Textbook Question
Find each sum or difference. See Example 1. 9⁄10 - ( -4⁄3)
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0. Review of College Algebra
Solving Linear Equations
1:41 minutesProblem 37
Textbook Question
Find each product or quotient where possible. See Example 2. 5(-7)
Verified step by step guidance1
Identify the operation involved in the expression. Here, the expression is a product of two numbers: 5 and -7.
Recall that multiplication of a positive number by a negative number results in a negative number.
Write the product as \(5 \times (-7)\) to clearly represent the multiplication.
Multiply the absolute values of the numbers: \(5 \times 7 = 35\).
Apply the sign rule: since one number is positive and the other is negative, the product is negative, so the result is \(-35\).
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Multiplication of Integers
Multiplying integers involves combining their values according to sign rules: the product of two numbers with the same sign is positive, while the product of numbers with different signs is negative. For example, 5 × (-7) results in -35 because the signs differ.
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Order of Operations
The order of operations dictates the sequence in which mathematical operations are performed. Multiplication and division are performed before addition and subtraction, ensuring expressions like 5(-7) are evaluated correctly as a multiplication.
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Interpreting Mathematical Notation
Understanding that juxtaposition, such as 5(-7), implies multiplication is essential. This notation means 5 multiplied by -7, even without an explicit multiplication sign, which is common in algebra and arithmetic.
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