Problem 38 - Algebra 2

Question

How to evaluate \(a+b[(c+d) \div e],\) if you were given the values for \(a, b, c, d,\) and \(e .\)

Step-by-Step Solution

Answer

Evaluate each operation step-by-step: parentheses, division, multiplication, then addition.

Step 1: Understand the Expression

The expression to evaluate is \(a + b[(c + d) \div e]\). It signifies the operation order to follow based on PEMDAS/BODMAS rules: Parentheses/Brackets, Exponents/Orders, Multiplication-Division (left to right), Addition-Subtraction.

Step 2: Calculate Inside the Parentheses

First, solve the expression inside the parentheses (also called brackets in this context): \(c + d\). Sum the values of \(c\) and \(d\).

Step 3: Division Operation

Divide the result from Step 2 by \(e\). This gives \((c + d) \div e\).

Step 4: Multiplication by \(b\)

Multiply the result of Step 3 by \(b\). Thus, compute \(b \times [(c + d) \div e]\).

Step 5: Addition with \(a\)

Add the result from Step 4 to the value of \(a\) to get the final result: \(a + b[(c + d) \div e]\).

Key Concepts

PEMDAS

PEMDAS is an acronym that helps you remember the order of operations when solving mathematical expressions. Each letter stands for a different operation you need to perform in a specific sequence:

• Parentheses
• Exponents (or Orders)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Using PEMDAS ensures calculations are done correctly and consistently. For example, in the expression \(a + b[(c + d) \div e]\), you must first solve what's inside the Parentheses, then Division, followed by Multiplication, and finally Addition. Remember, always do operations inside parentheses first to simplify expressions accurately.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operations that represent a mathematical situation. For example, the expression \(a + b[(c + d) \div e]\) contains the variables \(a\), \(b\), \(c\), \(d\), and \(e\). These variables can take on different values in different scenarios.

To evaluate an algebraic expression accurately:

• Substitute each variable with its given value.
• Follow the order of operations (PEMDAS) to simplify the expression.

This process allows you to find a specific numeric outcome based on the variable values. It's like solving a puzzle where each number fits into a specific spot to reveal the answer.

Mathematical Operations

Mathematical operations are the actions we perform on numbers or variables to achieve a result. Common operations include addition, subtraction, multiplication, and division.

In the expression \(a + b[(c + d) \div e]\):

• Addition is used to combine quantities, such as adding \(a\) to the multiplied result of the other operations.
• Multiplication and Division are used to scale and distribute quantities effectively. In our example, you first divide \((c + d)\) by \(e\) then multiply the result by \(b\).

These operations help transform algebraic expressions into solved equations, step by step. Practice with different expressions helps improve your skills in identifying which operations to apply and in what order to find the solution.