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Chapter 2: Problem 61

Evaluate. The product of \(-3\) and \(5,\) divided by 1 less than 6

Short Answer

Expert verified
The result is \(-3\).

Step by step solution

01

Identify the product

First, identify and calculate the product of \(-3\) and \(5\).
02

Calculate the product

Multiply \(-3\) by \(5\): \(-3 \times 5 = -15\).
03

Determine the divisor

Identify the divisor as \(1\) less than \(6\), which is \(6 - 1 = 5\).
04

Perform the division

Divide the product \(-15\) by the divisor \(5\): \frac{-15}{5} = -3\.

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Key Concepts

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

Arithmetic Operations
Arithmetic operations form the foundation of mathematics. They include the basic operations of addition, subtraction, multiplication, and division. These operations are essential for solving a wide variety of mathematical problems.

In the given exercise, we need to perform two of these operations: multiplication and division. It's important to follow the correct order of operations. This ensures that you evaluate expressions accurately.

To start, recognize what each operation requires and how they interact with each other:
  • Multiplication: This operation combines equal groups of quantities.
  • Division: This splits a quantity into equal parts.
Understanding each step is crucial to avoid mistakes.
Multiplication
Multiplication is one of the simplest yet most powerful arithmetic operations. It involves finding the total of one number added repeatedly, based on another number.

In this exercise, we start by multiplying \(-3\) by \5\. The operation can be written as:
\[-3 \times 5\]

Multiplication rules tell us that multiplying a negative number by a positive number results in a negative product. Thus:
\(-3 \times 5 = -15\)

Key points to remember about multiplication:
  • The product of two positive numbers is positive.
  • The product of two negative numbers is positive.
  • The product of a positive and a negative number is negative.
Division
Division is the process of distributing a quantity into equal parts. It鈥檚 crucial to identify the correct divisor to perform this operation accurately.

In the exercise, after finding the product \(-3 \times 5 = -15\), we need to divide this product by \1\ less than \6\.

First, determine the divisor:
\6 - 1 = 5\

Now perform the division:
\[\frac{-15}{5} = -3\]

Some essential points about division:
  • A number divided by a smaller positive number results in a larger negative quotient if the original number is negative.
  • Division by zero is undefined.
  • Division distributes evenly if there is no remainder.
Always ensure to check the result by reversing the operation if necessary.

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Most popular questions from this chapter

Solve each equation, and check your solution. $$ 0.006(x+2)=0.007 x+0.009 $$

Solve each inequality. Give the solution set in both interval and graph form. See Examples 1鈥�5.$$ 2 x-8 \geq-2 x $$

Solve each problem. See Section 2.2. Use \(P=a+b+c\) to find \(a\) if \(b=13, c=14,\) and \(P=46\)

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\}\) and \(D=\\{4\\} .\) Specify each set. See Examples I and 5. $$ B \cap A $$

Solve each problem imolving consecutive integers. Find four consecutive integers such that the sum of the first three is 54 more than the fourth.
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