Question

Write each fraction as a percent. $$\frac{2}{5}$$

Short answer

Answer: The percentage representation of the fraction $$\frac{2}{5}$$ is $$40\%$$.

Step-by-step solution

Divide the numerator by the denominator

To begin, divide the numerator (2) by the denominator (5): $$\frac{2}{5} = 0.4$$

Multiply the result by 100

Now, to convert the decimal into a percentage, multiply the result by 100: $$0.4 \times 100 = 40$$

Write the result as a percent

The final step is to write the result as a percentage: $$40\%$$ So, the fraction $$\frac{2}{5}$$ is equal to $$40\%$$.

Key concepts

Numerator and Denominator

When learning about fractions, two crucial components to understand are the numerator and the denominator. A fraction is generally written as \(\frac{a}{b}\), where:

• The numerator is the top number, "a," indicating how many parts of the whole you have.
• The denominator is the bottom number, "b," showing into how many equal parts the whole is divided.

In the fraction \(\frac{2}{5}\), the number 2 is the numerator and it tells us we have 2 parts. Meanwhile, the number 5 is the denominator and it conveys that the whole is divided into 5 equal parts. Understanding these roles is essential as they drive the process for converting fractions into decimals and eventually percents. Each fraction part plays a unique role in determining its converted value, so always keep a clear vision of what each number represents.

Decimal Conversion

Decimal conversion is a critical step in translating fractions into percentages. The primary task here is converting the fraction \(\frac{2}{5}\) into a decimal. This is done by dividing the numerator by the denominator. For our example: \[ \frac{2}{5} = 0.4 \] This calculation involves simple division and turns the fraction into a number that is easier to work with when finding equivalent percentages. To clarify:

• Perform the division operation by taking 2 and dividing it by 5.
• The result is 0.4, a decimal representation of the fraction.

Decimal conversion serves as a bridge that connects fractions to percents. By following this step, you pave the way for smooth conversion through multiplication.

Multiplication by 100

Once you have your decimal, the next logical step is multiplication by 100. Multiplying the decimal helps us switch from a base 1 value to a percentage format. Here's how it works using our example fraction \(\frac{2}{5}\):

• We have our decimal: 0.4.
• Multiplying it by 100 gives: \[ 0.4 \times 100 = 40 \]

As you can see, moving the decimal two places to the right (which is what multiplying by 100 does) provides the percentage form, 40%. This step transforms the decimal into a number that directly expresses the fraction as parts out of 100, making it easily recognizable as a percentage. Understanding this step is key to successfully converting any fraction into its percentage form.