by its reciprocal! This method makes fraction calculations much easier because you can use the simple multiplication rules you already know.

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

Yes! Always check if your answer can be simplified. Look for common factors in the numerator and denominator, like how $ \frac{4}{10} $ becomes $ \frac{2}{5} $ when you divide both by 2.

Fraction Division with Reciprocal Method

$\frac{4}{5}:2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Any number divided by 1 always equals itself

00:14 Let's convert division to multiplication by reciprocal

00:26 Make sure to multiply numerator by numerator and denominator by denominator

00:32 Let's calculate the multiplications

00:37 Let's reduce what we can

00:43 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

$\frac{4}{5}:2=$

Step-by-step solution

To solve the problem of dividing the fraction $\frac{4}{5}$ by 2, we can utilize the method of multiplying by the reciprocal. Here’s how you can systematically approach it:

Given the division $\frac{4}{5} : 2$ , we first express the division by finding the reciprocal.
Step 1: The reciprocal of 2 is $\frac{1}{2}$ .

Step 2: Now, multiply the fraction $\frac{4}{5}$ by $\frac{1}{2}$ :

$\frac{4}{5} \times \frac{1}{2} = \frac{4 \times 1}{5 \times 2} = \frac{4}{10}$

Step 3: Simplify the resulting fraction:

The numerator and the denominator have a common factor of 2. Dividing both by 2 gives:

$\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$

Therefore, the solution to the problem $\frac{4}{5} : 2$ is $\frac{2}{5}$ .

Final Answer

$\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by a whole number equals multiplication by its reciprocal
Technique: $\frac{4}{5} ÷ 2 = \frac{4}{5} × \frac{1}{2} = \frac{4}{10}$
Check: Simplify $\frac{4}{10} = \frac{2}{5}$ by dividing both parts by 2 ✓

Common Mistakes

Avoid these frequent errors

Adding denominators when dividing fractions
Don't think $\frac{4}{5} ÷ 2 = \frac{4}{5+2} = \frac{4}{7}$ ! Division doesn't combine denominators like addition does. Always convert division to multiplication by the reciprocal first.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

What does 'reciprocal' mean exactly?

The reciprocal of a number is what you get when you flip it upside down! For whole numbers like 2, write it as $\frac{2}{1}$ first, then flip to get $\frac{1}{2}$ .

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

Dividing by a number is exactly the same as multiplying by its reciprocal! This method makes fraction calculations much easier because you can use the simple multiplication rules you already know.

Do I always need to simplify my final answer?

Yes! Always check if your answer can be simplified. Look for common factors in the numerator and denominator, like how $\frac{4}{10}$ becomes $\frac{2}{5}$ when you divide both by 2.

What if I'm dividing by a fraction instead of a whole number?

The same rule applies! Find the reciprocal of the fraction you're dividing by. For example, the reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$ .

How can I check if my answer is correct?

Multiply your answer by the original divisor. For this problem: $\frac{2}{5} × 2 = \frac{4}{5}$ ✓ This matches our starting fraction!

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