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Chapter 10: Problem 66

Simplify. $$ 10(-5)+1(-1) $$

Short Answer

Expert verified
-51

Step by step solution

01

Simplify inside the parentheses

First, look at the expression inside the parentheses. Here, we have 10(-5) and 1(-1). There is no further simplification needed for the expressions inside the parentheses.
02

Perform the multiplication operations

Next, perform the multiplications:10(-5) = -50 and 1(-1) = -1. This results in:-50 + (-1).
03

Combine the results

Finally, add the results together:-50 + (-1) = -51.

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Key Concepts

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

Simplifying Multiplication with Negative Numbers
In this exercise, we encounter multiplication involving negative numbers, which can be tricky. Remember, when you multiply a positive number by a negative number, the result is always negative. For instance, in the example given, we have 10(-5). Here, 10 is positive and -5 is negative. So, multiplying these two together gives us -50.

Another example from the exercise: 1(-1). Again, 1 is positive, and -1 is negative. When multiplied, we get -1. Always keep in mind the rule: A positive number multiplied by a negative number equals a negative number.
Understanding this rule helps simplify such expressions easily!
Addition of Negative Numbers
Once we've handled the multiplication steps, we'll move on to addition, particularly involving negative numbers. Adding negative numbers involves combining their absolute values and keeping the negative sign. In our example: -50 + (-1), think of -50 and -1 as two debts. If you owe \(50 and then borrow another \)1, your total debt becomes $51.

This can be confusing initially, but just remember to add their absolute values (50 + 1 = 51) and then keep the negative sign in the result. Thus, -50 + -1 results in -51. By breaking down the process into simpler steps, adding negative numbers becomes much easier!
Understanding Negative Numbers
Negative numbers represent values less than zero. They are typically used to denote loss or absence. In arithmetic operations:
  • Multiplying two negative numbers results in a positive number (e.g., -3 * -2 = 6).
  • Multiplying a positive number by a negative number results in a negative (e.g., 4 * -2 = -8).
  • Adding a negative number is like subtracting its absolute value (e.g., 5 + (-3) is the same as 5 - 3).


It's critical to understand these rules when simplifying expressions. Knowing how negative numbers interact in multiplication and addition makes solving problems like the one given straightforward. The rules may seem strict, but they help maintain consistency in mathematical operations.

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