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Chapter 1: Problem 43

Evaluate each of the following expressions, if possible. $$(12-4)(3-8)$$

Short Answer

Expert verified
-40

Step by step solution

01

Evaluate the first parenthesis

Calculate the expression inside the first parenthesis: \(12 - 4\). This gives: \(12 - 4 = 8\).
02

Evaluate the second parenthesis

Calculate the expression inside the second parenthesis: \(3 - 8\). This gives: \(3 - 8 = -5\).
03

Multiply the results

Multiply the results from the two previous steps: \(8\) and \(-5\). This gives: \(8 \times -5 = -40\).

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Key Concepts

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

Parentheses in Algebra
Parentheses play a crucial role in algebraic expressions. They dictate the order in which operations should be performed.
When you see an expression with parentheses, always start by evaluating the expressions inside them first.
For example, in the expression \( (12-4)(3-8) \), you need to handle the calculations inside the parentheses separately before doing anything else.
By following this rule, you can avoid mistakes and ensure your solution is correct. Parentheses can change the outcome of an expression, so it's important to respect their order.
Evaluating Arithmetic Expressions
Evaluating arithmetic expressions involves performing basic mathematical operations such as addition, subtraction, multiplication, and division.
To solve an expression accurately, follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
In our example, \( (12-4)(3-8) \), we first evaluate the expressions inside the parentheses: \( 12 - 4 = 8 \) and \( 3 - 8 = -5 \).
After dealing with the parentheses, we proceed to the next step, which in this case is multiplication.
Multiplication in Algebra
Multiplication in algebra is straightforward but it requires careful attention, especially if negative numbers are involved.
After simplifying expressions inside parentheses, you might need to multiply the results.
Take the example \( (12-4)(3-8) \).
Upon solving within the parentheses, you get \( 8 \) and \( -5 \).
Next, multiply these two results: \( 8 \times -5 = -40 \).
Remember, whenever multiplying two numbers, if one is negative the result will be negative. Conversely, if both numbers were negative or both positive, the result would be positive.
Understanding these rules can make solving algebraic problems much easier.

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Most popular questions from this chapter

Sketch the given set on a number line. $$\\{x | 3

Factor the given number into its prime factors. If the number is prime, say so. $$3,024$$

We know that multiplication means repeated addition. That is, 4 times 3 means add 3 four times. In view of this and the rule for adding negative integers, what should 4 times \(-3\) be equal to?

Try to find an approximate value for a square root of \(3 .\) That is, try to find a number that when multiplied by itself gives a product of \(3 .\) Give answers correct to the nearest whole number, nearest tenth, nearest hundredth, and nearest thousandth. Use a calculator to help with the multiplication, but not to compute the square root itself.

Compute the given expression. Round off your answer to two decimal places where necessary. $$0.28(56)-0.36(63)$$
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