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Chapter 3: Problem 47

Simplify by dividing the numerator by the denominator. $$\frac{3}{1}$$

Short Answer

Expert verified
The simplified form is 3.

Step by step solution

01

Understanding the Problem

We are asked to simplify the fraction \( \frac{3}{1} \) by dividing the numerator by the denominator. This means we need to perform the division of the top number (numerator), which is 3, by the bottom number (denominator), which is 1.
02

Perform Division

Divide the numerator by the denominator: \( \frac{3}{1} = 3 \). This division is straightforward because any number divided by 1 is the number itself.
03

Interpret the Result

The result of the division is 3. Therefore, the simplified form of \( \frac{3}{1} \) is simply 3.

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Key Concepts

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

Understanding the Numerator and Denominator
When dealing with fractions, understanding the roles of the numerator and denominator is crucial. A fraction is composed of two parts: the numerator, found on the top, and the denominator, pathed below by the horizontal bar.
  • The numerator represents how many parts of the whole are being considered.
  • The denominator indicates the total number of equal parts that make up the whole.
For example, in the fraction \( \frac{3}{1} \), 3 is the numerator. It signifies the quantity we are focusing on. The denominator is 1, which means that the whole is not divided into smaller sections. Therefore, 3 out of 1 means we are dealing with the entire number itself, 3. This showcases how fractions can simplify to whole numbers, emphasizing the significance of understanding these parts.
The Division Process in Fractions
Division plays a pivotal role in simplifying fractions. Here, it involves dividing the numerator by the denominator. In the fraction \( \frac{3}{1} \), we perform the operation by dividing the top number (3) by the bottom number (1).
  • When dividing by 1, the result remains the same as the numerator.
  • This is because dividing anything by 1 leaves it unchanged.
Hence, \( \frac{3}{1} = 3 \). This is an example of how division simplifies fractions effortlessly, illustrating that a fraction with a denominator of 1 is equivalent to the numerator itself. Effortless operations like these are essential basic arithmetic skills, highlighting the simplicity of division in fractions.
Using Basic Arithmetic to Simplify Fractions
Basic arithmetic is fundamental to mastering fractions. It allows for straightforward simplification by utilizing operations like division to shorten expressions.
When encountering fractions such as \( \frac{3}{1} \), notice how arithmetic processes like division immediately clear the path to simplification.
  • Division helps transform a fraction into a simpler expression.
  • Basic operations also assist in recognizing patterns and shortcuts in fractions.
  • It aids in understanding that division by 1 does not change the value of the numerator.
As shown, \( \frac{3}{1} = 3 \) demonstrates that basic arithmetic is not just about numbers but also the strategies behind simplifying any problem into its most understandable form. Emphasizing these fundamentals makes handling fractions intuitive and quick for anyone learning or practicing math.

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Most popular questions from this chapter

Multiply or divide as indicated. $$\frac{9}{10}+\frac{7}{10}$$

Divide. $$10 \div 3$$

These problems review the four basic operations with fractions from this chapter. Perform the indicated operations. $$\frac{3}{7}-\frac{2}{7}$$

Multiply or divide as indicated. $$\frac{3}{4} \div \frac{5}{6}$$

A dress manufacturer usually buys two rolls of cloth, one of \(32 \frac{1}{2}\) yards and the other of \(25 \frac{1}{3}\) yards, to fill his weekly orders. If his orders double one week, how much of the cloth should he order? (Give the total yardage.)
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