Objective- To simplify problems involving subtraction of real numbers and percents. Algebraic Definition of Subtraction
a - b = a + -b
Evaluate if x = 4.5 and y = - 3.7
- y = 4.5 - ( - 3.7 ) = 4.5 + 3.7 = 2) y - x = - 3.7 - ( 4.5 ) = - 8.2
1) x
8.2
Simplify.
1)
- 10 - ( - y ) =
2) 5x + 3y - 2 - x = 3) 5x - y - 3(x - y) =
Simplify.
1)
- 10 - ( - y ) =
- 10 + y = y - 10
4x + 3y - 2 5x - y
2) 5x + 3y - 2 - x = 3) 5x - y - 3(x - y) =
- 3x + 3y
2x + 2y
Geometric Model for Subtraction
5 12 x
x = 12
x = 7
- 5
Percent Discount
Sweater = $85 Find the new price after a 20% discount.
Long Way
original price - discount
Shortcut
new price
$85 - 20% of $85 85 - .20 ( 85) 85 - 17 $68
( Subtracts the $ )
(100% - 20%) of $85 80% of $85 .80 (85) $68
( Subtracts the % )
Find the new price.
1) Price P is discounted 20%. 2) Price Y is discounted 35%. .80P .65Y .53M .835J
3) Price M is discounted 47%.
4) Price J is discounted 16.5%.
Find the new price.
1) Price X is marked up 12%. 2) Price L is increased 70%. 1.12X 1.70L 1.16P 1.0825K
3) Price P is marked up 16%.
4) Price K after sales tax of 8.25%.
Range- Difference between the highest value and lowest value in a set of numbers.
Temperatures in Alaska last night :
32 27 19 7 8 15 24
Range = High - Low Range = 32 - 8 Range = 40
Find the range.
1) High Test Score = 94 Low Test Score = 68
2) High Temp. = 73 Low Temp. = 25