Problem 53 - Algebra 1

Question

Evaluate the expression. \(-6.3+4.1-9.5\)

Step-by-Step Solution

Answer

The expression equals \(-11.7\).

Step 1: Add the First Two Numbers

First, add the first two numbers: \(-6.3+4.1 = -2.2\). This gives us a new expression, which is now \(-2.2-9.5\).

Step 2: Subtract the Third Number

Next, subtract the third number from the result of the addition: \(-2.2-9.5 = -11.7\).

Key Concepts

Addition of Negative Numbers

When adding negative numbers, it's helpful to think of moving left on a number line. Negative numbers represent values less than zero. Thus, adding a negative number means decreasing in value.
For instance, when we have

• \(-6.3+4.1\)

we are adding a negative number, \(-6.3\), to a positive number, \(4.1\).
Imagine starting at zero, moving left (negative) by 6.3, and then right (positive) by 4.1.
Doing this will effectively give us our new position on the number line, which is \(-2.2\). It's important to keep track of whether the addition results in a positive or negative number.
This can be determined by comparing the absolute values of the numbers being added. The resulting number will have the sign of the number with the greater absolute value.

Subtraction of Negative Numbers

Subtracting negative numbers might seem tricky at first, but it's easier when you think of it as removing or taking away.

• When you see an expression like \(-2.2 - 9.5\), you're effectively decreasing the value further on the number line.

Starting at \(-2.2\), we subtract 9.5, which means we move 9.5 units further left on the number line, making the resulting number \(-11.7\).
Subtracting a negative number is similar to adding its absolute value.
However, remember: in cases where both numbers are negative in subtraction, the sign of the larger absolute number typically prevails unless specific conditions apply.

Order of Operations

The order of operations is crucial to solving algebraic expressions correctly. It's a set of rules that indicate the sequence in which the operations should be performed. A common acronym to remember is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

• In our given example, \(-6.3+4.1-9.5\),

we only deal with addition and subtraction.
According to PEMDAS, we perform any operations that appear from left to right.
This confirms why we add \(-6.3+4.1\) before subtracting 9.5.
Following the correct order is necessary to always arrive at the correct solution. Deviating may lead to incorrect results.
In more complex expressions involving multiple operations and parentheses, make sure to apply the order of operations meticulously.