Problem 71 - Algebra 1: Concepts and Skills

Question

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

Step-by-Step Solution

Answer

The fraction \(\frac{2}{5}\) is equal to 40%.

Step 1: Convert Fraction to Decimal

To convert a fraction to a decimal, the numerator is divided by the denominator. So, divide 2 by 5. The calculation \(\frac{2}{5} = 0.4\) yields the result as a decimal.

Step 2: Convert Decimal to Percent

To convert the decimal into a percentage, multiply by 100. So, execute the operation \(0.4 * 100 = 40\). Thus, the decimal 0.4 equals 40% when expressed as a percentage.

Key Concepts

Fraction to Decimal Conversion

Fractions represent a part of a whole, and converting them to decimal form is often an essential step in many math calculations. To convert a fraction like \(\frac{2}{5}\) into a decimal, we need to perform a division operation. Here, the numerator, 2, is divided by the denominator, 5.

• The numerator is the top number in a fraction, representing the number of parts we have.
• The denominator is the bottom number, signifying the total number of equal parts.

Performing the division \(2 \div 5\) results in \(0.4\). This decimal represents the exact same value as the fraction. It just expresses it in a different form, making it easier to work with in some cases.

Decimal to Percent Conversion

Once we have a number in decimal form, converting it to a percent is straightforward. Percentages are essentially decimals multiplied by 100 to express a quantity out of 100. For example, to convert the decimal \(0.4\) into a percent:

• Multiply the decimal by 100: \(0.4 \times 100\).
• This operation moves the decimal point two places to the right.

The result of this multiplication is \(40\). Hence, \(0.4\) is equivalent to \(40\) percent. This conversion is useful for comparing ratios, understanding statistics, or determining proportions in everyday scenarios.

Basic Arithmetic Operations

Arithmetic operations form the foundation of mathematics, with addition, subtraction, multiplication, and division being the core operations. When converting fractions and decimals, we primarily use division and multiplication.

• Division helps in breaking down a fraction into its decimal form. For example, dividing 2 by 5 to get 0.4.
• Multiplication is used when converting decimals to percents, where the decimal is multiplied by 100.

Understanding and practicing these two operations allows one to effortlessly transition between fractions, decimals, and percentages, enhancing both computational skills and number literacy.