Solve the Fraction Division: 12/16 ÷ 3 Step-by-Step

Q: Why do I need to use the reciprocal when dividing by a whole number?

Division by any number is the same as multiplication by its reciprocal. Since 3 = $ \frac{3}{1} $, its reciprocal is $ \frac{1}{3} $. This rule works for all division problems!

Q: How do I find the reciprocal of a whole number like 3?

The reciprocal of any whole number is 1 divided by that number. So the reciprocal of 3 is $ \frac{1}{3} $, reciprocal of 5 is $ \frac{1}{5} $, and so on.

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

Yes, always simplify! In this problem, $ \frac{12}{48} $ simplifies to $ \frac{1}{4} $ by dividing both numerator and denominator by their GCD of 12.

Q: What's the fastest way to find the GCD to simplify fractions?

List the factors of both numbers or use the division method: keep dividing both by the same number until you can't anymore. For $ \frac{12}{48} $: both divide by 12, giving $ \frac{1}{4} $.

Q: Can I convert the original fraction to a decimal first?

You could, but it's not recommended! Working with fractions keeps your answer exact. Converting $ \frac{12}{16} $ to 0.75 then dividing by 3 gives 0.25, but $ \frac{1}{4} $ is the precise answer.

Fraction Division with Whole Number Divisors

Complete the following exercise:

$\frac{12}{16}:3=\text{?}$

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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

00:17 Let's calculate the quotients

00:21 We want to reduce the fraction as much as possible

00:24 Make sure to divide both numerator and denominator

00:33 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

Complete the following exercise:

$\frac{12}{16}:3=\text{?}$

Step-by-step solution

To solve the problem $\frac{12}{16} : 3$ , we will follow these steps:

Step 1: Restate the division as a multiplication by using the reciprocal of the divisor. The reciprocal of 3 is $\frac{1}{3}$ .
Step 2: Multiply the fraction by the reciprocal of the divisor: $\frac{12}{16} \times \frac{1}{3}$ .
Step 3: Multiply the numerators: $12 \times 1 = 12$ .
Step 4: Multiply the denominators: $16 \times 3 = 48$ .
Step 5: Simplify the resulting fraction $\frac{12}{48}$ .
Step 6: Both the numerator and the denominator can be divided by 12, which is the greatest common divisor: $\frac{12 \div 12}{48 \div 12} = \frac{1}{4}$ .

Therefore, the solution to the problem is $\frac{1}{4}$ .

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by a whole number means multiply by its reciprocal
Technique: Convert $\frac{12}{16} ÷ 3$ to $\frac{12}{16} × \frac{1}{3} = \frac{12}{48}$
Check: Simplify $\frac{12}{48}$ by dividing both parts by GCD of 12 ✓

Common Mistakes

Avoid these frequent errors

Multiplying the denominator by the whole number instead of using reciprocal
Don't just multiply 16 × 3 = 48 and write $\frac{12}{48}$ = wrong method! This skips the reciprocal step and confuses division with multiplication. Always convert division to multiplication by the reciprocal: $÷3 = ×\frac{1}{3}$ .

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 use the reciprocal when dividing by a whole number?

Division by any number is the same as multiplication by its reciprocal. Since 3 = $\frac{3}{1}$ , its reciprocal is $\frac{1}{3}$ . This rule works for all division problems!

How do I find the reciprocal of a whole number like 3?

The reciprocal of any whole number is 1 divided by that number. So the reciprocal of 3 is $\frac{1}{3}$ , reciprocal of 5 is $\frac{1}{5}$ , and so on.

Do I always need to simplify my final answer?

Yes, always simplify! In this problem, $\frac{12}{48}$ simplifies to $\frac{1}{4}$ by dividing both numerator and denominator by their GCD of 12.

What's the fastest way to find the GCD to simplify fractions?

List the factors of both numbers or use the division method: keep dividing both by the same number until you can't anymore. For $\frac{12}{48}$ : both divide by 12, giving $\frac{1}{4}$ .

Can I convert the original fraction to a decimal first?

You could, but it's not recommended! Working with fractions keeps your answer exact. Converting $\frac{12}{16}$ to 0.75 then dividing by 3 gives 0.25, but $\frac{1}{4}$ is the precise answer.

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