Problem 26 $-32+(-16)$... [FREE SOLUTION]

91影视

Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 26

$-32+(-16)$

Short Answer

Expert verified

-48

Step by step solution

Understanding the Problem

The problem requires us to solve $ -32 + (-16) $. It's important to remember that when adding negative numbers, they become more negative.

Addition of Negative Numbers

So, you'll add $32 + 16$ without considering the negative signs, that gets us $48$. Since the original numbers were negative, the result will also be 鈥�-鈥� as the sum magnifies the negative value. Hence, the answer is $ -48 $.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative Numbers

Negative numbers may seem tricky at first. They are numbers less than zero, represented with a minus sign (-).

Imagine you owe money: if you owe $5, your balance is -5. Negative numbers work similarly; they are opposite to positive numbers.

They lie to the left of zero on the number line.
They follow specific rules when participating in mathematical operations.

Negative numbers can represent losses, debts, or decreases. Understanding them is key to handling various real-world scenarios.

Once you grasp the concept, you'll find it easier to perform calculations involving these numbers.

Addition Rules

When adding numbers, specific rules apply, especially when they are negative.

Here's how the rules work:

**Adding two positive numbers:** Sum is positive. Example: 3 + 5 = 8.
**Adding two negative numbers:** Sum is more negative. Example: -3 + (-5) = -8.
**Adding a positive and a negative number:** Subtract the smaller absolute value from the larger. Retain the sign of the number with the larger absolute value.

In the original exercise, adding -32 and -16 results in -48.

Both numbers are negative, so you simply add their absolute values and apply a negative sign to the result. Understanding these rules helps in recognizing patterns in more complex problems.

Integer Operations

Integer operations include addition, subtraction, multiplication, and division of whole numbers.

Here鈥檚 a brief guide:

**Addition:** Use the addition rules mentioned earlier. Combine absolute values, adjust the sign accordingly.
**Subtraction:** Convert to addition by changing the sign of the number being subtracted. Example: 5 - (-3) becomes 5 + 3.
**Multiplication/Division:** If two numbers have the same sign, the result is positive. If different signs, it is negative.

For integers, negative and positive numbers come together in operations. Always pay attention to signs and apply the operations accordingly.

This understanding leads to better problem-solving skills. It can also help in managing algebraic expressions and equations. Knowing integer operations lays the foundation for future learning in mathematics.

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91影视

\(-32+(-16)\)

Short Answer

Step by step solution

Understanding the Problem

Addition of Negative Numbers

Key Concepts

Negative Numbers

Addition Rules

Integer Operations

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