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Chapter 3: Problem 72

In the following exercises, translate and solve. \(150 \%\) of 90 is what number?

Short Answer

Expert verified
135

Step by step solution

01

- Understand the Problem

The exercise asks to find what number represents 150% of 90. Mathematically, this can be expressed as 150% * 90.
02

- Convert Percentage to Decimal

Convert 150% to a decimal. To do this, divide 150 by 100: 150% = 1.50.
03

- Multiply the Decimal by the Number

Multiply 1.50 by 90 to find the number: 1.50 * 90.
04

- Perform the Calculation

Complete the multiplication: 1.50 * 90 = 135.
05

- State the Result

The number that represents 150% of 90 is 135.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percentage to decimal conversion
Before solving any percentage problem, converting percentages to decimals is a critical step. This makes mathematical operations easier and more straightforward.
Percentages are essentially fractions with a denominator of 100. For example, 150% can be viewed as 150 out of 100. To convert a percentage to a decimal, divide the percentage by 100.
For instance, 150% as a decimal is calculated as:
\(\frac{150}{100} = 1.50\)
This conversion is necessary because it simplifies multiplication in further steps.
basic multiplication
Multiplication is a fundamental concept in mathematics that you'll need when solving percentage problems.
Once you have converted the percentage to a decimal, the next step is to multiply that decimal by the given number.
Using our example, we need to find 150% of 90. We first converted 150% to 1.50. Now we multiply 1.50 by 90:
\(1.50 \times 90 = 135\)
Multiplication can be done step-by-step:
  • First, multiply 1.50 by 10 to get 15.
  • Then, multiply 15 by 9 to get 135.
This makes solving problems straightforward and systematic.
understanding percentages
Understanding percentages is vital for solving a wide range of real-life and mathematical problems.
A percentage represents a part out of 100. For example, saying 150% means 150 parts out of 100. This can be more than 100%, an important concept when dealing with increases.
In our example, finding 150% of 90 means figuring out what number is 1.5 times larger than 90.
Knowing how to work with percentages helps in financial calculations, statistics, and even everyday scenarios like calculating discounts or interest rates. By converting percentages to decimals and then multiplying, you can easily find the result you're looking for.

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Most popular questions from this chapter

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