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Chapter 6: Problem 1

Answer each question. In a fraction, what operation does the fraction bar represent?

Short Answer

Expert verified
The fraction bar represents division.

Step by step solution

01

Understand the Fraction Bar

A fraction has two parts: the numerator (the top number) and the denominator (the bottom number). The fraction bar is the line that separates these two numbers.
02

Identify the Operation

The fraction bar represents division. It indicates that the numerator should be divided by the denominator.
03

Example

Consider the fraction \(\frac{3}{4}\). This means 3 (numerator) divided by 4 (denominator), which is \(\frac{3}{4} = 0.75\).

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Key Concepts

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

fractions
A fraction is a way to represent parts of a whole. It is composed of two numbers separated by a fraction bar. The top number is called the numerator, and the bottom number is called the denominator. Together, they show how many parts of a whole you're considering and how many of those parts exist.
numerator and denominator
In a fraction, the numerator is the top number. It tells us how many parts of the whole are being considered. The denominator is the bottom number. It tells us the total number of equal parts the whole is divided into.

For example, in the fraction \(\frac{3}{4}\), the numerator is 3 and the denominator is 4. This means we are considering 3 parts out of 4 equal parts.

Understanding the numerator and denominator is crucial for performing operations with fractions.
division in mathematics
The fraction bar in a fraction represents the mathematical operation of division. When you see a fraction like \(\frac{3}{4}\), it means 3 divided by 4.

Dividing fractions is straightforward once you understand this concept. For instance, the fraction \(\frac{3}{4}\) can be interpreted as 3 divided by 4, resulting in 0.75.

This relationship between fractions and division is key to many aspects of math, from basic arithmetic to more complex algebraic expressions.

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Most popular questions from this chapter

Simplify each complex fraction. Use either method. $$ \frac{6+\frac{2}{r}}{\frac{3 r+1}{4}} $$

In the movie Little Big League, young Billy Heywood inherits the Minnesota Twins baseball team and becomes its manager. Before the biggest game of the year, he can't keep his mind on his job because a homework problem is giving him trouble. If Joe can paint a house in \(3 \mathrm{hr}\) and Sam can paint the same house in \(5 \mathrm{hr},\) how long does it take for them to do it together? With the help of one of his players, Billy solves the problem. Solve the following problem using the method of Example \(3 .\) Then solve it using the formula obtained in Exercise \(47 .\) How do the answers compare? A screen printer can complete a \(t\) -shirt order for a Little League baseball organization in 15 hr using a large machine. The same order would take \(30 \mathrm{hr}\) using a smaller machine. How long would it take to complete the order using both machines together?

These exercises involve factoring sums and differences of cubes. Write each rational expression in lowest terms. $$ \frac{x^{3}-27}{x-3} $$

These exercises involve grouping symbols, factoring by grouping, and factoring sums and differences of cubes. Multiply or divide as indicated. Write each answer in lowest terms. \(\frac{3 a-3 b-a^{2}+b^{2}}{4 a^{2}-4 a b+b^{2}} \cdot \frac{4 a^{2}-b^{2}}{2 a^{2}-a b-b^{2}}\)

Simplify each complex fraction. Use either method. $$ \frac{\frac{5}{8}+\frac{2}{3}}{\frac{7}{3}-\frac{1}{4}} $$
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