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Chapter 7: Problem 40

Solve. \(4.8 \%\) of 32 is what number?

Short Answer

Expert verified
1.536

Step by step solution

01

Understand the Problem

We need to find what number corresponds to 4.8% of 32.
02

Convert Percentage to Decimal

To convert 4.8% into a decimal, divide by 100. So, 4.8% becomes 0.048.
03

Multiply by the Whole

Now, multiply the decimal 0.048 by the whole number 32. This will give us the part of 32 that corresponds to 4.8%.
04

Perform the Calculation

Calculate: \(0.048 \times 32 = 1.536\). This is the number that is 4.8% of 32.

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Key Concepts

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

Decimal Conversion
When working with percentages, converting them into decimals is a crucial step. This allows you to perform arithmetic operations more easily. To convert a percentage into a decimal, you divide the percentage by 100.
For example, let's take 4.8%. This step involves moving the decimal point two places to the left, essentially making it smaller.
So, 4.8 becomes 0.048.
This is because in mathematics, a percentage is just a fraction with a denominator of 100. Thus, converting it into a decimal gives you a more manageable format to work with in calculations.
Multiplication
Multiplication is a basic arithmetic operation and a key step in finding the part of a whole in percentage problems. Once we have converted the percentage into a decimal, we need to multiply this decimal by the whole number.
In our example, the decimal 0.048 represents 4.8%, and 32 is the whole.
Therefore, the operation we perform is 0.048 times 32.
This means you're finding 0.048 parts of 32, which yields 1.536 after calculation.
Multiplication in this context is used to scale down the whole number to the part indicated by the percentage.
Basic Arithmetic
To solve percentage problems like the one given, understanding basic arithmetic processes is essential. These processes include addition, subtraction, multiplication, and division.
In percentage calculations, division is primarily used in converting percentages to decimals, such as dividing 4.8 by 100 to get 0.048.
Multiplication, on the other hand, is applied to find what part of the whole number is represented by this decimal. For example, multiplying 0.048 by 32 gives 1.536, which is the answer.
These basic operations demonstrate how mathematics provides the tools to quantify and simplify everyday problems, making it vital to understand them thoroughly.

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Most popular questions from this chapter

A house recently sold for \(\$ 562,560 .\) The commission rate on the sale is \(5.5 \% .\) If the real estate agent is to receive \(60 \%\) of the commission, find the amount received by the agent.

Solve. \(140 \%\) of what number is \(105 ?\)

Perform each indicated operation. See Sections 4.3 through \(4.5,4.7,\) and 5.2 through \(5.4 .\) $$2 \frac{4}{5}-3 \frac{9}{10}$$

Add or subtract the decimals. $$\begin{array}{r}2.38 \\\\-0.19 \\\\\hline\end{array}$$

Add or subtract the decimals. $$\begin{array}{r}16.37 \\\\-\quad 2.61 \\\\\hline\end{array}$$
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