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Chapter 1: Problem 94

Write a numerical expression for each phrase and simplify. The product of 4 and \(-7,\) added to \(-12\)

Short Answer

Expert verified
-40

Step by step solution

01

Identify Key Operations

Determine the operations described in the phrase. Here, 'The product of 4 and -7' indicates multiplication, and 'added to -12' indicates addition.
02

Write the Expression

Convert the phrase into a numerical expression. The product of 4 and -7 is written as \(4 \times (-7)\) and adding -12 gives: \(4 \times (-7) + (-12)\).
03

Perform the Multiplication

Calculate the product of 4 and -7. \(4 \times (-7) = -28\).
04

Perform the Addition

Add -12 to the result of the multiplication. \(-28 + (-12) = -40\).
05

Simplify the Expression

The simplified expression is: \(-40\).

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Key Concepts

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

Multiplication
Multiplication is one of the basic arithmetic operations. It is a way to add a number to itself a certain number of times. In multiplication, we have two numbers called factors, and the result is called the product. For instance, in the expression \(4 \times (-7)\), the numbers 4 and -7 are the factors. To perform multiplication:
  • Multiply the numbers as if they were both positive.
  • If one factor is negative, the product will be negative.
For our exercise, we multiply 4 by -7, giving us -28.
Addition
Addition is another fundamental arithmetic operation. It combines two or more numbers into a single sum. When adding positive and negative numbers, it鈥檚 important to understand how their signs affect the outcome:
  • Adding a positive number increases the sum.
  • Adding a negative number decreases the sum.
In the expression \(-28 + (-12)\), adding -12 to -28 results in a more negative number because you are adding a negative value. The simplified result is -40.
Simplification
Simplification is the process of reducing a mathematical expression to its simplest form. This often involves combining like terms and performing all possible operations. In our problem, we simplified the expression \(4 \times (-7) + (-12)\) in several steps:
  • First, we calculated the multiplication: \(4 \times (-7) = -28\).
  • Next, we performed the addition: \(-28 + (-12) = -40\).
The final simplified form of the expression is -40, making it easier to understand and work with.

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Most popular questions from this chapter

The top of Mt. Whitney, visible from Death Valley, has an altitude of \(14,494\) ft above sea level. The bottom of Death Valley is 282 ft below sea level. Using 0 as sea level, find the difference between these two elevations.

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 4 if its last two digits form a number divisible by \(4,\) and not otherwise. Show that (a) \(6,221,464\) is divisible by 4 and (b) \(2,876,335\) is not divisible by 4

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