Find each product or quotient where possible. See Example 2. 5(-7)

Verified step by step guidance

1. Identify the operation involved in the expression. Here, the expression is a product of two numbers: 5 and -7.
2. Recall that multiplication of a positive number by a negative number results in a negative number.
3. Write the product as \(5 \times (-7)\) to clearly represent the multiplication.
4. Multiply the absolute values of the numbers: \(5 \times 7 = 35\).
5. Apply the sign rule: since one number is positive and the other is negative, the product is negative, so the result is \(-35\).

Key Concepts

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.

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.

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.