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Chapter 1: Problem 76

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

Short Answer

Expert verified
50

Step by step solution

01

Evaluate the expressions inside the parentheses

First, evaluate the expressions inside each pair of parentheses separately. For the first set, calculate the difference of 30 and 5. For the second set, calculate the difference of 4 and 2: \[30 - 5 = 25\] \[4 - 2 = 2\]
02

Multiply the results

Next, take the results from Step 1 and multiply them together: \[25 \times 2 = 50\]

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Key Concepts

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

Evaluating Expressions
When you encounter a mathematical expression, you need to evaluate it to find its value. This means solving the expression step by step, following the correct order of operations. Each part of the expression must be simplified in the correct sequence.
In our given problem, we have the expression \( (30-5)(4-2) \). To find its value, we need to break it down into simpler steps. This process makes sure we get the right answer.
Parentheses
Parentheses tell us which parts of an expression to solve first. They are essential in making sure we follow the right order of operations.
In our exercise, we have two expressions inside parentheses: \( (30-5) \) and \( (4-2) \). We need to solve these parts first before doing anything else.
Step inside each set of parentheses and perform the operations:
  • For \(30 - 5\), subtract 5 from 30 to get 25.
  • For \(4 - 2\), subtract 2 from 4 to get 2.
By dealing with the parentheses first, we simplify the expression to just multiplication.
Multiplication
Once parentheses have been dealt with, the next step is multiplication. Multiplication involves combining two numbers to get a product.
In our simplified expression, we now have \(25 \times 2\). By multiplying these two numbers together, we get 50.
Thus, the final value of the original expression \( (30-5)(4-2) \) is 50.

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Most popular questions from this chapter

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

Explain how you could use the commutative and/or associative properties to make the following computations easier to do. (a) \(-1.7+12.9-8.3\) (b) 10( 7)\((-2.3)\) (c) \(\frac{-10(3.2)}{-1.6}\) (d) \(-30\left(\frac{1.6}{3}\right)(-10)\)

Consider the following statements. If the statement is true, explain why. If the statement is false, explain why and/or give an example illustrating why. (a) Every rational number is an integer. (b) Every integer is a rational number. (c) \(-15\) is greater than \(-10\) (d) The absolute value of \(-15\) is greater than the absolute value of \(-10 .\) (e) A rational number must be positive. (f) An integer must be positive. (g) Every real number is a rational number. (h) Every rational number is a real number.

Describe each of the following expressions as a sum or a product. If the expression is a sum, list the terms. If the expression is a product, list the factors. (a) \(x+y+z\) (b) \(x y z\) (c) \(x y+z\) (d) \(x(y+z)\)

Compute the given expression. Round off your answer to two decimal places where necessary. $$\frac{-8.4}{1.2}$$
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