Converting Fraction 7/15 to Percentage: Step-by-Step Solution

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

A percentage means 'per hundred', so you need to express your fraction as parts out of 100. Multiplying by 100 converts any decimal or fraction to show how many parts out of 100 it represents.

Q: Should I round 46.6666... or leave it exact?

For practical purposes, round to 2 decimal places (46.67%). However, you can also write it as $ 46.\overline{6}\% $ to show the 6 repeats forever, which is mathematically exact.

Q: Can I convert 7/15 to a simpler fraction first?

No need! The fraction $ \frac{7}{15} $ is already in lowest terms since 7 and 15 share no common factors. You can work directly with this fraction.

Q: What if I get confused with the division?

Think of it step by step: $ \frac{7}{15} \times 100 = \frac{7 \times 100}{15} = \frac{700}{15} $. Then divide: 700 ÷ 15 = 46.67. The % sign comes from multiplying by 100.

Q: How do I check if 46.67% equals 7/15?

Convert back! Take 46.67% ÷ 100 = 0.4667. Also calculate $ \frac{7}{15} = 0.4667 $ (rounded). If they match, you're correct!

Fraction to Percentage with Division Rounding

Write the fraction $\frac{7}{15}$ as a percentage

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert fractions to percentages

00:05 Multiply by 100 to convert to a percentage

00:15 Break down 15 into factors of 5 and 3, and 100 into factors of 5 and 20

00:25 Simplify wherever possible

00:30 Move the multiplication to the numerator

00:42 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the fraction $\frac{7}{15}$ as a percentage

Step-by-step solution

To solve this problem, we need to convert the fraction $\frac{7}{15}$ into a percentage. We will do this by multiplying the fraction by 100. The process is as follows:

Step 1: Start with the fraction $\frac{7}{15}$ .
Step 2: Convert the fraction to a percentage by using the formula: $(\frac{7}{15}) \times 100$ .

Now, let's perform the calculation:

$\frac{7}{15} \times 100 = \frac{700}{15}$

Next, divide 700 by 15 to get the percentage:

$700 \div 15 = 46.6667\ldots$

For a percentage, we typically round to two decimal places, so we round 46.6667 to 46.67%. Thus, the fraction $\frac{7}{15}$ expressed as a percentage is approximately 46.67%.

Therefore, the solution to the problem is 46.67%.

Final Answer

46.66%

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply fraction by 100 to convert to percentage
Technique: $\frac{7}{15} \times 100 = \frac{700}{15} = 46.\overline{6}\%$
Check: Convert back: 46.67% ÷ 100 = 0.4667 ≈ 7/15 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100
Don't just divide 7 by 15 and stop = 0.4667 as final answer! This gives you the decimal form, not the percentage. Always multiply your decimal result by 100 to convert to percentage form.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why do I multiply by 100 to get a percentage?

A percentage means 'per hundred', so you need to express your fraction as parts out of 100. Multiplying by 100 converts any decimal or fraction to show how many parts out of 100 it represents.

Should I round 46.6666... or leave it exact?

For practical purposes, round to 2 decimal places (46.67%). However, you can also write it as $46.\overline{6}\%$ to show the 6 repeats forever, which is mathematically exact.

Can I convert 7/15 to a simpler fraction first?

No need! The fraction $\frac{7}{15}$ is already in lowest terms since 7 and 15 share no common factors. You can work directly with this fraction.

What if I get confused with the division?

Think of it step by step: $\frac{7}{15} \times 100 = \frac{7 \times 100}{15} = \frac{700}{15}$ . Then divide: 700 ÷ 15 = 46.67. The % sign comes from multiplying by 100.

How do I check if 46.67% equals 7/15?

Convert back! Take 46.67% ÷ 100 = 0.4667. Also calculate $\frac{7}{15} = 0.4667$ (rounded). If they match, you're correct!

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