Problem 76 - Prealgebra

Question

Write as a percent. Write the remainder in fractional form. $$\frac{3}{8}$$

Step-by-Step Solution

Answer

\( \frac{3}{8} = 37.5\% \) with remainder included in decimal form (\(0.375\)).

Step 1: Understand the Fraction

We start with the fraction \( \frac{3}{8} \). This fraction represents the part of a whole, where the numerator is 3 and the denominator is 8.

Step 2: Convert Fraction to Decimal

Convert the fraction to a decimal by dividing the numerator by the denominator. So we perform the division: \( 3 \div 8 = 0.375 \).

Step 3: Convert Decimal to Percentage

To convert the decimal to a percentage, multiply it by 100. So, \( 0.375 \times 100 = 37.5 \% \).

Step 4: State the Remainder in Fractional Form

When converting \( \frac{3}{8} \) to a percentage, no remainder exists beyond the decimal. As \( 0.375 \) converts directly to \( 37.5 \% \), any remainder in fractional form is already included within the decimal.

Key Concepts

Understanding Fractions

Fractions represent parts of a whole in mathematics, helping us visualize division and proportional relationships. They consist of two parts: a numerator and a denominator.

• The numerator (top number) indicates how many parts we are considering.
• The denominator (bottom number) tells us into how many equal parts the whole is divided.

For the fraction \(\frac{3}{8}\), the numerator is 3, which signifies that we have 3 parts of something that is divided into 8 equal parts. When you understand fractions, you can easily see how much of something you have. Break up your work to look at one component at a time, first focusing on the numerator and then the denominator. Remember, fractions can represent parts of a bigger picture and are key in many fields beyond math, including science and real-life scenarios.

Decimal Conversion

Decimal conversion is an important skill that helps in performing calculations efficiently. It refers to converting a fraction into a decimal format, which is a numerical form based on the number 10. You do this by dividing the numerator by the denominator.
In this case, you're looking at \(\frac{3}{8}\). By dividing 3 by 8, you get \(0.375\). This step makes it easier to perform further mathematical operations, such as converting to percentages or comparing values.
Decimals provide a clear and concise method of expressing fractions and can seem more intuitive to work with in complex calculations. They are widely used in financial transactions, measurements, and other applications where precision is crucial.

Understanding Percentages

Percentages help represent parts of a whole as parts per hundred, making comparisons easier to understand. The conversion from a decimal to a percentage is straightforward: simply multiply the decimal by 100.

• If you have \(0.375\) from converting \(\frac{3}{8}\), then multiply it by 100 to obtain \(37.5\%\).

This means that \(3/8\) of something can also be described as 37.5 parts out of 100.
Percentages are vital for understanding data, calculating discounts in shopping, and indicating changes in statistics. They make comparisons between different quantities simpler and universal by relating them all back to the base of 100 parts. Whether you're calculating your grades, finding discount prices, or interpreting data sets, percentages offer a meaningful way to express portions of any quantity.