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Chapter 3: Problem 99

For problems 99-102, solve. \(m=\frac{10-4}{5-3}\)

Short Answer

Expert verified
m = 3

Step by step solution

01

- Identify Numerator and Denominator

Identify the parts of the fraction. The numerator is \( 10-4 \) and the denominator is \( 5-3 \).
02

- Simplify Numerator

Simplify the numerator: \( 10-4 = 6 \).
03

- Simplify Denominator

Simplify the denominator: \( 5-3 = 2 \).
04

- Calculate the Fraction

Divide the simplified numerator by the simplified denominator: \( \frac{6}{2} = 3 \).

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Key Concepts

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

Fractions
Fractions represent parts of a whole and are written as one number divided by another. The top number is the **numerator**, which shows how many parts we have.
The bottom number is the **denominator**, which tells us into how many parts the whole is divided.
In the exercise, the fraction is given by the expression \(\frac{10-4}{5-3}\).Understanding the structure of fractions helps in manipulating and simplifying them.
Simplifying Expressions
Simplification involves reducing expressions to their simplest form. It requires performing basic arithmetic on the terms.
In the given exercise, we start by simplifying the numerator and the denominator.
  • First, we simplify the numerator, \(10-4\), which equals 6.
  • Next, we simplify the denominator, \(5-3\), which equals 2.
This step makes the fraction easier to work with.
Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations are the foundation for solving algebra problems.
In this exercise, we use subtraction:
\(10-4 = 6\) (numerator)
\(5-3 = 2\) (denominator)
Finally, we use division:
\( \frac{6}{2} = 3\)
Mastery of these basic operations is essential for success in algebra.
Step-by-Step Solutions
Following a step-by-step approach ensures clarity and accuracy when solving algebra problems.
  • **Step 1:** Identify the parts of the fraction (numerator and denominator).
  • **Step 2:** Simplify the numerator.
  • **Step 3:** Simplify the denominator.
  • **Step 4:** Divide the simplified numerator by the simplified denominator.
Breaking down the problem into smaller steps can make it easier to understand and solve.
This methodical approach ensures no steps are skipped and makes the solution clearer.

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Most popular questions from this chapter

Balanced Rock in Arches National Park is \(55 \mathrm{ft}\) tall and weighs 3500 tons. Find its height in meters. Round to the nearest tenth. \((1 \mathrm{~m} \approx 3.2808 \mathrm{ft}\).) (Source: www.desertusa .com)

Use a graphing calculator to graph each equation. Choose a window that shows the \(x\)-intercept and \(y\)-intercept. Sketch the graph; describe the window. \(y=\frac{1}{2} x-8\)

(a) graph the given points, and draw a line through the points. (b) use the graph to find the slope of the line. (c) use the slope formula to find the slope of the line. \((1,5) ;(3,-3)\)

Use the slope formula to find the slope of the line that passes through the points. ( \(3 \mathrm{hr}, \$ 45) ;(7 \mathrm{hr}, \$ 105)\)

Use the slope formula to find the slope of the line that passes through the points. \((-20,45) ;(-15,90)\)
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