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Chapter 6: Problem 98

Translate and solve. What number is 45% of 120?

Short Answer

Expert verified
45% of 120 is 54.

Step by step solution

01

Understand the Problem

We need to find what number is 45% of 120. This involves calculating a percentage of a given quantity.
02

Convert Percentage to Decimal

Convert the percentage (45%) to a decimal by dividing by 100. \[ 45\text{%} = \frac{45}{100} = 0.45 \]
03

Multiply the Decimal by the Quantity

Multiply the decimal (0.45) by the quantity (120). \[ 0.45 \times 120 \]
04

Perform the Multiplication

Calculate the product of 0.45 and 120. \[ 0.45 \times 120 = 54 \]
05

Interpret the Result

The result of the multiplication is 54. Therefore, 45% of 120 is 54.

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Key Concepts

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

Convert Percentage to Decimal
When solving percentage problems, you often need to convert a percentage into a decimal. This is the first crucial step. Percentages are parts of a whole, specifically out of 100. To convert a percentage to a decimal, you simply divide by 100.
For example, with 45%, you perform the conversion like this: \ 45% becomes \[\frac{45}{100} = 0.45\].
  • Divide the percentage value by 100.
  • Write down the result as a decimal.
This decimal form can now be used in multiplication steps to find the desired quantity.
Multiply Decimal by Quantity
Once you have converted the percentage to a decimal, the next step is to multiply this decimal by the given quantity. Multiplication is straightforward and it allows you to find a part of the total amount.
In our example, you would have the decimal 0.45 and the quantity 120. The multiplication looks like this: \ \[0.45 \times 120\]
Here are the steps to perform it:
  • Position the decimal and the quantity.
  • Multiply the numbers as if they were whole numbers.
  • Adjust the product to place the decimal in the correct spot based on the initial decimal's positions.
Interpret Result
After performing the multiplication, you need to interpret the result. This step involves understanding what the resultant number means in the context of your original problem.
Continuing with our example: \ \[0.45 \times 120 = 54\]
  • The final value obtained (54) represents the portion defined by the percentage.
  • Identify that this is the answer to our question: 45% of 120 is 54.
The result helps you understand part of a whole, making percentage calculations valuable in various practical scenarios.

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