Convert 3÷12 to a Fraction: Step-by-Step Division

Q: Why does 3÷12 become a fraction with 3 on top?

In division, the first number (3) is the dividend and becomes the numerator (top). The second number (12) is the divisor and becomes the denominator (bottom). Think of it as "3 divided by 12."

Q: How do I know what number to divide both parts by?

Find the Greatest Common Divisor (GCD) of both numbers. For 3 and 12, list their factors: 3 has factors 1,3 and 12 has factors 1,2,3,4,6,12. The largest common factor is 3!

Q: Can I leave my answer as 3/12?

While $ \frac{3}{12} $ is correct, it's not in simplest form. Always reduce fractions to their lowest terms. $ \frac{1}{4} $ is much cleaner and easier to work with!

Division to Fractions with Simplification

What fraction results from dividing 3 by 12?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the fraction

00:05 Write division as a fraction

00:11 Let's reduce the fraction, make sure to divide both numerator and denominator

00:25 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

What fraction results from dividing 3 by 12?

Step-by-step solution

Let's write the division exercise:

$3:12$

Now let's write it in the form of a simple fraction, remembering that the numerator is on top and the denominator is on the bottom:

$\frac{3}{12}$

We'll divide both the numerator and denominator by a number that divides into both of them, in this case, the number is 3:

$\frac{3:3}{12:3}=\frac{1}{4}$

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Division creates a fraction: dividend becomes numerator, divisor becomes denominator
Technique: Simplify by dividing both parts by their GCD: $\frac{3}{12} = \frac{3÷3}{12÷3} = \frac{1}{4}$
Check: Verify by multiplication: $\frac{1}{4} × 12 = 3$ ✓

Common Mistakes

Avoid these frequent errors

Writing the division backwards
Don't write 3÷12 as $\frac{12}{3}$ = wrong result 4! This flips the dividend and divisor, completely changing the value. Always remember: the first number (dividend) goes on top as the numerator.

Practice Quiz

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Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

Why does 3÷12 become a fraction with 3 on top?

In division, the first number (3) is the dividend and becomes the numerator (top). The second number (12) is the divisor and becomes the denominator (bottom). Think of it as "3 divided by 12."

How do I know what number to divide both parts by?

Find the Greatest Common Divisor (GCD) of both numbers. For 3 and 12, list their factors: 3 has factors 1,3 and 12 has factors 1,2,3,4,6,12. The largest common factor is 3!

Can I leave my answer as 3/12?

While $\frac{3}{12}$ is correct, it's not in simplest form. Always reduce fractions to their lowest terms. $\frac{1}{4}$ is much cleaner and easier to work with!

What if the division gives me a whole number?

If the dividend is divisible by the divisor (like 12÷3), you get a whole number (4). But when the dividend is smaller than the divisor (like 3÷12), you always get a proper fraction less than 1.

How can I check if my simplified fraction is correct?

Multiply your simplified fraction by the original denominator: $\frac{1}{4} × 12 = 3$ . If you get the original dividend, you're right! You can also convert to decimals: both $\frac{3}{12}$ and $\frac{1}{4}$ equal 0.25.

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