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Chapter 11: Problem 36

Find the value of each expression. $$-8(5 m+8 n), \text { if } m=0 \text { and } n=-1$$

Short Answer

Expert verified
The value of the expression is 64.

Step by step solution

01

Substitute the Values of Variables

Given the expression \(-8(5m + 8n)\). First, substitute \(m = 0\) and \(n = -1\) into the expression. This gives:\[-8(5(0) + 8(-1))\]
02

Simplify Inside the Parentheses

Simplify the expression inside the parentheses. Calculate \(5 \times 0\) and \(8 \times -1\):\[5 \times 0 = 0 \8 \times -1 = -8\]Substitute these into the expression:\[-8(0 - 8)\]
03

Further Simplify Inside the Parentheses

Now simplify the expression inside the parentheses:\[0 - 8 = -8\]The expression becomes:\[-8(-8)\]
04

Multiply the Outer Coefficient

Finally, multiply \(-8\) by \(-8\):\[-8 \times -8 = 64\]

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Key Concepts

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

Substitution
Substitution is all about replacing variables in an algebraic expression with specific values. In our exercise, we're given the expression \(-8(5m + 8n)\) and the specific values \(m = 0\) and \(n = -1\). The goal is to find the value of this expression by substituting these values in place of the variables.
  • Why do we substitute? - It helps convert the expression from one dealing with variables to one that contains only numbers, making it easier to simplify and solve.
  • How do we substitute? - Wherever you see \(m\) in the expression, replace it with \(0\), and wherever you see \(n\), replace it with \(-1\). So, \(-8(5m + 8n)\) becomes \(-8(5 \times 0 + 8 \times -1)\).
Remember, substitution is a key step in solving algebraic problems, making them much more manageable.
Simplification
Simplification is the process of making an expression easier to work with by reducing it to its simplest form. In our example, we started with the expression \(-8(5 \times 0 + 8 \times -1)\). After performing substitution, simplification allows us to break it down into more simple and manageable terms.
  • First, calculate each term: \(5 \times 0 = 0\) and \(8 \times -1 = -8\).
  • Then, you'll have \(-8(0 - 8)\).
  • Next, simplify within the parentheses: \(0 - 8 = -8\).
Simplification doesn't change the value of an expression; it just makes it easier to handle. It often requires performing arithmetic operations like multiplication and addition to combine terms or reduce expressions.
Multiplication of Integers
Multiplication of integers is a fundamental arithmetic operation used when simplifying expressions. When you multiply integers, you follow specific rules based on the signs of the numbers involved.
  • Same sign: Multiplying two positive or two negative integers results in a positive product. For instance, \(-8 \times -8\) gives us \(64\).
  • Different signs: Multiplying a positive and a negative integer results in a negative product. For example, \(-2 \times 3 = -6\).
In our exercise, after simplification, we had \(-8(-8)\). Applying the rule above, multiplying two negative numbers yields a positive result, which is \(64\). Understanding these rules ensures that your solutions are accurate when dealing with multiplication in algebraic expressions.

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Most popular questions from this chapter

Translate each phrase or sentence to a mathematical expression or equation. A number minus the opposite of five.

For problems \(57-140\), solve each equation. $$ -3 x+8=-7 $$

Translate each phrase or sentence to a mathematical expression or equation. A number divided by seven, plus two, is seventeen.

For problems \(57-140\), solve each equation. $$ \frac{2 x}{3}-5=8 $$

Translate each phrase or sentence to a mathematical expression or equation. Twice a number is decreased by seven. This result is decreased by four times the number. The result is negative the original number, minus six.
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