Integers: Addition, Subtraction, and Ordering Quiz

11 Questions

What is the result of $(-7) + (-4)$?

-11

For the integers $-9$ and $6$, what is the result of the addition $(-9) + 6$?

-3

Given integers $-2$ and $8$, what is the correct result for their subtraction: $8 - (-2)$?

How is the subtraction operation of integers related to addition?

It involves adding the opposite of the second number.

If you have two integers, one positive and one negative with different absolute values, how do you determine their sum?

Add their absolute values and keep the sign of the number with the larger absolute value.

If you are comparing two integers that have opposite signs, what can you say about their relative positions on the number line?

$-5$ is greater than $2$

When adding integers, if the signs are different, what should be compared?

The absolute values

In the expression $6 - (-2)$, why is it necessary to find the opposite of $-2$ first?

To make the number positive

Which of the following statements is true about comparing integers with different signs?

$-3 > 2$

In ordering integers, if the signs are different, what determines which number is larger?

Their absolute values

Which property of integers is crucial for understanding the relationship between numbers with different signs?

Absolute value property

Study Notes

Integers: Addition, Subtraction, and Ordering

Integers, a fundamental component of mathematics and computer science, are whole numbers that can be either positive, negative, or zero. They are represented by the set (\mathbb{Z} = \ldots, -3, -2, -1, 0, 1, 2, 3, \ldots). Understanding the basic operations and ordering of integers is crucial for solving a wide variety of mathematical problems.

Addition of Integers

Adding integers is straightforward but requires a careful understanding of the signs. If both numbers have the same sign, add their absolute values and keep the same sign. If the signs are different, subtract the smaller absolute value from the larger one, and assign the sign of the number with the larger absolute value.

For example:

[ (-3) + (-5) = -8 ]

Here, both numbers have negative signs. So, we add their absolute values: (3 + 5 = 8), and keep the negative sign since the absolute values are greater than zero.

[ (-2) + 6 = 4 ]

Here, the signs are opposite. Assign the sign of (6) ((+)) since it has a larger absolute value: (2 + 6 = 8). Then, subtract the smaller absolute value ((2)) from the larger one ((6)): (8 - 2 = 6).

Subtraction of Integers

Subtracting integers is the same as adding the opposite of the second number.

For example:

[ (-3) - (-5) = -3 + 5 = 2 ]

Here, we find the opposite of the second number by changing its sign: ((-5) = +5). Then, we add: (-3 + 5 = 2).

[ 6 - (-2) = 6 + 2 = 8 ]

Here, the second number is negative, so we find its opposite: ((-2) = +2). Then, we add: (6 + 2 = 8).

Ordering Integers

Comparing and ordering integers is essential for problem-solving and understanding the structure of numbers.

If the signs are the same, the larger number has the greater absolute value.

For example: (-3 < -2) since the absolute value of (-3) ((3)) is less than the absolute value of (-2) ((2)).

If the signs are different, compare the absolute values. The number with the smaller absolute value is smaller, and the number with the larger absolute value is larger.

For example: (-3 > 2) since the absolute value of (-3) ((3)) is greater than the absolute value of (2) ((2)).

Understanding these fundamentals of integers will help you move on to more advanced topics such as multiplication, division, and the properties of integers that will provide a strong foundation in math and computer science.