Evaluate ((-4+3)*(4+2)-5)*3
The question here is asking for the evaluation of a given mathematical expression which includes multiple operations: addition, subtraction, multiplication, and the use of parentheses. You'll need to follow the order of operations—often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)—to correctly compute the value of the entire expression. It entails adding and subtracting integers within the parentheses, multiplying the results of those operations, subtracting another integer, and then finally multiplying by 3 to find the answer to the expression.
$\left(\right. \left(\right. - 4 + 3 \left.\right) \cdot \left(\right. 4 + 2 \left.\right) - 5 \left.\right) \cdot 3$
Answer
Solution:
Step 1: Break down the expression into simpler parts.
Step 1.1: Combine $-4$ and $3$ to get $(-1) \cdot (4 + 2) - 5) \cdot 3$.
Step 1.2: Add together $4$ and $2$ to form $(-1) \cdot 6 - 5) \cdot 3$.
Step 1.3: Multiply $-1$ by $6$ resulting in $(-6 - 5) \cdot 3$.
Step 2: Continue simplifying the expression.
Step 2.1: Add $-6$ and $-5$ together to get $-11 \cdot 3$.
Step 2.2: Finally, multiply $-11$ by $3$ to obtain $-33$.
Knowledge Notes:
The process of evaluating an arithmetic expression involves several steps that can be broken down systematically. Here are the relevant knowledge points for this problem:
Order of Operations: When solving mathematical expressions, the order of operations must be followed. This is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Addition and Subtraction: These are basic arithmetic operations. When numbers have the same sign, you add their absolute values and keep the sign. When they have different signs, you subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.
Multiplication: This operation combines two numbers to find their product. When multiplying two numbers with the same sign, the result is positive. When multiplying numbers with different signs, the result is negative.
Combining Like Terms: This is a process used to simplify an expression or equation. Terms that have the same variables raised to the same power are combined by adding or subtracting their coefficients.
Simplification: This involves combining like terms and performing arithmetic operations to rewrite an expression in a simpler form.
In the given problem, we first simplify inside the parentheses by adding and multiplying as needed. Then we proceed to multiply the result by the number outside the parentheses. The final result is a single number, which is the evaluation of the given expression.
