90 Is $75\%$ Of What Number?

Feb 26, 2025 by ADMIN 31 views

$90 is $75\%$ of what number?$

Introduction

In mathematics, percentages are a way to express a value as a fraction of a whole. When we say that 90 is $75%$ of a certain number, we are essentially asking for the value of that number. This problem can be solved using simple algebra and a basic understanding of percentages.

Understanding Percentages

To start, let's understand what a percentage is. A percentage is a way to express a value as a fraction of a whole. For example, $75%$ means $75$ out of $100$, or $\frac{75}{100}$. When we say that 90 is $75%$ of a certain number, we are essentially saying that 90 is equal to $75%$ of that number.

Setting Up the Equation

Let's call the unknown number $x$. We can set up an equation to represent the problem:

90 = \frac{75}{100}x

Solving the Equation

To solve for $x$, we can start by simplifying the fraction on the right-hand side of the equation:

\frac{75}{100} = \frac{3}{4}

So, the equation becomes:

90 = \frac{3}{4}x

Multiplying Both Sides

To get rid of the fraction, we can multiply both sides of the equation by $4$:

4 \times 90 = 3x

360 = 3x

Dividing Both Sides

Now, we can divide both sides of the equation by $3$ to solve for $x$:

\frac{360}{3} = x

120 = x

Conclusion

Therefore, 90 is $75%$ of $120$. This problem can be solved using simple algebra and a basic understanding of percentages.

Real-World Applications

Understanding percentages is an important skill in many real-world applications, such as finance, business, and economics. For example, if a company's sales increase by $25%$, we can calculate the new sales figure by multiplying the original sales figure by $1.25$.

Practice Problems

Here are a few practice problems to help you understand percentages better:

80 is $60%$ of what number?
120 is $80%$ of what number?
150 is $75%$ of what number?

Solutions to Practice Problems

80 is $60%$ of $133\frac{1}{3}$.
120 is $80%$ of $150$.
150 is $75%$ of $200$.

Conclusion

In conclusion, understanding percentages is an important skill in mathematics and has many real-world applications. By using simple algebra and a basic understanding of percentages, we can solve problems like "90 is $75%$ of what number?" and many others.

Final Thoughts

Percentages are a fundamental concept in mathematics, and understanding them is essential for success in many fields. By practicing problems like the ones above, you can improve your skills and become more confident in your ability to solve percentage problems.

Additional Resources

For more information on percentages and other mathematical concepts, check out the following resources:

Khan Academy: Percentages
Mathway: Percentages
Wolfram Alpha: Percentages

Frequently Asked Questions

Q: What is a percentage? A: A percentage is a way to express a value as a fraction of a whole.
Q: How do I calculate a percentage? A: To calculate a percentage, multiply the value by the percentage as a decimal.
Q: What is the difference between a percentage and a fraction? A: A percentage is a way to express a value as a fraction of a whole, while a fraction is a way to express a value as a ratio of two numbers.

Glossary

Percentage: A way to express a value as a fraction of a whole.
Fraction: A way to express a value as a ratio of two numbers.
Decimal: A way to express a value as a number with a decimal point.

References

"Percentages" by Khan Academy
"Percentages" by Mathway
"Percentages" by Wolfram Alpha

Introduction

In our previous article, we discussed how to solve the problem "90 is $75%$ of what number?" using simple algebra and a basic understanding of percentages. In this article, we will answer some frequently asked questions related to percentages and provide additional resources for further learning.

Q&A

Q: What is a percentage?

A: A percentage is a way to express a value as a fraction of a whole. For example, $75%$ means $75$ out of $100$, or $\frac{75}{100}$.

Q: How do I calculate a percentage?

A: To calculate a percentage, multiply the value by the percentage as a decimal. For example, to calculate $75%$ of $100$, you would multiply $100$ by $0.75$.

Q: What is the difference between a percentage and a fraction?

A: A percentage is a way to express a value as a fraction of a whole, while a fraction is a way to express a value as a ratio of two numbers. For example, $\frac{3}{4}$ is a fraction, while $75%$ is a percentage.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, divide the percentage by $100$. For example, to convert $75%$ to a decimal, you would divide $75$ by $100$, which equals $0.75$.

Q: How do I convert a decimal to a percentage?

A: To convert a decimal to a percentage, multiply the decimal by $100$. For example, to convert $0.75$ to a percentage, you would multiply $0.75$ by $100$, which equals $75%$.

Q: What is the formula for calculating a percentage?

A: The formula for calculating a percentage is:

\text{Percentage} = \frac{\text{Value}}{\text{Total}} \times 100

For example, to calculate $75%$ of $100$, you would use the formula:

\text{Percentage} = \frac{100}{100} \times 75 = 75\%

Q: How do I calculate a percentage increase?

A: To calculate a percentage increase, use the formula:

\text{Percentage Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100

For example, if the old value is $100$ and the new value is $120$, the percentage increase would be:

\text{Percentage Increase} = \frac{120 - 100}{100} \times 100 = 20\%

Q: How do I calculate a percentage decrease?

A: To calculate a percentage decrease, use the formula:

\text{Percentage Decrease} = \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \times 100

For example, if the old value is $100$ and the new value is $80$, the percentage decrease would be:

\text{Percentage Decrease} = \frac{100 - 80}{100} \times 100 = 20\%