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Chapter 6: Problem 102

Translate and solve. 250% of 65 is what number?

Short Answer

Expert verified
162.5

Step by step solution

01

- Understand the Problem

You need to find 250% of 65. In other words, determine what number is equivalent to 250% of 65.
02

- Convert Percentage to Decimal

Convert 250% to a decimal by dividing by 100. \[250\text{%} = \frac{250}{100} = 2.5\]
03

- Multiply the Decimal by the Number

Multiply 2.5 (the decimal equivalent of 250%) by 65. \[2.5 \times 65 = 162.5\]

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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 working with percentages, it's often necessary to convert them into decimals to make calculations easier. Let's take the example of 250%.
To convert a percentage to a decimal, you divide by 100. This shifts the decimal point two places to the left. So, for 250%, you'd calculate:
\[250\% = \frac{250}{100} = 2.5\]
Now, 250% is the same as 2.5 in decimal form.
This step is crucial because multiplying with decimals is straightforward and often simpler than working with percentages directly.
multiplication in percentage problems
Once you have your percentage converted to a decimal, the next step is to multiply that decimal by the number in question. Here's where our example continues:
We need to find 250% of 65. After converting 250% to 2.5, we then multiply it by 65:
\[2.5 \times 65 = 162.5\]
This step tells us that 250% of 65 is 162.5.
Multiplication in percentage problems can seem tricky at first, but by converting the percentage to a decimal, it becomes straightforward. Remember, multiply the decimal form of the percentage by the given number to find the solution.
understanding percentage
Understanding the concept of a percentage is essential in math. A percentage is a way of expressing a number as a fraction of 100. For instance, 250% means 250 out of 100.
Percentages are often used to compare relative sizes of numbers and have practical applications in discounts, interest rates, statistics, and more.
Here are a few important points about percentages:
  • Percent means 'per hundred'. So, 50% is 50 out of 100.
  • Percentages can be greater than 100%. In our example, 250% means more than double.
  • To find the percentage of a number, convert the percentage to a decimal and multiply it by the number.
By understanding these principles, you can solve various percentage problems with ease.

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