Problem 84 - Algebra 1

Question

Evaluate the expression. $$ 89-8 \cdot 5-27 $$

Step-by-Step Solution

Answer

22

Step 1: Multiply

Start by performing the multiplication operation in the given expression: \(89-8 \cdot 5-27\). This is done before subtraction due to the order of operations. So, this looks like: \(89 - (8 \cdot 5) - 27\). Calculation of \(8 \cdot 5\) equals to 40. Replace \(8 \cdot 5\) with 40 in the expression.

Step 2: Simplify

Once you have completed the multiplication, the expression should look like this: \(89 - 40 - 27\). Now you can perform the subtraction operations from left to right to obtain the final answer.

Step 3: Subtract

First, calculate \(89 - 40\), which equals to 49. Substitute this into the expression and the expression simplifies to \(49 - 27\). Now, calculate \(49 - 27\), which equals to 22.

Key Concepts

Understanding Multiplication in Expressions

Multiplication is one of the fundamental operations in mathematics used to calculate total amounts when a number is repeated a certain number of times. In expressions, multiplication takes precedence over addition and subtraction according to the order of operations (often remembered by the acronym PEMDAS - Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right)).

In our exercise, we have an expression that includes multiplication: \( 89 - 8 \cdot 5 - 27 \). Before addressing the subtraction, it's essential to complete the multiplication first. Here, 8 and 5 are multiplied together to get 40. This is a crucial step because if you mistakenly perform subtraction first, you arrive at an incorrect result.

Always remember:

• Identify multiplication operations in an expression.
• Perform them before moving on to addition or subtraction.
• Use parentheses to keep track of your calculations and values easily.

Subtraction and Its Role in Solving Expressions

Subtraction is the mathematical operation of deducting one number from another. In expressions, subtraction is performed after multiplication and division. This ensures that the calculations are accurate and follow the correct order.

In the given expression \( 89 - 8 \cdot 5 - 27 \), after completing the multiplication, the expression becomes \( 89 - 40 - 27 \). The subtraction is carried out from left to right. First, you subtract 40 from 89, resulting in 49. Next, subtract 27 from 49 to finally get 22.

Key points to remember about subtraction:

• Subtraction is executed after multiplication.
• Work through subtraction operations from left to right.
• Ensure each step is clear to avoid errors in your calculations.

Expressions and the Order of Operations

Expressions in mathematics are combinations of numbers and operations. Evaluating expressions correctly involves adhering to the order of operations. This order determines the sequence in which operations are performed to ensure consistent results, regardless of who calculates them.

The expression \( 89 - 8 \cdot 5 - 27 \) might look simple, but maintaining the correct order is crucial. The operations should be completed as:

• First, handle any operations inside parentheses (not applicable here, but important to remember).
• Next, perform multiplication (8 \cdot 5 = 40).
• Finally, proceed with subtraction as it appears from left to right: (89 - 40 = 49), then (49 - 27 = 22).

Following these rules ensures that anyone evaluating the expression arrives at the correct result. It's a good habit to practice these steps to build confidence in handling more complex expressions as you advance in mathematics.