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Chapter 1: Problem 45

For Problems 41-60, simplify each numerical expression. $$ (-3)(-8)+(-9)(-5) $$

Short Answer

Expert verified
The simplified expression is 69.

Step by step solution

01

Multiply the first set of parentheses

The expression includes two separate multiplication operations. The first operation is \(-3\times(-8)\). When multiplying two negative numbers, the result is positive. So, \(-3\times(-8) = 24\).
02

Multiply the second set of parentheses

Next, focus on the second multiplication: \((-9)\times(-5)\). Again, multiplying two negative numbers yields a positive result, so \((-9)\times(-5) = 45\).
03

Add the results together

Now that you have the results from both multiplications, add them together: \(24+45\). Adding these two results gives \(69\).

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Key Concepts

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

Multiplication of Negative Numbers
Did you know that multiplying negative numbers can actually give you a positive result? It might seem surprising at first, but let's break it down. When two negative numbers are multiplied, they "cancel out" each other's negative signs, making the product positive.
For example:
  • \(-3 \times (-8) = 24\)
  • \((-9) \times (-5) = 45\)
Here, the negative signs in each pair multiply to become positive.
Each time you multiply two negative numbers, remember: you're turning negativity into positivity!
Addition
Once you have your positive products from multiplying negative numbers, the next step is simple: addition. Addition involves calculating the sum of two or more numbers.
In this case, now that we have two positive numbers, 24 and 45, we simply add them together to attain a new total.
Addition is often one of the first arithmetic operations that make numbers grow larger.
Here's how it works:
  • Start with 24.
  • Add 45 to it.
  • You get 69 as the sum.
This process is straightforward, but it requires careful attention to accuracy. Adding numbers correctly is key to reaching the right answer!
Numerical Expressions
A numerical expression is like a math sentence that involves numbers and operations such as addition, subtraction, multiplication, and division. These expressions do not have an equal sign, unlike equations.
To simplify a numerical expression, you perform the operations given in the expression.
Here's an example from our original problem:
  • The expression is \((-3)(-8)+(-9)(-5)\).
  • After performing the multiplications, you simplify it to \(24 + 45\).
  • Finally, by completing the addition, you achieve \(69\).
Solving numerical expressions requires step-by-step operations, and each step is critical to derive the correct final result.

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Most popular questions from this chapter

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$[5(-8)] 4=5[-8(4)]$$

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \((a-b)-(a+b)\) for \(a=19\) and \(b=-17\)

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$37(-42-58)$$

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$(25)(-18)(-4)$$

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \((x+12)-(x-14)\) for \(x=-11\)
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