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Chapter 3: Problem 75

Find each quotient. $$ \frac{4-2}{8-5} $$

Short Answer

Expert verified
\(\frac{2}{3}\)

Step by step solution

01

Simplify the Numerator

First, simplify the numerator by performing the subtraction inside the parentheses: \(4 - 2 = 2\)
02

Simplify the Denominator

Next, simplify the denominator by performing the subtraction inside the parentheses: \(8 - 5 = 3\)
03

Divide the Simplified Numerator by the Simplified Denominator

Now, divide the simplified numerator by the simplified denominator: \(\frac{2}{3} = \frac{2}{3}\)

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Key Concepts

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

Quotient
When you divide one number by another, you get a result called the quotient. In algebra, the quotient is the answer you get when you divide the numerator by the denominator. For example, in the expression \(\frac{4-2}{8-5}\), after simplifying, the quotient is \(\frac{2}{3}\).
  • The numerator is the number on top.
  • The denominator is the number on the bottom.
To find the quotient, you perform the division step. So, understanding how to solve for the quotient is key in most basic algebra division problems.
Simplification
Simplification is the process of reducing an expression to its simplest form. In our example \(\frac{4-2}{8-5}\), we simplify the expression by first performing the subtractions both in the numerator and the denominator.
  • First, simplify the numerator from 4-2 to get 2.
  • Next, simplify the denominator from 8-5 to get 3.
After these steps, we are left with the simpler expression \(\frac{2}{3}\). This makes it easier to understand and solve the problem. Always perform any possible simplification steps first in algebra.
Numerator and Denominator
In fractions, the numerator and denominator are key components. The numerator is the number above the division line, and the denominator is the number below it. For the fraction \(\frac{4-2}{8-5}\):
  • The numerator is 4 - 2, which simplifies to 2.
  • The denominator is 8 - 5, which simplifies to 3.
The fraction tells us how many parts of a whole we have (numerator) and how many parts the whole is divided into (denominator). A clearer understanding helps in computing the final quotient.
Subtraction
Subtraction is vital in simplifying expressions in algebra. In the expression \(\frac{4-2}{8-5}\), we perform subtraction to simplify both the numerator and the denominator.
  • Performing the subtraction in the numerator, 4 - 2 gives us 2.
  • Performing the subtraction in the denominator, 8 - 5 gives us 3.
Only after completing these subtraction operations can we divide to find the quotient. Mastering subtraction ensures you can simplify more complex algebraic expressions efficiently.

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Most popular questions from this chapter

The maximum benefit for the heart from exercising occurs if the heart rate is in the target heart rate zone. The lower limit of this target zone can be approximated by the linear equation $$ y=-0.65 x+143 $$ where \(x\) represents age and \(y\) represents heartbeats per minute. (Source: The Gazette.) (a) Complete the table of values for this linear equation. (b) Write the data from the table of values as ordered pairs. (c) Make a scatter diagram of the data. Do the points lie in an approximately linear pattern?

Graph each linear equation. \(x=-y+6\)

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What is the equation of the \(x\) -axis? What is the equation of the \(y\) -axis?

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