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Beginning Algebra Applications using Subtraction Applications Using Subtraction Objective 2. To simplify expressions containing subtraction using the rule for order of operations. Objective 3. To translate sentences from English into symbols then simplify. Objective 4. To find the complement and supplement of an angle. Applications Using Subtraction Translate sentences from English into symbols then simplify. 1. Subtract -5 from 13. 2. Subtract -3 from the sum of 9 and 7. 3. What number do you subtract from 2 to get 8? Translating English phrases and sentences: 1. Subtract - 5 from 13. Put negative numbers in ( ) The object of the preposition “from” comes first. 13 – (- 5) add opposite 13 + 5 = 18 Translating English phrases and sentences: 2. Subtract -3 from the sum of 9 and 7. Put negative numbers in ( ) Write the object of the preposition “of ” in ( 9 + 7) Subtract (-3) from the sum (9 + 7). The object of the preposition “from” (9 + 7) comes first. ( 9 + 7) – (- 3) add opposite 16 + 3 = 19 Translating English phrases and sentences: 3. What number do you subtract from -2 to get 8? Put negative numbers in ( ) Subtract n from (- 2) to get 8 = The object of the preposition “from” (- 2) comes first. ( - 2) – n = 8 add opposite add opposites to both sides ( - 2) + (-n) = 8 n = - 10 ( - 2) + ( - 8) = n Check: ( - 2) - (-10) = 8 or ( - 2) + (10) = 8 GEOMETRY Circles have 360o around the Center 360 The number of degrees swept out by the radius as it rotates once around the circle is 360. The number of degrees in a circle is 360. GEOMETRY Complementary and Supplementary Angles The number of degrees in a square angle is 90 and two angles whose sum is 90 are called complementary. (A & B) Complement: B = 90 – A The number of degrees on a straight angle is 180 and two angles whose sum is 180 are called supplementary. (C & D) Supplement: D = 180 – C A B A + B = 90 C D C + D = 180 GEOMETRY Complementary and Supplementary Angles A square angle has 90 so x + 30 = 90 x 30 Use subtraction: x = 90 - 30 or x = 60 A straight angle has 180 so x + 130 =180 x 130 Use subtraction: x = 180 - 130 or x = 50 Translating English Sentences: In algebra subtraction is “adding the opposite” not “taking away”. In arithmetic the result is a positive number, sometimes it is small and sometimes large, but in algebra the result can also be a negative number with a small or large absolute value. All operations are performed by particular and exact properties. Some Words that imply subtraction: Minus, Less, Less than, Difference, Decrease, Lose, Has dropped (temperature), Depreciated by, Withdrawal, Distance, length comparison (shorter, longer) … Translating English Sentences: Problem Involving Subtraction The Weather Channel announced that a cold front had come through the area. At noon the temperature was at a high of 82F. By 3:00 pm the temperature had dropped 17F and by 6:00 pm it had dropped another 12F. Write an expression to indicate the temperature changes and find the temperature at 6 pm. (82 – 17) – 12 65 – 12 = 53 The temperature at 6 pm was 53F Translating English Sentences: Problem Involving Subtraction Depreciation: A computer that costs $5225 has a value of $4075 after one year. a) How much less is this value? Depreciation means to find the difference in the values. Difference = $5225 – $4075 = $1150 The original value of the computer depreciated by the amount of $1150 in the first year. Translating English Sentences: Problem Involving Subtraction The original value of the computer depreciated by the amount of $1150 in each of the first four years. Write a sequence of numbers that gives the value of the computer system at the beginning of each of the first four years. Can this sequence be considered an arithmetic sequence? Yes, it has a common difference: - $1,150) Problem Involving Subtraction b) The sequence for each of the first four years. Year: 1 Value: $5,225 2 $5,225 – $1,150 Sequence: $5,225 $4,075 3 4 $5,225 $5,225 – $1,1502 $2,925 – $1,1503 $1,775 THE END