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Chapter 1: Problem 44

Evaluate each of the following expressions, if possible. $$(11-6)(2-7)$$

Short Answer

Expert verified
-25

Step by step solution

01

Evaluate the first parenthesis

Solve the expression inside the first parenthesis by subtracting 6 from 11. $$11 - 6 = 5$$
02

Evaluate the second parenthesis

Solve the expression inside the second parenthesis by subtracting 7 from 2. $$2 - 7 = -5$$
03

Multiply the results

Multiply the results from Step 1 and Step 2: $$5 \times (-5) = -25$$

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Key Concepts

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

Order of Operations
Understanding the order of operations is essential in elementary algebra. It's like a set of rules we follow to ensure everyone solves problems the same way and gets the same answer. The order in which we tackle operations matters.
Think of the acronym PEMDAS to remember the sequence:
  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction
When you see an expression, always start with whatever is inside parentheses. Then handle any exponents before moving on to multiplication and division, and finally addition and subtraction. This method ensures no mix-ups and leads to consistent math answers.
In our exercise, we begin by solving inside the parentheses first, even before any multiplication is tackled.
Evaluating Expressions
Evaluating expressions means calculating them to find their value. It's like following a recipe step-by-step to bake a cake. You do one step at a time according to the rules.
In our exercise, we start by solving the expressions inside each of the parentheses individually. First, we solve the expression inside the first parenthesis: \(11 - 6 \). This simplifies directly to 5.
Next, we move to the second parenthesis, evaluating \(2 - 7 \). Here, we get -5.
Once we solve the expressions inside the parentheses, we can then move on to the next part, which is the multiplication.
Parentheses
Parentheses play a special role in math. They tell us to solve the enclosed operations first before dealing with anything outside. Think of parentheses as the first priority instructions in algebra.
In our exercise \( (11-6)(2-7) \), we must solve the operations inside the parentheses before doing anything else.
  • First parenthesis: \(11 - 6 \) becomes 5
  • Second parenthesis: \(2 - 7 \) becomes -5
Only after simplifying the expressions within the parentheses do we proceed to multiply the results together.
By handling what's inside the parentheses first, we employ the correct order of operations and ensure accurate results in our computations.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$30-5(4-2)$$

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$-4.8$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$0.831-0.746-0.294$$

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.
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