Problem 90 - Elementary Algebra Within Reach

Question

Solve the percent equation. What number is \(45 \%\) of 90 ?

Step-by-Step Solution

Answer

The number that is 45% of 90 is 40.5.

Step 1: Convert Percentage to Decimal

Firstly, the Percentage has to be converted into its equivalent decimal form. Percentages can be converted to decimal by dividing by 100. So, \(45 \% = 45 / 100 = 0.45\).

Step 2: Multiply Decimal with Given Number

Now, the decimal equivalent of the percentage (0.45) should be multiplied with the given number, which is 90. So, \(0.45 * 90 = 40.5\).

Key Concepts

Converting Percentages to Decimals

Understanding how to convert percentages to decimals is a critical skill that forms the foundation of most percentage calculations. In essence, a percentage represents a fraction with a denominator of 100. To convert a percentage into a decimal, you divide it by 100. This is synonymous with simply moving the decimal point two places to the left.

For example, to convert 45% to a decimal, take the number 45 and divide it by 100, which gives us 0.45. It's as simple as that. There's no need for complex mathematics – remembering this small step can take you a long way!

• Remember: To convert a percentage to a decimal, divide by 100.
• Example: 75% becomes 0.75, 20% becomes 0.20, and so on.

Multiplication with Decimals

Once you have converted your percentage to a decimal, the next step is often to use this decimal in a multiplication problem. Multiplication with decimals follows the same basic principles as multiplication with whole numbers, but it's important to keep track of where the decimal point goes in the answer.

Take the decimal and multiply it as if it were a whole number. After the multiplication, count the total number of digits to the right of the decimal points in the numbers you are multiplying. The answer should have the same number of digits to the right of its decimal point. In our example, multiplying 0.45 (two digits to the right of the decimal) by 90 (no digits to the right of the decimal) results in 40.5.

• Tip: Line up the numbers by the right-most digit before multiplying, ignoring the decimal points momentarily, and then insert the decimal in the answer afterwards.
• Example: When multiplying 0.5 (one digit right) by 3 (no digits right), we get 1.5 with one digit to the right of the decimal.

Percentage Word Problems

Percentage word problems often involve finding a part of a whole or comparing changes in numbers in terms of percent. The key to solving these problems is translating the language of the problem into a mathematical equation involving percentages.

Let's consider our example problem: What number is 45% of 90? We can see that we are being asked to find a portion (45%) of another number (90). By converting our percentage to a decimal and then multiplying, we determine the result to be 40.5. The word 'of' typically indicates multiplication in mathematics.

• Strategy: Identify the 'part', the 'whole', and the 'percentage' in the problem and translate them into a mathematical expression.
• Example: Finding 20% of 200 involves converting 20% to 0.20 and multiplying it by 200, resulting in 40.