Simplify the Fraction: Reducing 30/150 to Lowest Terms

Q: How do I find the GCD of 30 and 150?

List the factors of each number: 30 has factors 1, 2, 3, 5, 6, 10, 15, 30. The number 150 has factors including 1, 2, 3, 5, 6, 10, 15, 30, 50, 75, 150. The greatest common factor is 30!

Q: Why can't I just use a calculator to divide 30 ÷ 150?

You absolutely can! But simplifying first helps you understand the fraction better and makes mental math easier. Plus, $ \frac{1}{5} $ is much cleaner than $ \frac{30}{150} $.

Q: What if the GCD is 1?

If the GCD is 1, your fraction is already in lowest terms! This means the numerator and denominator share no common factors other than 1.

Q: Is 0.2 the same as 20%?

Yes! The decimal 0.2 equals $ \frac{1}{5} $ which is the same as 20 out of 100 or 20%. They're all different ways to express the same value.

Q: Do I always need to convert fractions to decimals?

Not always! It depends on what the question asks for. Sometimes keeping the answer as a simplified fraction like $ \frac{1}{5} $ is perfectly acceptable and even preferred.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 We want the denominator to be some multiple of 10 and 10

00:07 We'll reduce the fraction, making sure to divide both numerator and denominator

00:17 Convert from fraction to decimal fraction

00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\frac{30}{150}=$

2

Step-by-step solution

To convert the fraction $\frac{30}{150}$ into a decimal, let's follow these steps:

Step 1: Simplify the fraction $\frac{30}{150}$ by finding the greatest common divisor (GCD) of 30 and 150, which is 30.
Step 2: Divide both the numerator and the denominator by the GCD. So, $\frac{30}{150} = \frac{30 \div 30}{150 \div 30} = \frac{1}{5}$ .
Step 3: Convert the simplified fraction $\frac{1}{5}$ to a decimal by performing the division 1 divided by 5.

Now let's do the division:
Step 3: $\frac{1}{5} = 0.2$ . Performing the division gives 0.2 as the result.

Therefore, the solution to the problem is $0.2$ .

3

Final Answer

$0.2$

Key Points to Remember

Essential concepts to master this topic

GCD Rule: Find greatest common divisor to simplify fractions completely
Division Method: Divide both 30 and 150 by GCD of 30
Decimal Check: Convert $\frac{1}{5}$ gives 0.2 ✓

Common Mistakes

Avoid these frequent errors

Converting to decimal without simplifying first
Don't divide 30 ÷ 150 directly = messy calculations and potential errors! This makes the division harder and increases chances of mistakes. Always find the GCD and simplify the fraction first, then convert to decimal.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

How do I find the GCD of 30 and 150?

+

List the factors of each number: 30 has factors 1, 2, 3, 5, 6, 10, 15, 30. The number 150 has factors including 1, 2, 3, 5, 6, 10, 15, 30, 50, 75, 150. The greatest common factor is 30!

Why can't I just use a calculator to divide 30 ÷ 150?

+

You absolutely can! But simplifying first helps you understand the fraction better and makes mental math easier. Plus, $\frac{1}{5}$ is much cleaner than $\frac{30}{150}$ .

What if the GCD is 1?

+

If the GCD is 1, your fraction is already in lowest terms! This means the numerator and denominator share no common factors other than 1.

Is 0.2 the same as 20%?

+

Yes! The decimal 0.2 equals $\frac{1}{5}$ which is the same as 20 out of 100 or 20%. They're all different ways to express the same value.

Do I always need to convert fractions to decimals?

+

Not always! It depends on what the question asks for. Sometimes keeping the answer as a simplified fraction like $\frac{1}{5}$ is perfectly acceptable and even preferred.

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