Evaluate each expression. 15/5*4/6-8 / -6-(-5)-8/2

Verified step by step guidance

1. Start by simplifying the expression step by step, focusing on the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
2. First, handle the division and multiplication from left to right: \( \frac{15}{5} \times \frac{4}{6} \).
3. Simplify \( \frac{15}{5} \) to get 3, and \( \frac{4}{6} \) to get \( \frac{2}{3} \).
4. Multiply the results: \( 3 \times \frac{2}{3} \).
5. Next, address the subtraction and division: \( -8 / -6 - (-5) - 8/2 \).

Key Concepts

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Following these rules is crucial when evaluating complex expressions to avoid errors.

Fractions and Division

Fractions represent a part of a whole and are expressed as a numerator over a denominator. Division of fractions involves multiplying by the reciprocal of the divisor. Understanding how to manipulate fractions, including simplifying and performing operations like addition, subtraction, multiplication, and division, is essential for evaluating expressions that include them.

Negative Numbers and Their Operations

Negative numbers are values less than zero and can affect the outcome of mathematical operations. When performing operations involving negative numbers, such as subtraction or division, it is important to keep track of the signs, as they can change the result significantly. Understanding how to handle negative numbers is vital for accurately evaluating expressions that include them.