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Chapter 7: Problem 31

Solve the percent problems with an unknown amount. Find \(112 \%\) of 500 .

Short Answer

Expert verified
112% of 500 is 560.

Step by step solution

01

Understand the Given Problem

The problem asks to find what 112% of 500 is. This means determining 112% of the number 500.
02

Convert the Percentage to a Decimal

Convert 112% to a decimal. To do this, divide by 100. So, 112% = \( \frac{112}{100} = 1.12 \)
03

Multiply by the Given Number

Multiply the decimal form of the percentage by the given number.Therefore, we need to compute \( 1.12 \times 500 \).
04

Perform the Multiplication

Calculate the result of the multiplication. \[ 1.12 \times 500 = 560 \]
05

State the Answer

The final answer is the result of the calculation. Thus, 112% of 500 is 560.

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Key Concepts

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

percentage conversion
When solving percent problems, converting percentages to decimals is a fundamental step. This ensures accurate and simple calculations. A percentage represents a part out of 100, so to convert it to a decimal, you divide by 100. For example, convert 112% to a decimal by performing the division: \(\frac{112}{100} = 1.12\). This means 112% is equivalent to 1.12 in decimal form. This decimal form can then be used for further calculations like multiplication.
multiplication
Multiplication is the arithmetic operation used to find the value when a number is increased by a certain percentage. After converting the percentage to a decimal, you multiply this decimal by the given number. In this exercise, 112% of 500 requires multiplying the decimal 1.12 by 500. The calculation is as follows: \[ 1.12 \times 500 = 560 \]. Performing this multiplication gives the final result. Multiplication ensures that the percentage is appropriately applied to the initial amount.
problem solving
Problem solving with percentages involves a structured approach. The steps to follow include: identifying the given values, converting percentages to decimals, performing arithmetic operations (usually multiplication), and stating the final answer. In the exercise, we identified that we needed to find 112% of 500. By converting 112% to 1.12 and then multiplying 1.12 by 500, we determined the answer to be 560. Breaking down problems into clear steps, understanding each part and why it鈥檚 done, leads to accurate and confident problem solving.

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Most popular questions from this chapter

The amount of 8000 dollar is invested at \(4 \%\) for 3 years. a. Compute the ending balance if the bank calculates simple interese? b. Compute the ending balance if the bank calculates interest compounded annually. c. How much more interest is earned in the account with compound interest? (TABLE CAN NOT COPY)

Explain the difference between \(\frac{3}{4}\) and \(\frac{3}{4} \%\)

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{3}{13}$$

The point \(P\) lies in the first quadrant on the graph of the line \(y=7-3 x\). From the point \(P\), perpendiculars are drawn to both the \(x\) -axis and the \(y\) -axis. What is the largest possible area for the rectangle thus formed?

Harvard University reported that 232 African American students were admitted to the freshman class in a recent year. If this represents \(11 \%\) of the total freshman class, how many freshmen were admitted?
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