Problem 45 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(-4.1(-5)(h)\) when \(h=2\)

Step-by-Step Solution

Answer

The expression \(-4.1(-5)(h)\) when \(h=2\) evaluates to 41.

Step 1: Substitute for h

Substitute \(h=2\) into the given expression to get \(-4.1(-5)(2)\).

Step 2: Apply multiplication from left to right

Using BIDMAS/BODMAS principle, carry out the multiplication from left to right. First, multiply -4.1 by -5 to get 20.5, thus the expression becomes \(20.5*2\). Then multiply 20.5 by 2 to get 41.

Key Concepts

Substitution in Algebra

Understanding how to evaluate algebraic expressions is a cornerstone of algebra. The process of substituting a given value into an expression is like substituting ingredients in a recipe. Imagine you have a recipe that calls for 'x amount of sugar', and you are told that 'x equals 2 cups'. In algebra, if an expression includes a variable, like 'h', and you're told that 'h equals 2', you replace 'h' with 2 in the expression.

Let's practice substituting using the problem given. We have the expression (-4.1)(-5)(h), and we know that 'h' is 2. So, we substitute 2 for 'h', and our new expression is (-4.1)(-5)(2). Substituting correctly sets us up for the next steps of solving the expression.

BIDMAS/BODMAS Order of Operations

The BIDMAS/BODMAS rule helps us understand the order in which we should solve parts of a mathematical expression. The acronym stands for Brackets, Indices/Orders (powers and roots), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).

In our current problem, we have multiplication only, but it’s crucial to note that multiplication of terms should still follow the left-to-right rule. We start with -4.1 times -5, which equals 20.5. Then we multiply 20.5 by 2, giving us 41 as the final answer. The lack of brackets or other operations makes this a straightforward application of BODMAS, focusing solely on the multiplication aspect.

Multiplication of Negative Numbers

When dealing with multiplication, one of the key rules is knowing how to multiply negative numbers. The rule is simple: a negative number multiplied by another negative number gives a positive result. Conversely, a negative number multiplied by a positive number results in a negative.

In our example, -4.1 is negative, and -5 is also negative; multiplying them gives us a positive number, 20.5. This is because two 'negatives' cancel each other out. It's similar to saying, 'not unhappy' is the same as being happy – the double negative becomes a positive. This crucial rule helps to simplify and solve expressions correctly, ensuring accurate results every time.