Problem 13 Find each sum or difference. $... [FREE SOLUTION]

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Chapter 0: Problem 13

Find each sum or difference. $$ -15+6 $$

Short Answer

Expert verified

-9

Step by step solution

Identify the numbers involved

The problem involves the addition of -15 and 6.

Understand addition of a negative and a positive number

When adding a negative number to a positive number, subtract the absolute value of the negative number from the positive number. Here, subtract 15 from 6.

Perform the subtraction

Calculate the result of 6 - 15. This is equivalent to moving 15 units to the left from 6 on a number line.

Calculate the result

6 - 15 equals -9.

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Key Concepts

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

adding negative numbers

Adding negative numbers might seem tricky at first. But with a little practice, it becomes easy. When you are dealing with addition of a negative number and a positive number, you are essentially performing a subtraction. For instance, in the problem $-15 + 6$, we can think of $-15$ as needing to be subtracted from 6. You can visualize this process using a number line. Start at 6 and then move 15 steps to the left. You end up at -9. This shows the sum: $-15 + 6 = -9$. The general rule is:

When adding a positive and a negative number, subtract the smaller absolute value from the larger absolute value.
The result takes the sign of the number with the larger absolute value.

absolute value

The concept of absolute value is crucial for understanding how to add negative numbers. The absolute value of a number is its distance from zero on the number line, without considering direction. It is always a non-negative number. For example:

The absolute value of -15 is 15, written as \[ |-15| = 15 \].
The absolute value of 6 is 6, written as \[ |6| = 6 \].
Absolute value helps in comparing and performing arithmetic operations involving negative numbers.

Remember, absolute value strips the sign from a number, making it easier to perform operations like addition or subtraction.

number line

The number line is a great tool for visualizing basic arithmetic operations, especially when dealing with negative numbers. It is a straight line with numbers placed at equal intervals.
To visualize $-15 + 6$ on a number line, follow these steps:

Start at $+6$.
Move 15 units to the left because you are subtracting $|-15| = 15$.
You will land on $-9$ which is the sum.

The number line visually reinforces that moving leftward represents subtracting or decreasing values, while moving rightward represents adding or increasing values. Keep practicing with different examples, and soon this will become second nature. Understanding the number line can help demystify and simplify operations involving negative numbers and absolute values.

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91影视

Find each sum or difference. $$ -15+6 $$

Short Answer

Step by step solution

Identify the numbers involved

Understand addition of a negative and a positive number

Perform the subtraction

Calculate the result

Key Concepts

adding negative numbers

absolute value

number line

One App. One Place for Learning.

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