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Chapter 3: Problem 69

In the following exercises, translate and solve. What number is \(24 \%\) of \(112 ?\)

Short Answer

Expert verified
The number is 26.88.

Step by step solution

01

- Understand the Problem

Read the problem carefully. The task is to find what number is 24% of 112. This means you need to calculate 24% of 112.
02

- Convert Percentage to Decimal

Convert the percentage to a decimal by dividing by 100. So, 24% becomes \(\frac{24}{100} = 0.24\).
03

- Multiply by the Whole Number

To find 24% of 112, multiply the decimal (0.24) by 112. So, you calculate \(0.24 \times 112\).
04

- Perform the Calculation

Now multiply: \(0.24 \times 112 = 26.88\).
05

- State the Final Answer

The number that is 24% of 112 is 26.88.

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Key Concepts

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

Convert Percentage to Decimal
To begin calculating a percentage, it's crucial to convert the given percentage to a decimal. This transformation makes the problem simpler to solve. Percentages are parts of a hundred, so converting them involves a straightforward division by 100.

Let's dive into an example. Suppose we need to find what number is 24% of 112. First, we convert the percentage (24%) into a decimal. This is done by dividing 24 by 100. Hence, \[ 24 \% = \frac{24}{100} = 0.24 \] Note that dividing by 100 essentially shifts the decimal point two places to the left.

Some quick tips:
  • If the percentage is a whole number (like 24%), just place the decimal point two spots to the left.
  • If the percentage already has a decimal (like 12.5%), move that decimal two spots to the left.
  • Always ensure to double-check your conversion for accuracy.
Multiply by Whole Number
After converting the percentage to a decimal, our next step is to multiply this decimal by the given whole number.

Continuing with our example, we have converted 24% to 0.24. Now, we need to find 24% of 112. This requires you to multiply the decimal (0.24) by the whole number (112).

In mathematical terms:
\[ 0.24 \times 112 \]

Multiplication tips:
  • Align numbers by their rightmost digit for manual calculation.
  • Double-check each step to ensure accuracy.
  • If handling large numbers, consider using a calculator to avoid mistakes.
This multiplication essentially scales the whole number (112) by the fraction (0.24).
Perform Calculation
Finally, it's time to perform the actual multiplication to find the answer. This step involves completing the arithmetic operation you've set up.

Let's break down the calculation:
Multiplying 0.24 by 112 will give us:
\[ 0.24 \times 112 = 26.88 \]
This result means that 24% of 112 is equal to 26.88.

Quick pointers to ensure accurate results:
  • Use a calculator for precision, especially with decimal points.
  • Recheck your work by performing the multiplication again.
  • Write out each step if doing manually to avoid mistakes.
And voila! You've successfully calculated the desired percentage of the given whole number.

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