BeginningAlgebra

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 sentencesTranslate sentences from EnglishEnglish into symbolssymbols then simplifysimplify.

Applications Using Subtraction

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:

13 – (- 5)

of the preposition “from”The object

1. Subtract - 5 from 13.

comes first.

Put negative numbers in ( )

add opposite

13 + 5 = 18

2. Subtract -3 from the sum of 9 and 7.

Translating English phrases and sentences:

16 + 3 = 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) fromfrom the sum (9 + 7).

( 9 + 7) – (- 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 ( )

SubtractSubtract n from (- 2) to getto get 88

( - 2) – n = 8

=

( - 2) + (-n) = 8 add opposites to both sides

n = - 10

( - 2) - (-10) = 8 ( - 2) + (10) = 8orCheck:

add opposite ( - 2) – n = 8

Circles have 360o 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

AB

The number of degreesnumber of degrees in a square angle is 90 and two angles whose sum is 90 are called complementary. (A & B)

The number of degreesnumber 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

x30

A square angle has 90 so x + 30 = 90

A straight angle has 180 so x + 130 =180

Complementary and Supplementary Angles

Use subtraction: x = 90 - 30 or x = 60

Use subtraction: x = 180 - 130 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 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

Problem Involving SubtractionTranslating English Sentences:

DepreciationDepreciation: A computer that costscosts $5225 has a valuevalue of $4075 after one year.

Problem Involving SubtractionTranslating English Sentences:

DepreciationDepreciation means to find the difference in the valuesvalues.

Difference = $5225 – $4075 = $1150$1150

The original value of the computer depreciated by the amount of $1150$1150 in the first year.

a) How much less is this value?

Problem Involving SubtractionTranslating English Sentences:

The original value of the computer depreciated by the amount of $1150$1150 in eacheach 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 – $1,1502 – $1,1503

Problem Involving Subtraction

b) The sequence for each of the first four years.

Year: 1 2 3 4

THEEND