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Chapter 6: Problem 100

Translate and solve. What number is 24% of 112?

Short Answer

Expert verified
The number is 26.88.

Step by step solution

01

Translate the problem

Identify the parts of the problem. We need to find what number is 24% of 112. This translates to finding 24% of 112.
02

Convert percentage to decimal

Convert 24% to a decimal by dividing by 100. This gives us 0.24.
03

Multiply to find the number

Multiply 0.24 by 112 to find the number. This is \( 0.24 \times 112 = 26.88 \).

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Key Concepts

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

Translating Word Problems
When faced with a word problem, the first step is to translate it into a mathematical expression. This means understanding the key components of the problem. For example, in the problem 'What number is 24% of 112?', the important parts are '24%' and 'of 112'. Here, '24%' indicates a percentage, and 'of' usually denotes a multiplication operation. So, translating this problem means converting '24% of 112' into a multiplication problem where 24%, or 0.24, is multiplied by 112.
Decimal Conversion
Converting percentages to decimals is essential in many math problems. A percentage is a fraction out of 100. So, to convert a percentage to a decimal, you divide the percentage by 100. For instance, to convert 24% to a decimal, you perform the division 24 梅 100. This results in 0.24. As another example, 50% becomes 0.50 after conversion (since 50 梅 100 = 0.50). Using decimals makes further calculations straightforward and avoids the need for dealing with large fractions.
Multiplication
Once you have translated the problem and converted any percentages to decimals, the next step is to perform the necessary multiplication. In our example, we need to multiply 0.24 by 112. This can be done using a calculator or by hand. For multiplication: \(0.24 \times 112 = 26.88\). This means that 24% of 112 is 26.88. Another example includes finding 15% of 200, first converting 15% to 0.15, and then multiplying: \(0.15 \times 200 = 30\).

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