7.6 finding the opposite of a real number
- 1. Opposite Numbers GUIDED EXAMPLE 1 Find the opposite of each situation. SITUATION a. A deposit of $38.25 into a checking account OPPOSITE b. A population growth of 1394 people c. Losing 15 pounds of weight d. A loss of 8 yards in a football game e. Climbing up (ascending) a mountain that is 2135 feet in elevation A withdrawal of $38.25 from the checking account A population decline of 1394 people Gaining 15 pounds of weight A gain of 8 yards in a football game Climbing down (descending) a mountain that is 2135 feet in elevation
- 2. Finding the Opposite of a Number GUIDED EXAMPLE 2 Find the opposite of the number using a number line. SOLUTION STEP RESULT The opposite of is Locate the number on a number line. Find the number that is the same distance from zero, but on the opposite side of the number line. Answer
- 3. Finding the Opposite of a Number GUIDED EXAMPLE 3 Find the opposite of each of the following numbers. REAL NUMBER INSERT A MINUS SIGN OPPOSITE a. b. c. d. e. f.
- 4. Finding the Opposite of an Absolute Value GUIDED EXAMPLE 4 Find the opposite of each of the following absolute values. ABSOLUTE VALUE INSERT A MINUS SIGN OPPOSITE a. b. c. d. e. f.
- 5. Additive Inverses GUIDED EXAMPLE 5 Find the additive inverse, or opposite, of each number. Then add the additive inverse to the number. REAL NUMBER ADDITIVE INVERSE (OPPOSITE) SUM a. b. c. d. e. f.
- 6. Study Guide In everyday life, we consider positive numbers as the opposite of negative numbers. • A gain of 5 yards in a football game is the opposite of… • A check written for $28.50 on a checking account is the opposite of… Definition: OPPOSITE NUMBERS Opposite numbers are two numbers that differ only in sign. They are the same distance from zero on a number line but in opposite directions. Each positive number has an opposite negative number. Similarly, each negative number has an opposite positive number. Note: The opposite of a number is the negative of that number. The symbol for “the opposite of” a number is the minus (or negative) sign, “–”. If a is a real number, then the opposite of a, denoted equals The opposite of is
- 7. Study Guide Procedure: FINDING THE OPPOSITE OF A NUMBER To find the opposite of a number, change the sign of the number. The absolute value of a number is its distance from zero on a number line. The symbol for absolute value is . Notice that for any real number a, but Be careful to notice that these two expressions are not equal. Note: Any pair of opposite numbers has the same absolute value since they are the same distance from 0 on a number line. Note: Any number plus its opposite is equal to zero. Definition: ADDITIVE INVERSE Two numbers are additive inverses, or opposites, if they add to equal zero.