Simplify the Fraction: Converting 12/300 to Its Simplest Form

Q: Why can't I just divide both numbers by any common factor?

You can divide by any common factor, but using the Greatest Common Factor (GCD) gets you to the simplest form in one step! For $ \frac{12}{300} $, the GCD is 12, giving us $ \frac{1}{25} $ directly.

Q: How do I convert the simplified fraction to a decimal?

Divide the numerator by the denominator: $ 1 \div 25 = 0.04 $. You can also think of it as "how many times does 25 go into 1.00?" - it goes in 4 times after moving the decimal point.

Q: What's wrong with the explanation that says the answer is 4.0?

The explanation incorrectly treats $ \frac{4}{100} $ as "4.0" instead of properly converting it to a decimal. Remember: $ \frac{4}{100} = 4 \div 100 = 0.04 $, not 4.0!

Q: Is there a faster way to see this equals 0.04?

Yes! Notice that $ \frac{12}{300} = \frac{12}{3 \times 100} = \frac{4}{100} = 4\% = 0.04 $. When the denominator is a power of 10 (like 100), just move the decimal point left!

Q: How can I check my decimal answer is correct?

Multiply your decimal by the original denominator: $ 0.04 \times 300 = 12 $ ✓. This should equal the original numerator, confirming $ \frac{12}{300} = 0.04 $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's convert it to a decimal fraction. Ready?

00:08 First, change the fraction so the bottom number is a multiple of 10.

00:13 Make sure to divide both the top and bottom numbers equally.

00:17 Next, write down the top number just as it is.

00:22 Now, move the decimal point to the left, based on the number of zeros.

00:27 Here, we have two zeros, so move the decimal point two places left.

00:35 And that's the answer to our question! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\frac{12}{300}=\text{ ?}$

2

Step-by-step solution

First we will divide both the numerator and denominator by 3 to get 100 in the denominator:

$\frac{12:3}{300:3}=\frac{4}{100}$

Now we'll rewrite the simple fraction as a decimal fraction:

$4.0$

Since the fraction divides by 100, we'll move the decimal point two places to the left:

$.040$

Now we will add the zero before the decimal point to get:

$0.040=0.04$

3

Final Answer

0.04

Key Points to Remember

Essential concepts to master this topic

Greatest Common Factor: Find GCD of numerator and denominator first
Technique: Divide 12÷12 and 300÷12 to get $\frac{1}{25}$
Check: Convert $\frac{1}{25} = 0.04$ by dividing 1÷25 ✓

Common Mistakes

Avoid these frequent errors

Dividing by wrong common factors
Don't divide 12 and 300 by 3 to get $\frac{4}{100}$ = 4.0! This skips finding the greatest common factor and leads to incorrect decimal conversion. Always find the GCD first (12) to get $\frac{1}{25} = 0.04$ .

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{1}{100}=$

FAQ

Everything you need to know about this question

Why can't I just divide both numbers by any common factor?

+

You can divide by any common factor, but using the Greatest Common Factor (GCD) gets you to the simplest form in one step! For $\frac{12}{300}$ , the GCD is 12, giving us $\frac{1}{25}$ directly.

How do I convert the simplified fraction to a decimal?

+

Divide the numerator by the denominator: $1 \div 25 = 0.04$ . You can also think of it as "how many times does 25 go into 1.00?" - it goes in 4 times after moving the decimal point.

What's wrong with the explanation that says the answer is 4.0?

+

The explanation incorrectly treats $\frac{4}{100}$ as "4.0" instead of properly converting it to a decimal. Remember: $\frac{4}{100} = 4 \div 100 = 0.04$ , not 4.0!

Is there a faster way to see this equals 0.04?

+

Yes! Notice that $\frac{12}{300} = \frac{12}{3 \times 100} = \frac{4}{100} = 4\% = 0.04$ . When the denominator is a power of 10 (like 100), just move the decimal point left!

How can I check my decimal answer is correct?

+

Multiply your decimal by the original denominator: $0.04 \times 300 = 12$ ✓. This should equal the original numerator, confirming $\frac{12}{300} = 0.04$ .

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Simplify the Fraction: Converting 12/300 to Its Simplest Form

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