Problem 72 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. ( 7)\((r)\) when \(r=11\)

Step-by-Step Solution

Answer

The evaluated expression is 77.

Step 1: Substitution

Start by replacing the variable \(r\) in the expression \(7r\) with the given value, which is 11: \(7 * 11\).

Step 2: Multiply

Then perform the multiplication: \(7 * 11 = 77\).

Step 3: Result

The result of the multiplication, 77, is the answer.

Key Concepts

Substitution in Algebra

Substitution is a fundamental technique in algebra where we replace variables with their given numerical values to simplify expressions or solve equations. Consider an algebraic expression like 7r. Here, r represents a variable, which can take on any value. When we are asked to evaluate this expression for r = 11, we are essentially being instructed to substitute '11' in place of 'r'.

To perform substitution properly, make sure to take note of the following:

• Preserve the operations and structure of the original expression.
• Replace each instance of the variable with the value given.
• Be attentive to any signs (plus or minus) associated with the variable.

By applying substitution, algebraic expressions become manageable numerical values that can be easily evaluated.

Multiplication in Algebra

After substituting the given values into an algebraic expression, we often encounter the need to multiply numbers. This is an essential operation in algebra as it helps us combine like terms and evaluate expressions. Multiplication involves taking one number and adding it to itself a number of times equal to the second number. For instance, in our problem where we substituted the value 11 for the variable r, the next step is to multiply 7 by 11.

Here are some multiplication tips:

• Remember the basic multiplication tables for efficiency.
• Use the distributive property if necessary to make multiplication easier.
• When multiplying with variables, you typically write the number (coefficient) before the variable for clarity.

Learning and practicing these tips will enhance your ability to handle multiplication in algebra with ease.

Algebraic Expressions Solutions

Solving algebraic expressions is the process of finding the value of the expression for given values of variables. The solution we have worked with is a simple example, but the same basic steps apply even with more complex expressions: substitute the known values for variables, perform the arithmetic operations like multiplication or division, and simplify if necessary.

Remember to solve expressions by following the order of operations, commonly known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). By adhering to these steps, you will arrive at a correct solution systematically. Ultimately, practicing these steps will help you gain confidence and proficiency in evaluating all kinds of algebraic expressions.