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Chapter 5: Problem 207

Convert each fraction to a decimal. \(\frac{11}{4}\)

Short Answer

Expert verified
2.75

Step by step solution

01

Understand the Fraction

Identify the numerator (11) and the denominator (4) in the fraction \(\frac{11}{4}\).
02

Set Up the Division

The fraction \(\frac{11}{4}\) can be interpreted as the division of 11 by 4. Set up the division as 11 divided by 4.
03

Perform the Division

Divide 11 by 4. When 11 is divided by 4, the result is 2.75 since 11 divided by 4 equals 2 with a remainder of 3, and 3 divided by 4 equals 0.75.
04

Combine Results

Combine the results from the division to get the decimal form of the fraction. Thus, \(\frac{11}{4}\) = 2.75.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Numerator and Denominator
When working with fractions, it is essential to understand the roles of the numerator and the denominator. A fraction, such as \(\frac{11}{4}\), is composed of two parts: the numerator (11) and the denominator (4).
The numerator is the top number in the fraction and represents the number of parts we have. The denominator is the bottom number and signifies the number of equal parts into which the whole is divided.
For example, in a pizza sliced into 4 equal pieces, each piece represents a denominator of 4. If you have 11 slices, the fraction would be \(\frac{11}{4}\), indicating you have more slices than a single pizza sliced into 4 parts.
Division of Fractions
Turning a fraction into a decimal involves the concept of division. Essentially, a fraction is a division problem in disguise. Let's take our fraction \(\frac{11}{4}\).
Here, we need to divide 11 by 4. This can be written as 11 梅 4. Performing this operation:
  • 11 divided by 4 equals 2 with a remainder of 3.
  • Next, to handle the remainder, we convert it into a decimal by dividing further.
  • 3 divided by 4 equals 0.75.
Combining these two results, we get 2 + 0.75, which equals 2.75. Hence, \(\frac{11}{4}\) as a decimal is 2.75.
Decimal Representation
Decimals are another way to represent fractions. They are especially useful because they fit into our base-10 number system, which makes calculations and comparisons easier.
To convert the fraction \(\frac{11}{4}\) into a decimal, we divide the numerator by the denominator. The result of this division gives us the decimal representation.
Performing the division 11 梅 4, we get 2.75. This means that \(\frac{11}{4}\) is exactly equivalent to 2.75 in decimal form. Understanding decimals helps in various fields such as science, engineering, and daily life, where they ease the process of mathematical computations.

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