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.

Translate sentencesEnglish symbolssimplify Translate sentences from English into symbols then simplify. Applications Using Subtraction 1. Subtract -5 from Subtract -3 from the sum of 9 and What number do you subtract from 2 to get 8?8?

Translating English phrases and sentences: 13 – (- (- 5)5) of the preposition “from”The object 1. Subtract - 5 from 13. comes first. Put negative numbers in ( ) add opposite = 18

2. Subtract -3 from the sum of 9 and 7. Translating English phrases and sentences: = 19 The object of the preposition “from” (9 + 7) comes first. Put negative numbers in ( ) Write the object of the preposition “of ” in ( 9 + 7) Subtract (-3) from from the sum (9 + 7). ( 9 + 7) – (- (- 3)3) add opposite

3. What number do you subtract from -2 to get 8? Translating English phrases and sentences: ( - 2) + ( - 8) = n The object of the preposition “from” (- 2) comes first. Put negative numbers in ( )  Subtract Subtract n from (- 2) to get get 8 ( - 2) – n = 8 = ( - + (-n) = 8 add opposites to both sides  n = - 10 ( - 2) - (-10) = 8( - 2) + (10) = 8 or Check: add opposite ( - 2) – n = 8

Circles have 360 o around the Center The number of degrees swept out by the radius as it rotates once around the circle is 360 . 360  Radius  The number of degrees in a circle is 360 . GEOMETRY

Complementary and Supplementary Angles C D A B number of degrees The number of degrees in a square angle is 90  and two angles whose sum is 90  are called complementary. (A & B) number of degrees The number of degrees on a straight angle is 180  and two angles whose sum is 180  are called supplementary. (C & D) Complement: B = 90  – A Supplement: D = 180  – C A + B = 90  C + D = 180  GEOMETRY

x 130  x 30  A square angle has 90  so x + 30  = 90  A straight angle has 180  so x  =180  Complementary and Supplementary Angles Use subtraction: x = 90  - 30  or x = 60  Use subtraction : x = 180   or x = 50  GEOMETRY

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. Translating English Sentences: Some Words that imply subtraction: Minus, Less, Less than, Difference, Decrease, Lose, Has dropped (temperature), Depreciated by, Withdrawal, Distance, length comparison (shorter, longer) …

The Weather Channel announced that a cold front had come through the area. At noon the temperature was at a high of 82  F. By 3:00 pm the temperature had dropped 17  F and by 6:00 pm it had dropped another 12  F. Write an expression to indicate the temperature changes and find the temperature at 6 pm. (82 – 17) – – 12 = 53 The temperature at 6 pm was 53  F Problem Involving Subtraction Translating English Sentences:

Depreciation Depreciation: A computer that costs costs $5225 has a value value of $4075 after one year. Problem Involving Subtraction Translating English Sentences: Depreciation Depreciation means to find the difference in the values values. $1150 Difference = $5225 – $4075 = $1150 $1150 The original value of the computer depreciated by the amount of $1150 in the first year. a) How much less is this value?

Problem Involving Subtraction Translating English Sentences: $1150each 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)

Sequence : $5,225 $4,075 $2,925 $1,775 Value: $5,225 $5,225 $5,225 $5,225 – $1,150 – $1,150  2 – $1,150  3 Problem Involving Subtraction b) The sequence for each of the first four years. Year:

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