Solve the Fraction Division: 3/5 ÷ 3 Step-by-Step

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

Division by a number is the same as multiplication by its reciprocal. Since 3 = $ \frac{3}{1} $, its reciprocal is $ \frac{1}{3} $. This rule makes fraction division much easier!

Q: What's the difference between ÷ and : in math?

Both symbols mean division! The colon (:) is commonly used in some countries while ÷ is used in others. $ \frac{3}{5} : 3 $ means exactly the same as $ \frac{3}{5} ÷ 3 $.

Q: How do I know when to simplify my answer?

Always simplify when possible! Look for common factors in the numerator and denominator. Since 3 and 15 share the factor 3, $ \frac{3}{15} = \frac{1}{5} $.

Q: Can I just multiply the denominator by the whole number instead?

Yes, that's another way! $ \frac{3}{5} ÷ 3 = \frac{3}{5×3} = \frac{3}{15} $. Both methods work, but learning the reciprocal method helps with more complex problems later.

Fraction Division with Whole Number Conversion

Solve the following exercise:

$\frac{3}{5}:3=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Let's write the number as a fraction

00:08 Any number divided by 1 is always equal to itself

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

00:20 Let's calculate the quotients

00:23 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:

$\frac{3}{5}:3=\text{?}$

Step-by-step solution

We need to solve the expression $\frac{3}{5} : 3$ .

The division of a fraction by a whole number can be rewritten as the multiplication of the fraction by the reciprocal of the whole number.

The given problem transforms as follows:

$\frac{3}{5} : 3 = \frac{3}{5} \times \frac{1}{3}$

Performing the multiplication, we multiply the numerators together and the denominators together:

$\frac{3 \times 1}{5 \times 3} = \frac{3}{15}$

Now, simplify $\frac{3}{15}$ by finding their greatest common divisor (GCD), which is 3:

$\frac{3 \div 3}{15 \div 3} = \frac{1}{5}$

Thus, the answer to the division is $\frac{1}{5}$ .

Therefore, the solution to the problem $\frac{3}{5} : 3$ is $\frac{1}{5}$ , which corresponds to choice 4.

Final Answer

$\frac{1}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by a whole number equals multiplying by its reciprocal
Technique: $\frac{3}{5} ÷ 3 = \frac{3}{5} × \frac{1}{3} = \frac{3}{15}$
Check: Simplify final answer by finding GCD: $\frac{3}{15} = \frac{1}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing the numerator by the whole number incorrectly
Don't just divide 3 ÷ 3 = 1 and write $\frac{1}{5}$ directly! This skips the conversion step and doesn't show proper understanding. Always convert division to multiplication by the reciprocal first: $\frac{3}{5} ÷ 3 = \frac{3}{5} × \frac{1}{3}$ .

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{1}{2}:\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to flip the whole number when dividing?

Division by a number is the same as multiplication by its reciprocal. Since 3 = $\frac{3}{1}$ , its reciprocal is $\frac{1}{3}$ . This rule makes fraction division much easier!

What's the difference between ÷ and : in math?

Both symbols mean division! The colon (:) is commonly used in some countries while ÷ is used in others. $\frac{3}{5} : 3$ means exactly the same as $\frac{3}{5} ÷ 3$ .

How do I know when to simplify my answer?

Always simplify when possible! Look for common factors in the numerator and denominator. Since 3 and 15 share the factor 3, $\frac{3}{15} = \frac{1}{5}$ .

Can I just multiply the denominator by the whole number instead?

Yes, that's another way! $\frac{3}{5} ÷ 3 = \frac{3}{5×3} = \frac{3}{15}$ . Both methods work, but learning the reciprocal method helps with more complex problems later.

What if my fraction doesn't simplify evenly?

That's okay! Not all fractions can be simplified. Just make sure you've found the greatest common divisor (GCD) correctly. If the GCD is 1, your fraction is already in simplest form.

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