Problem 117 - Prealgebra and Introductory Algebra

Question

Evaluate the expression for the given values of the variables. $$10 t, \text { when } t=-4.8$$

Step-by-Step Solution

Answer

The evaluated result of the expression \(10t\) when \(t = -4.8\) is -48.

Step 1: Identify the Expression and the Variable Value

The algebraic expression given is \(10t\) and the value of \(t\) given is -4.8. We need to substitute this value into the expression.

Step 2: Substitute the Variable Value into the Expression

Substitute \(t = -4.8\) into the expression \(10t\). So, the expression becomes \(10 \times -4.8\).

Step 3: Simplify the Expression

Multiply 10 with -4.8, which results in -48.

Key Concepts

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and arithmetic operations. Think of it like a code that represents a numerical value, but it's flexible because you can change that value by changing the variables. For instance, in the problem you're working with, the expression is '10t'. This one is a simple multiplication of the number 10 and the variable 't'. When you're given a specific value for the variable, you can figure out the exact number that the expression is equal to.

Substitution Method

The substitution method involves replacing the variables in an algebraic expression with their given values. This allows for the evaluation of the expression to find its numerical value. When you are faced with a problem like '\(10t\)' where '\(t=-4.8\)', you use substitution by putting '-4.8' in place of every 't' in the expression. It's like swapping out the placeholder (the variable 't') with its actual value to find out what the entire expression equals when 't' is '-4.8'.

Simplifying Expressions

Simplifying an expression means performing all the possible arithmetic operations to reduce it to its simplest form. This might involve adding, subtracting, multiplying, or dividing numbers and combining like terms. For the expression '10t' with 't' substituted for '-4.8', you are left with '10 multiplied by -4.8'. To simplify, you just carry out the multiplication to get a single number. In our case, that's '-48'. Remember, the goal is to make the expression as straightforward as possible.

Arithmetic Operations

Arithmetic operations are the foundation of all algebraic manipulations. They include addition, subtraction, multiplication, and division. When you evaluate algebraic expressions, you're performing these operations following the order of operations (remember PEMDAS? That's Parentheses, Exponents, Multiplication & Division, and Addition & Subtraction). In the exercise with the expression '\(10t\)' and the variable '\(t = -4.8\)', the main arithmetic operation needed to solve it is multiplication. By multiplying 10 by -4.8, you are using arithmetic to simplify the expression.