Problem 280 - Intermediate Algebra

Question

In the following exercises, convert each fraction to a decimal. $$ \frac{17}{4} $$

Step-by-Step Solution

Answer

4.25

Step 1: Understanding Fractions

Recall that a fraction represents division. Here, the fraction \(\frac{17}{4}\) means 17 divided by 4.

Step 2: Perform the Division

Divide the numerator (17) by the denominator (4). Calculate \(17 \div 4\).

Step 3: Calculate the Quotient

17 divided by 4 equals 4 with a remainder of 1. This can be written as 4.25 in decimal form because 1 (the remainder) divided by 4 is 0.25.

Step 4: Write the Decimal

Therefore, \(\frac{17}{4}\) converted to a decimal is 4.25.

Key Concepts

Fraction Division

The process of converting a fraction to a decimal starts by understanding the concept of fraction division. A fraction, like \(\frac{17}{4}\), essentially represents the division of 17 by 4.
When you see a fraction, think of it as a division problem waiting to be solved.
Here's a step-by-step guide to help you:

• The numerator is the number on top (here, it's 17).
• The denominator is the number on the bottom (here, it's 4).
• Divide the numerator by the denominator (i.e., 17 divided by 4).

By following these steps, you'll be well on your way to converting fractions into decimals.

Decimal Conversion

Converting fractions to decimals is a straightforward process once fraction division is grasped. After performing the division (17 divided by 4), you obtain a quotient.
Let's break it down:

• When you divide 17 by 4, the result is 4 with a remainder.
• The remainder here is 1 (since 4 multiplied by 4 is 16, and 17 minus 16 is 1).
• To convert this remainder into a decimal, divide it by the original denominator (1 divided by 4).

The result is 0.25. Therefore, the complete decimal form is 4.25 (since we add 4 + 0.25).
Decimal conversion makes it easier sometimes to compare and use numbers.

Basic Arithmetic

Mastering basic arithmetic is essential for converting fractions to decimals. It involves several critical skills:

• Understanding division well.
• Knowing how to handle remainders.
• Being comfortable with both whole numbers and decimal numbers.

To recap with our example of \(\frac{17}{4}\):

• Perform basic division: 17 divided by 4 is 4 with a remainder of 1.
• Convert the remainder (1) to a decimal: 1 divided by 4 is 0.25.
• Add the whole part (4) and the decimal part (0.25): The result is 4.25.

Practicing these basic arithmetic skills will give you the confidence to tackle more complex math problems.
Remember, it’s all about breaking down steps and taking your time to understand each part!