Evaluate -5+1*3-(7-2^3)
In this problem, you are being asked to perform a series of arithmetic operations according to the order of operations, also known as PEMDAS/BODMAS rules. This acronym stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). You will need to calculate the value of the given expression by applying these rules correctly. The expression includes a negative number, an addition, a multiplication, a subtraction, and an exponentiation operation within a set of parentheses.
$- 5 + 1 \cdot 3 - \left(\right. 7 - 2^{3} \left.\right)$
Answer
Solution:
Step 1: Break down the expression
Simplify the expression step by step.
Step 1.1: Perform multiplication
Calculate $1 \times 3$. The expression becomes $-5 + 3 - (7 - 2^3)$.
Step 1.2: Simplify the expression
Break down the expression into simpler parts.
Step 1.2.1: Calculate the exponent
Compute $2^3$. The expression now is $-5 + 3 - (7 - 8)$.
Step 1.2.2: Simplify the subtraction
Evaluate $7 - 8$. The expression simplifies to $-5 + 3 - (-1)$.
Step 1.3: Simplify the negative sign
Resolve the double negative. The expression is now $-5 + 3 + 1$.
Step 1.4: Combine like terms
Combine terms that are alike. The expression simplifies to $-5 + 3 + 1$.
Step 2: Add the numbers
Combine all numbers to simplify the expression further.
Step 2.1: Add the first two numbers
Combine $-5$ and $3$. The expression becomes $-2 + 1$.
Step 2.2: Add the remaining numbers
Add $-2$ and $1$ to get the final result: $-1$.
Knowledge Notes:
To solve an arithmetic expression like $-5 + 1 \times 3 - (7 - 2^3)$, we follow the order of operations, often remembered by the acronym PEMDAS:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Parentheses: Solve expressions inside parentheses first. In this case, we have $(7 - 2^3)$.
Exponents: Calculate any exponents within the parentheses. Here, we compute $2^3$.
Multiplication and Division: Perform any multiplication or division next. In this problem, we multiply $1 \times 3$.
Addition and Subtraction: Finally, we perform all additions and subtractions from left to right. We combine like terms and simplify the expression to find the result.
When dealing with negative signs, remember that subtracting a negative number is equivalent to adding the positive number (e.g., $- (-1)$ is the same as $+1$). This is important when simplifying expressions with multiple negative signs.
