Problem 110 - Algebra 1

Question

EVALUATING EXPRESSIONS Evaluate the expression. $$ 6+(-13)+(-5) $$

Step-by-Step Solution

Answer

The result of evaluating the expression is -12.

Step 1: Identify the numbers

In the expression \(6 + (-13) + (-5)\), the numbers to be added are 6, -13, and -5.

Step 2: Add the numbers

Perform the addition operation. The addition of negative numbers actually results in subtraction. So, the equation becomes: \(6 - 13 - 5\)

Step 3: Evaluate the expression

Follow the subtraction in steps: first do \(6-13 = -7\), then do \(-7-5 = -12\)

Key Concepts

Addition of Integers

Adding integers involves combining whole numbers, which can either be positive or negative. In essence, addition means bringing quantities together. However, the involvement of negative numbers can sometimes make this operation a bit tricky. Here's how to approach it with ease:

• When you add two positive integers, the result is simply the sum of the two. For example, adding 3 and 4 gives you 7.
• When adding a positive and a negative integer, you essentially subtract the absolute value of the negative integer from the positive one. For instance, 5 + (-3) equals 2 because you subtract 3 from 5.
• If both numbers are negative, add their absolute values and keep the negative sign. For example, -2 + (-4) results in -6.

When faced with a combination of multiple numbers, it's often helpful to reorganize them in a way that makes the arithmetic more intuitive, by pairing positives and negatives.

Negative Numbers

Negative numbers are those that are less than zero, symbolized by a minus sign (-) in front of the number. They represent values that are opposite in direction or sense to positive numbers, which are greater than zero.

• Negative numbers are used in various contexts, such as expressing debt, freezing temperatures, or declines.
• Visualizing them on a number line helps: they are positioned to the left of zero, while positive numbers are to the right.
• Any number multiplied by a negative number flips its sign. For instance, multiplying 5 by -1 results in -5.

Understanding negative numbers is crucial as they are common in algebraic expressions and appear frequently in real-world applications.

Subtraction

Subtraction is about finding the difference between numbers. In simple terms, it involves removing or taking away one quantity from another.

• Standard subtraction involves two numbers: the minuend (from which you subtract) and the subtrahend (which is subtracted). For example, in 10 - 3, 10 is the minuend and 3 is the subtrahend.
• When incorporating negative numbers into subtraction, signs can change. Subtracting a negative number is equivalent to adding its opposite positive value. For instance, 7 - (-2) is the same as 7 + 2, resulting in 9.
• It is essential to maintain the correct order in subtraction, as switching numbers will result in a different answer. For example, 5 - 3 equals 2, but 3 - 5 gives -2 due to reversing the order.

Practicing subtraction with various combinations of integers, both positive and negative, builds a deeper understanding of mathematical operations and enhances problem-solving skills.