Textbook Question
Simplify each expression. See Example 8. 0.25(8 + 4p) - 0.5(6 + 2p)
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem R.2.85
Evaluate each expression. See Example 5. 10 + 30 ÷ 2 • 3
Verified step by step guidance1
Identify the order of operations to evaluate the expression correctly. Recall that division and multiplication have higher precedence than addition, and they are evaluated from left to right.
Rewrite the expression clearly: \(10 + 30 \div 2 \times 3\).
First, perform the division: calculate \(30 \div 2\).
Next, multiply the result of the division by 3: multiply the value from the previous step by 3.
Finally, add 10 to the result of the multiplication to complete the evaluation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Order of Operations
The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Multiplication and division are performed from left to right before addition and subtraction.
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Algebraic Operations on Vectors
Division and Multiplication as Equal Priority Operations
Division and multiplication share the same priority level in the order of operations and are evaluated from left to right. This means when both appear in an expression, you perform whichever comes first as you move left to right, rather than doing all multiplication before division or vice versa.
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Evaluating Arithmetic Expressions
Evaluating arithmetic expressions involves systematically applying the order of operations to simplify the expression step-by-step. This process ensures that complex expressions with multiple operations are simplified correctly to a single numerical value.
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