Chapter 1: Integers

What is an integer?

An integer is a whole number that can be positive, negative, or zero.

What are the properties of integers?

Integers are closed under addition, subtraction, and multiplication.

What is the result of adding two negative integers?

The result is a negative integer.

What is the result of adding a positive integer and a negative integer?

The result depends on the absolute values; it can be positive, negative, or zero.

What is the additive identity for integers?

The additive identity is zero, since adding zero to an integer does not change its value.

What is the product of any integer and zero?

The product is always zero.

How do you subtract integers?

To subtract integers, add the opposite of the integer being subtracted.

What is the absolute value of an integer?

The absolute value of an integer is its distance from zero on the number line, regardless of direction.

What is the absolute value of -5?

The absolute value of -5 is 5.

Can integers be represented on a number line?

Yes, integers can be represented on a number line.

What is the result of subtracting -6 from 3?

The result is 9.

What does it mean for integers to be closed under an operation?

It means that performing the operation on any integers will always result in an integer.

What is a rational number?

A rational number is any number that can be expressed as a fraction of two integers.

Are all integers rational numbers?

Yes, all integers are considered rational numbers since they can be expressed as a fraction with a denominator of 1.

What is the inequality representation of integers?

Integers can be represented by the inequality: n ∈ Z, where Z is the set of integers.

What are positive integers?

Positive integers are all integers greater than zero.

What are negative integers?

Negative integers are all integers less than zero.

What does the term 'opposite integer' refer to?

An opposite integer refers to an integer that is the same distance from zero but in the opposite direction.

What is the opposite of 7?

The opposite of 7 is -7.

What is the sum of -4 and 4?

The sum is 0.

What is -10 + (-5)?

The sum is -15.

If a is an integer, what is the value of a + 0?

The value is a.

What is the difference between 5 and 3?

The difference is 2.

What is the product of -2 and -3?

The product is 6.

How do you find the quotient of two integers?

To find the quotient, divide the first integer by the second integer.

What is a key characteristic of the multiplication of integers?

The product of two integers is always an integer.

Is 0 an even or odd integer?

0 is considered an even integer.

What is the result of the expression -3 - 7?

The result is -10.

Is -5 greater than -8?

Yes, -5 is greater than -8.

What is the sequence of integers from -3 to 3?

The sequence is -3, -2, -1, 0, 1, 2, 3.

What is the least integer?

There is no least integer, but negative integers go on indefinitely.

What is the greatest integer?

There is no greatest integer, as positive integers extend infinitely.

What is the significance of the integer 1?

1 is the multiplicative identity for integers.

What is the outcome of -12 + 8?

The outcome is -4.

What do you call two integers that add up to zero?

They are called additive inverses.

What is an example of additive inverses?

5 and -5 are additive inverses.

What happens when you multiply an integer by -1?

The integer's sign is reversed.

When comparing integers, what is the sign of the larger integer?

The larger integer is positive if both are positive, or less negative if both are negative.

What represents a number less than zero?

Negative integers represent numbers less than zero.

What is -7 + 12?

The sum is 5.

What is the integer representation of the number ten?

The integer representation is simply 10.

What is the result of 15 - (-5)?

The result is 20.

Which is greater, -2 or 1?

1 is greater than -2.

What is the integer that follows -3?

The integer that follows -3 is -2.

What is the result of dividing -15 by 3?

The result is -5.

If an integer is multiplied by 1, what is the result?

The result is the integer itself.

What is the process for simplifying the expression -4 + 10?

The result is 6.

What do integers represent in a real-world scenario?

Integers can represent quantities such as temperature, elevation, and financial balance.

What trends can be seen with integers on a number line?

As you move left, the values decrease; as you move right, the values increase.

What is the integer that is 3 less than 2?

The integer that is 3 less than 2 is -1.

What is the formula for adding two integers?

To add two integers a and b, simply combine their values: a + b.

What is the sum of 8 and -3?

The sum is 5.

What is the significance of positive integers in counting?

Positive integers are used for counting and ordering.