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Chapter 1: Problem 35

Find each quotient. $$ \frac{15}{5} $$

Short Answer

Expert verified
The quotient is 3.

Step by step solution

01

Understand the Problem

Analyze what needs to be done. Here, it's necessary to find the quotient of the division \( \frac{15}{5} \). A quotient is the result of dividing one number by another.
02

Perform the Division

Divide the numerator by the denominator: \( \frac{15}{5} \). You need to determine how many times the number 5 can fit into 15.
03

Calculate the Results

By performing the division, \( 15 \div 5 = 3 \). Hence, the quotient is 3.

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Key Concepts

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

finding quotients
In algebra, a quotient represents the result you get after dividing one number by another. For example, to find the quotient of \( \frac{15}{5} \), you're essentially asking how many times the number 5 can be evenly distributed into 15. This process involves understanding the components of the division: the numerator (the number being divided) and the denominator (the number by which you're dividing). A clear comprehension of the roles of these components aids in the accurate calculation of the quotient.
basic division
Division is one of the fundamental operations in algebra and arithmetic. It involves determining how many times one number (the divisor) fits into another number (the dividend). For example, in the equation \( 15 \div 5\), 15 is the dividend and 5 is the divisor. To solve it:
  • Identify the dividend (15)
  • Identify the divisor (5)
  • Perform the division operation by seeing how many times the divisor fits into the dividend.
When you calculate \( 15 \div 5 \), you find that 5 fits into 15 exactly 3 times, so the quotient is 3. This method can be applied to more complex problems once the basic concept is mastered.
algebraic operations
Algebraic operations are the backbone of solving any algebra problem. These operations include addition, subtraction, multiplication, and division. Understanding how to perform these operations is crucial for tackling more advanced algebraic concepts. Let's break down some key points:
  • Addition: Combines quantities together.
  • Subtraction: Determines the difference between quantities.
  • Multiplication: Calculates the total when one number is taken multiple times.
  • Division: Distributes a quantity into equal parts or groups.
When dealing with algebraic fractions, such as \( \frac{15}{5} \), division plays a pivotal role. It helps simplify expressions and solve equations by isolating variables or making the calculations easier to handle. Mastery of these basic operations is essential for progressing in algebra.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. See Examples 8 and \(9 .\) The difference between 7 and \(-14\)

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