Integers and Rational Numbers

An integer is a whole number that can be positive, negative, or zero. Examples include -3, 0, and 5.

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Examples include 1/2, -3, and 0.

When adding two integers with the same sign, add their absolute values and keep the common sign. For example, -4 + -3 = -7.

When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value and take the sign of the integer with the larger absolute value. For example, 5 + -3 = 2.

The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, | -7 | = 7 and | 7 | = 7.

Subtracting a negative integer is the same as adding its positive counterpart. For example, 5 - (-3) = 5 + 3 = 8.

The product of two integers with the same sign is positive. For example, -2 * -3 = 6.

The product of two integers with different signs is negative. For example, -2 * 3 = -6.

When dividing integers, if the signs are the same, the result is positive; if the signs are different, the result is negative. For example, 6 ÷ 2 = 3 and -6 ÷ 2 = -3.

A mixed number is a whole number combined with a proper fraction. For example, 2 1/2 is a mixed number.