Problem 92 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 7.2-9-8.5 $$

Step-by-Step Solution

Answer

The solution to the expression 7.2 - 9 - 8.5 is -10.3.

Step 1: Subtraction Step 1

Start by subtracting 9 from 7.2: \(7.2 - 9 = -1.8\)

Step 2: Subtraction Step 2

Next, subtract 8.5 from -1.8: \(-1.8 - 8.5 = -10.3\)

Key Concepts

Subtraction

Subtraction is one of the basic operations in mathematics. It involves taking away a number from another number.
It's indicated by the minus sign (-). The first number is called the "minuend," and the number being subtracted is the "subtrahend."
The result of a subtraction operation is known as the "difference." For instance, in the expression \(7.2 - 9\), 7.2 is the minuend, 9 is the subtrahend, and the result, -1.8, is the difference.

• Start by checking your numbers carefully. Make sure that the minuend is the number from which you subtract.
• Line up any decimal points to maintain accuracy in subtraction problems involving decimals.

Step-by-Step Solution

A step-by-step solution is a systematic approach to solving mathematical problems.
This means breaking down a problem into smaller, more manageable parts, solving each part one by one.
By focusing on one step at a time, it’s easier to follow along and understand how we reach the final solution. In the given exercise:

• First, we subtract 9 from 7.2, which involves basic subtraction with a decimal, resulting in -1.8.
• Next, we subtract 8.5 from -1.8. This requires handling negative numbers carefully, resulting in -10.3.

Approaching complex expressions in this way makes it easier to track calculations. It minimizes errors and increases understanding.

• Ensure each step is completed sequentially.
• Double-check each calculation as you proceed to avoid mistakes.

Negative Numbers

Negative numbers are numbers less than zero, represented by a minus sign (-) in front of them.
They can be challenging when performing operations, as they behave differently from positive numbers.
Understanding how to work with negative numbers is crucial, especially when subtracting or adding them to other numbers.In subtraction, if the minuend is smaller than the subtrahend, the result will be a negative value.

• For instance, in the step \(7.2 - 9\), the result is -1.8 because 7.2 is less than 9.
• In \(-1.8 - 8.5\), the expression involves subtracting a positive number from a negative one, moving further into negative territory, resulting in -10.3.

When subtracting negative numbers or dealing with multiple steps involving them, it’s key to:

• Pay close attention to the signs of the numbers involved.
• Remember that subtracting a negative number is equivalent to adding its positive counterpart.