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Chapter 2: Problem 55

Solve. What is \(2 \%\) of \(40 ?\)

Short Answer

Expert verified
2% of 40 is 0.8.

Step by step solution

01

Understand the Percent Formula

The formula to calculate a percentage of a given number is: \[ \text{Percentage of a Number} = \frac{\text{Percentage}}{100} \times \text{Number} \]
02

Substitute the Values into the Formula

Substitute the given values into the formula. Here, the percentage is 2% and the number is 40. So the equation becomes: \[ \frac{2}{100} \times 40 \]
03

Perform the Calculation

Multiply the fraction by 40: \[ \frac{2}{100} \times 40 = 0.02 \times 40 \]
04

Simplify the Expression

Multiply 0.02 by 40 to get the final result: \[ 0.02 \times 40 = 0.8 \]
05

State the Final Answer

Therefore, 2% of 40 is 0.8.

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Key Concepts

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

percent formula
Understanding the percent formula is crucial. The percent formula helps you find what portion of a number another number represents. It can be expressed as: \[ \text{Percentage of a Number} = \frac{\text{Percentage}}{100} \times \text{Number} \] This formula essentially converts the percentage into a fraction by dividing it by 100, and then multiplies that fraction by the given number. For example, to find out what 2% of 40 is, you'd use: \[ \frac{2}{100} \times 40 \] This means 2% of 40 equals 0.8.
basic arithmetic
Basic arithmetic forms the foundation of almost all mathematical calculations. Arithmetic includes operations like addition, subtraction, multiplication, and division. In our problem, we mostly used multiplication.
For example: multiplying fractions with whole numbers can be done directly by multiplying the fraction's numerator with the whole number. Here, we see:
Multiplying 0.02 by 40: \[ 0.02 \times 40 = 0.8 \] Understanding how to perform these basic operations will help you solve many mathematics problems effectively.
fraction multiplication
Fraction multiplication is simple when you break it down. The key steps include:
  • Multiplying the numerators
  • Multiplying the denominators
For example, when calculating 2% of 40, the fraction multiplication step is: \[ \frac{2}{100} \times 40 \] The numerator 2 is multiplied by 40, and the denominator 100 remains unchanged because 40 is treated as a whole number: \[ \frac{2 \times 40}{100} = \frac{80}{100} \] Simplify the fraction if possible, but in this case, it equals 0.8 directly since 0.8 is already in its simplest form.
Fraction multiplication is useful in many contexts, and mastering it will make solving percentage problems easier.

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