Question

Find each result using any method you like. \(112 \%\) of 70

Short answer

78.4

Step-by-step solution

Convert Percentage to Decimal

To find 112% of 70, first convert the percentage to a decimal. To do this, divide 112 by 100: \[ 112\text{%} = \frac{112}{100} = 1.12 \]

Multiply by the Number

Next, multiply the decimal by the number. So, multiply 1.12 by 70: \[ 1.12 \times 70 = 78.4 \]

Write the Final Result

The result is 78.4. This means 112% of 70 is 78.4.

Key concepts

Convert percentage to decimal

When you need to calculate a percentage of a number, the first step is to convert the percentage into a decimal. Percentages are based on a value of 100, so you can do this by dividing the given percentage by 100. For instance:

To convert 112% to a decimal, divide 112 by 100:
\[ 112\% = \frac{112}{100} = 1.12 \]

This makes calculations easier and prepares the percentage for multiplication with the number. Remember, the conversion is vital to accurately pinpoint the part of the number you are analyzing.

Multiplication

Once you have your percentage converted to a decimal, your next step is to multiply it by the quantity in question. In our example, we want to find 112% of 70. We already have the decimal form of 112%, which is 1.12.

Now, multiply 1.12 by 70:
\[ 1.12 \times 70 = 78.4 \]

Multiplying 1.12 by 70 tells us how much 112% of 70 is. Multiplication in this context scales the original number (70) by the percentage (1.12), giving us our desired result.

Finding percentage

Finally, you need to understand how to interpret and use the percentage you have calculated. In our example, we found that 112% of 70 is 78.4. This tells us that if we increase 70 by 12% (because 112% is 100% + 12%), we get 78.4.

To find any percentage of a number, follow these steps:

• Convert the percentage to a decimal by dividing by 100.
• Multiply the decimal by the number in question.

Let's do a quick example. To find 50% of 30:

• Convert 50% to decimal: \[ 50\% = \frac{50}{100} = 0.5 \]
• Multiply 0.5 by 30: \[ 0.5 \times 30 = 15 \]

So, 50% of 30 is 15. These steps will help you understand and find percentages for any numbers you encounter.