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Chapter 0: Problem 54

For exercises 1-80, evaluate. $$ 90-3 \cdot 5 \cdot 2^{2} $$

Short Answer

Expert verified
30

Step by step solution

01

Evaluate the exponent

First, evaluate the exponent part of the expression. Here, it is important to follow the order of operations (PEMDAS/BODMAS). Calculate the exponent first: \[2^2 = 4\]
02

Perform the multiplication

Next, substitute the value of the exponent and perform the multiplication: \[3 \times 5 \times 4\]Calculate step by step: \[3 \times 5 = 15\] and then, \[15 \times 4 = 60\]
03

Perform the subtraction

Finally, subtract the result of the multiplication from 90: \[90 - 60 = 30\]

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Key Concepts

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

Understanding PEMDAS
PEMDAS is a helpful acronym to remember the order of operations when solving mathematical expressions. It stands for:
  • P - Parentheses
  • E - Exponents
  • M - Multiplication
  • D - Division
  • A - Addition
  • S - Subtraction
Following PEMDAS ensures that you perform each mathematical operation in the correct order, which is crucial to getting the right answer. In our example, we start with exponents, followed by multiplication, and finally subtraction.
Working with Exponents
Exponents are a way to express repeated multiplication of the same number. For instance, 2^2 means multiplying 2 by itself, which equals 4. In the given exercise, we first need to evaluate the exponent:
2^2 = 4.
Sometimes, students mix up the order of operations, but always remember that exponents come before multiplication and subtraction. Practicing problems with exponents helps in mastering this step.
Multiplication and Subtraction
After handling any exponents, the next steps are multiplication and then subtraction, as per PEMDAS. Let's break down the given problem further:
  • First, multiply 3 by 5 to get 15.
  • Next, multiply the result (15) by 4. This gives us 60.
  • Finally, subtract 60 from 90 to get 30.
Always resolve multiplication before subtraction to avoid wrong answers. Repeating exercises like this one will make you more comfortable with the order of operations.

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Most popular questions from this chapter

$$ \text { Find } 2.5 \% \text { of } 30 \text {. } $$

For exercises \(13-24\), rewrite the fraction as a decimal number. $$ \frac{1}{6} $$

For exercises \(85-108\), write \(>\) or \(<\) between the numbers to make a true statement. $$ \frac{3}{5} \quad \frac{2}{3} $$

$$ \text { Find } 20 \% \text { of } 40 \text {. } $$

For exercises 1-12, rewrite the decimal number as a fraction. Simplify the fraction to lowest terms. $$ 0.85 $$
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