Convert 3/5 into a Percentage: Detailed Math Example

Q: Why do we 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. So $ \frac{3}{5} $ becomes 60 parts out of 100, or 60%.

Q: Can I just divide 3 by 5 and multiply by 100?

Yes! That's the same thing. $ \frac{3}{5} \times 100 $ is the same as (3 ÷ 5) × 100. Both give you 60%. Use whichever method feels easier!

Q: How can I check if 60% is really equal to 3/5?

Convert both to decimals: 60% = 0.6 and $ \frac{3}{5} = 3 ÷ 5 = 0.6 $. Since both equal 0.6, your answer is correct!

Q: Is there a shortcut for fifths like 3/5?

Yes! For fifths, just multiply the numerator by 20. So $ \frac{3}{5} = 3 \times 20 = 60\% $. This works because $ \frac{100}{5} = 20 $.

Fraction to Percentage with Multiplication Method

Given the fraction $\frac{3}{5}$ convert the fraction into percentages.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's learn how to convert fractions into percentages.

00:10 First, multiply the fraction by one hundred. This will change it into a percentage.

00:23 Break down one hundred into factors of twenty and five. This makes multiplication easier.

00:30 Be sure to simplify wherever possible. This helps to make your final answer neat.

00:36 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the fraction $\frac{3}{5}$ convert the fraction into percentages.

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Interpret the fraction $\frac{3}{5}$ as a ratio.
Step 2: Convert this fraction to percentage by applying the conversion formula.
Step 3: Multiply $\frac{3}{5}$ by 100 to find the percentage.

Now, let's execute the solution:

Step 1: Identify the fraction: $\frac{3}{5}$ .

Step 2: Use the formula to convert to percentage:

\text{Percentage} = \left(\frac{3}{5}\right) \times 100\%.

Step 3: Calculate the percentage:

= \frac{3 \times 100}{5}

= \frac{300}{5}

= 60\%

Thus, the fraction $\frac{3}{5}$ is equivalent to 60%.

The correct option from the choices provided is choice 3: 60%.

Final Answer

60%

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply any fraction by 100 to convert to percentage
Technique: Calculate $\frac{3}{5} \times 100 = \frac{300}{5} = 60\%$
Check: Verify 60% = 0.6 and $\frac{3}{5} = 0.6$ ✓

Common Mistakes

Avoid these frequent errors

Converting fraction to decimal first then multiplying by 100
Don't convert $\frac{3}{5}$ to 0.6 then multiply by 100 = adds unnecessary steps and potential rounding errors! This makes simple problems complicated. Always multiply the fraction directly by 100 using $\frac{3}{5} \times 100$ .

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 we 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. So $\frac{3}{5}$ becomes 60 parts out of 100, or 60%.

Can I just divide 3 by 5 and multiply by 100?

Yes! That's the same thing. $\frac{3}{5} \times 100$ is the same as (3 ÷ 5) × 100. Both give you 60%. Use whichever method feels easier!

What if I get a fraction in my final percentage?

That's okay! Some fractions give percentages like 33⅓% or 66⅔%. Just make sure to simplify properly or convert to a decimal like 33.33%.

How can I check if 60% is really equal to 3/5?

Convert both to decimals: 60% = 0.6 and $\frac{3}{5} = 3 ÷ 5 = 0.6$ . Since both equal 0.6, your answer is correct!

Is there a shortcut for fifths like 3/5?

Yes! For fifths, just multiply the numerator by 20. So $\frac{3}{5} = 3 \times 20 = 60\%$ . This works because $\frac{100}{5} = 20$ .

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