1.1 Integers and Rational Numbers

www.ck12.org Chapter 1. Arithmetic ReviewNumbers and Their OppositesEvery number has an opposite, which represents the same distance from zero but in the other direction.A special situation arises when adding a number to its opposite. The sum is zero. This is summarized in the followingproperty.The Additive Inverse Property: For any real number a, a + −a = 0.Absolute ValueAbsolute value represents the distance from zero when graphed on a number line. For example, the number 7 is7 units away from zero. The number -7 is also 7 units away from zero. Therefore, the absolute value of 7 and theabsolute value of -7 are both 7.We write the absolute value of -7 like this: |−7|.We read the expression |x| like this: “the absolute value of x.”• Treat absolute value expressions like parentheses. If there is an operation inside the absolute value symbolsevaluate that operation first.• The absolute value of a number or an expression is always positive or zero. It cannot be negative. Withabsolute value, we are only interested in how far a number is from zero, not the direction.Example 5: Evaluate the following absolute value expressions.a) |5 + 4|b) 3 − |4 − 9|c) |−5 − 11|d) −|7 − 22|Solution:a)|5 + 4| = |9|= 9b)3 − |4 − 9| = 3 − |−5|= 3 − 5= −25