Adding and Subtracting Real Numbers objectives Add two numbers with the same sign. Add two numbers with different sign. Use the definition of subtraction. Use the rules for order of operations with real numbers. Translate words and phrases involving addition and subtraction. Use signed numbers to interpret data.

Objective 1 Add two numbers with the same sign Add the numbers. If both are positive, the sum is positive; if both are negative, the sum is negative. Add two positive numbers: 3+6= +3 +6 Add two negative numbers: -3 + (-6)= - 3 - 6

Objective 2 Add two numbers with the different sign Find the absolute values of the numbers and subtract the lesser absolute value from the grater. Give the answer the same sign as the number having the grater absolute value Example 3 Use a number line to find . –5 +8 Step 1 Draw an arrow from 0 to 8. Step 2 Then draw a second arrow 5 units to the left to represent adding –5. Step 3 The second arrow ends at the sum 3. Answer:

Objective 2 Add two numbers with the different sign Find the absolute values of the numbers and subtract the lesser absolute value from the grater. Give the answer the same sign as the number having the grater absolute value. Example 3 Example 4 Find the sum −𝟏𝟐+𝟓 . Find the sum . The sum will be positive , since 𝟖 > −𝟓 Answer . The sum will be negative , since −𝟏𝟐 > 𝟓 𝐀𝐧𝐬𝐰𝐞𝐫 . Example 2-1a

Adding Mentally Find 7+ −4 = Find −10+7= Find −8+12= Find −16+16= Example 2-2a

Objective 3 Subtracting real numbers To subtract signed numbers, add the opposite. (A.T.O.) and use the rules of addition. 6 – (+3) = 6 + (-3) = 6 – (-3) = 6 + (+3) = -8 – (+2) = -8 + (-2) = -30 – (-50) = -30 + (+50) =

Mental Math. Find each difference

Objective 4 Use the rules for order of operations with real numbers 𝑐. 2 3 − 1 12 − − 1 4 𝑎. −6−[2− 8+3 ] = 2 3 − 4 12 𝑏. 5+[ −3−2 − 4−1 ]

Objective 5 Translate words and phrases involving addition and subtraction 𝑎. 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 −8 𝑎𝑛𝑑 4 𝑎𝑛𝑑 6 g. 4 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡𝑒𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 8 𝑎𝑛𝑑 −3 𝑏. 3 𝑚𝑜𝑟𝑒 𝑡ℎ𝑎𝑛 −5, 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 12 ℎ. 4 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 −6 𝑐. 𝑇ℎ𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 −3 𝑎𝑛𝑑 −8 𝑑. 12 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡𝑒𝑑 𝑓𝑟𝑜𝑚 18 𝑁𝑜𝑡𝑖𝑐𝑒 𝑡ℎ𝑎𝑡 "4 less than−6" 𝑑𝑖𝑓𝑓𝑒𝑟𝑠 𝑓𝑟𝑜𝑚 "4 is less than −6 𝑒. 6 𝑙𝑒𝑠𝑠 5 𝑓. 6 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 5

Solving a Problem Involving Subtraction EXAMPLE 10 Solving a Problem Involving Subtraction The highest Fahrenheit temperature ever recorded in Barrow, Alaska, was 79°F, while the lowest was −56°F. What is difference between these highest and lowest temperatures? (Source: World Almanac and Book of Facts.) Solution: °° Slide 1.5-25

Objective 6 Use signed numbers to interpret data EXAMPLE 11 Using a Signed Number to Interpret Data Refer to Figure 17 and use a signed number to represent the change in the CPI from 2002 to 2003. Solution: Slide 1.5-27

Multiplying and dividing Real Numbers. Vocabulary: multiplicative inverse reciprocal What you’ll learn To find products and quotients of real numbers.

Multiplication of real numbers The product of two numbers having the same sign is positive. The product of two numbers having different sign is negative.

Multiply Rational Numbers Multiplying rational numbers is similar to multiplying integers. Example: Example: Simplify by 3 Simplify by 3 Simplify by 2

Evaluate expressions that contain rational numbers if

Multiplicative property of -1 The product of any number and -1 is its called additive inverse. For any number a, -1( a ) = a( -1 ) = - a Example:

Division of real numbers The quotient of two numbers having the same sign is positive. The quotient of two numbers having different sign is negative.

The fraction bar is a grouping symbol Simplify before dividing The fraction bar is a grouping symbol Example: Simplify the expression

Dividing Rational Numbers The sign rules for division with integers also apply to division with rational numbers. Remember that to divide by any nonzero number, multiply by the reciprocal of that number Example: Invert the denominator then multiply

Dividing Rational Numbers Example: Evaluate expressions that contain rational numbers if Evaluate