Convert 7.5/10 to Percentage: Step-by-Step Math Guide

Q: Why do I multiply by 100 to get a percentage?

Because percent means "per hundred"! When you multiply by 100, you're finding how many parts out of 100 your fraction represents. So $ \frac{7.5}{10} \times 100 = 75 $ means 75 parts out of 100.

Q: Can I convert the decimal first, then to percentage?

Absolutely! You can convert $ \frac{7.5}{10} = 0.75 $, then multiply by 100 to get 75%. Both methods work perfectly!

Q: How can I check if my percentage is reasonable?

Think logically: $ \frac{7.5}{10} $ is less than the whole (which would be $ \frac{10}{10} $ = 100%), so your answer should be less than 100%. 75% makes sense!

Q: Is there a shortcut for fractions with denominator 10?

Yes! For denominators of 10, just move the decimal point one place right and add the % sign. So 7.5 becomes 75%. This works because dividing by 10 then multiplying by 100 gives you ×10.

Decimal Fractions to Percentage Conversion

Convert the following fraction into a percentage:

$\frac{7.5}{10}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's convert fractions into percentages.

00:12 If a fraction's denominator is one hundred, the numerator is the percentage.

00:19 Now, let's apply this idea to our exercise.

00:27 Multiply both the numerator and denominator by ten, to make the denominator one hundred.

00:42 Let's go ahead and calculate that.

00:52 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert the following fraction into a percentage:

$\frac{7.5}{10}=\text{?}$

Step-by-step solution

To solve this problem of converting the fraction $\frac{7.5}{10}$ to a percentage, we will follow these steps:

Step 1: Calculate $\frac{7.5 \times 100}{10}$ .
Step 2: Simplify the expression $\frac{750}{10}$ .
Step 3: Perform the division to find the percentage.

Let's perform each calculation step by step:

Step 1:
First, multiply the numerator of the fraction by 100: $7.5 \times 100 = 750$ .

Step 2:
Now, divide the result by the denominator: $\frac{750}{10} = 75$ .

Step 3:
Therefore, $\frac{7.5}{10}$ converted to a percentage is 75%.

The correct choice from the given options is 75%.

Final Answer

75%

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply fraction by 100 to convert to percentage
Technique: Calculate $\frac{7.5 \times 100}{10} = \frac{750}{10} = 75$
Check: Convert back: 75% ÷ 100 = 0.75 = $\frac{7.5}{10}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100
Don't just convert $\frac{7.5}{10}$ to decimal 0.75 and call it 0.75%! This gives a percentage that's 100 times too small. Always multiply the fraction result by 100 to get the correct percentage.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction $\frac{75}{100}$

to a percentage:

FAQ

Everything you need to know about this question

Why do I multiply by 100 to get a percentage?

Because percent means "per hundred"! When you multiply by 100, you're finding how many parts out of 100 your fraction represents. So $\frac{7.5}{10} \times 100 = 75$ means 75 parts out of 100.

Can I convert the decimal first, then to percentage?

Absolutely! You can convert $\frac{7.5}{10} = 0.75$ , then multiply by 100 to get 75%. Both methods work perfectly!

What if my fraction has a decimal in the numerator?

No problem! Treat the decimal like any other number. Just multiply it by 100 and divide by the denominator. Decimals don't change the conversion process.

How can I check if my percentage is reasonable?

Think logically: $\frac{7.5}{10}$ is less than the whole (which would be $\frac{10}{10}$ = 100%), so your answer should be less than 100%. 75% makes sense!

Is there a shortcut for fractions with denominator 10?

Yes! For denominators of 10, just move the decimal point one place right and add the % sign. So 7.5 becomes 75%. This works because dividing by 10 then multiplying by 100 gives you ×10.

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