Solve: 3/5 Divided by 4 - Step-by-Step Fraction Division

Q: Why do I flip the whole number when dividing?

Division is the same as multiplication by the reciprocal! When you divide by 4, you're really multiplying by $ \frac{1}{4} $. This is why $ \frac{3}{5} ÷ 4 = \frac{3}{5} \times \frac{1}{4} $.

Q: How do I know if my answer should be smaller?

When you divide a fraction by a whole number greater than 1, your answer should always be smaller than the original fraction. Since $ \frac{3}{20} $ is smaller than $ \frac{3}{5} $, we're on the right track!

Q: Can I convert to decimals instead?

You could, but be careful with rounding! $ \frac{3}{5} = 0.6 $ and $ 0.6 ÷ 4 = 0.15 $. However, keeping the exact fraction $ \frac{3}{20} $ is more precise than the decimal 0.15.

Q: Why multiply numerators and denominators separately?

This is the fundamental rule of fraction multiplication! When multiplying $ \frac{3}{5} \times \frac{1}{4} $, multiply across: top × top and bottom × bottom to get $ \frac{3 \times 1}{5 \times 4} = \frac{3}{20} $.

Fraction Division with Whole Number

$\frac{3}{5}:4=$

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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 is always equal to itself

00:12 Let's convert division to multiplication by reciprocal

00:24 Make sure to multiply numerator by numerator and denominator by denominator

00:27 Let's calculate the multiplications

00:31 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

$\frac{3}{5}:4=$

Step-by-step solution

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

Step 1: Convert the whole number to a fraction and find its reciprocal.
Step 2: Multiply the given fraction by this reciprocal.
Step 3: Simplify the result, if possible.

Let's tackle each step:
Step 1: Convert $4$ to a fraction, which is $\frac{4}{1}$ , and find the reciprocal giving $\frac{1}{4}$ .
Step 2: Multiply $\frac{3}{5}$ by $\frac{1}{4}$ to get $\frac{3}{5} \times \frac{1}{4} = \frac{3 \times 1}{5 \times 4} = \frac{3}{20}$ .
Step 3: The fraction $\frac{3}{20}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{3}{20}$ .

Final Answer

$\frac{3}{20}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Dividing by a number equals multiplying by its reciprocal
Technique: Convert 4 to $\frac{4}{1}$ , then flip to get $\frac{1}{4}$
Check: Verify $\frac{3}{20} \times 4 = \frac{12}{20} = \frac{3}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying instead of dividing
Don't multiply $\frac{3}{5} \times 4 = \frac{12}{5}$ ! This gives a larger fraction instead of the smaller result division should produce. Always remember: dividing by a whole number means multiplying by its reciprocal.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I flip the whole number when dividing?

Division is the same as multiplication by the reciprocal! When you divide by 4, you're really multiplying by $\frac{1}{4}$ . This is why $\frac{3}{5} ÷ 4 = \frac{3}{5} \times \frac{1}{4}$ .

How do I know if my answer should be smaller?

When you divide a fraction by a whole number greater than 1, your answer should always be smaller than the original fraction. Since $\frac{3}{20}$ is smaller than $\frac{3}{5}$ , we're on the right track!

What if the fraction doesn't simplify?

That's perfectly normal! Not all fractions can be simplified. Check if the numerator and denominator share any common factors. Since 3 and 20 share no common factors except 1, $\frac{3}{20}$ is already in simplest form.

Can I convert to decimals instead?

You could, but be careful with rounding! $\frac{3}{5} = 0.6$ and $0.6 ÷ 4 = 0.15$ . However, keeping the exact fraction $\frac{3}{20}$ is more precise than the decimal 0.15.

Why multiply numerators and denominators separately?

This is the fundamental rule of fraction multiplication! When multiplying $\frac{3}{5} \times \frac{1}{4}$ , multiply across: top × top and bottom × bottom to get $\frac{3 \times 1}{5 \times 4} = \frac{3}{20}$ .

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