Problem 76 - Algebra 1

Question

Write the fraction as a decimal and as a percent. $$ \frac{3}{4} $$

Step-by-Step Solution

Answer

The decimal equivalent of the fraction \( \frac{3}{4} \) is 0.75 and the percentage equivalent is 75%.

Step 1: Conversion to Decimal

Divide the numerator by the denominator. Here, divide 3 (numerator) by 4 (denominator). The operation can be expressed as \( \frac{3}{4} = 0.75 \)

Step 2: Conversion to Percent

Convert the decimal to a percentage by multiplying by 100. This can be expressed as \( 0.75 * 100 = 75\% \)

Key Concepts

Converting Fractions

Fractions can sometimes seem a bit tricky, but turning them into decimals makes them easier to understand. To convert a fraction to a decimal, you simply divide the top number (numerator) by the bottom number (denominator). For the fraction \( \frac{3}{4} \), you divide 3 by 4, which equals 0.75. This means that 3/4 as a decimal is 0.75.
Performing this division can either be done manually or using a calculator, especially for more complicated fractions. Understanding that a fraction represents division can help you tackle this with confidence.
Remember, the result of this division gives you the decimal equivalent of the fraction, and it’s a great first step towards other conversions, like percent conversion.

Decimal to Percent

Converting a decimal into a percent is a straightforward process. Once you have your decimal, like we have 0.75 from \( \frac{3}{4} \), the next step is to change it to a percentage. You multiply the decimal by 100. For 0.75, multiplying by 100 gives you 75, which means \( 0.75 = 75\% \).
This method works because percentage literally means "per hundred," so you are calculating how much out of 100 your decimal represents. Thus, multiplying by 100 shifts your decimal two places to the right, providing the equivalent percentage.
This simple conversion is very useful in many practical situations, like understanding discounts or interest rates.

Basic Arithmetic Operations

Understanding basic arithmetic operations is essential when working with fractions and decimals. The main arithmetic operations include addition, subtraction, multiplication, and division. For converting fractions like \( \frac{3}{4} \) into decimals and percentages, division is your primary tool.
When you're converting, you're using division to understand how much one part (numerator) is in relation to the whole (denominator). This division transforms the fraction into a more usable decimal form.
Additionally, multiplication comes into play when you shift that decimal to a percentage by multiplying by 100. These basic operations are not only fundamental for conversions but also for solving everyday math problems efficiently. Embracing these operations will not only ease conversions but also enhance your overall math skills.