Pre-Algebra Percents Chapter 7
Write percent as a decimal
move decimal 2 places to the LEFT (62% = 0.62 .... 100% = 1.00 ....
Write decimal as a perceent
move decimal 2 places to the RIGHT (0.62 = 62% .... 1 = 100% .... 2.3 = 230%)
Percent of Change (indicates how much a quantity increases or decreases from the original amount)
Ratio of the amount of increase or decrease to the original amount. percent of change p% = Amount of increase or decrease ÷ Original amount
Write fraction as a percent
divide fraction into decimal, then write as % 3/4 = 0.75 = 75% repeating decimals: 5/3 = 1.666... = 166.6%
Interest
amount paid for the use of the money (ie., the "rent" on using the money)
Proportion
an equation that states that two ratios are equal. (Equiv. ratios: 2/3 = 8/12 bc 2/3 . 4/4 = 8/12) (Algebra: x/12 = 2/8 .. multiply each side by "12" .. x = 24/8 .. x = 3)
Find a part ( ex. what number is 40% of 180?)
b = 180 p = 40/100 a = ? a/180 = 40/100 (multiply each side by 180/1) a = 7200/100 = 72 ( 40% of 180 is 72)
Find percent of a number (ex. what is 40% of 6800?)
convert to decimal and multiply 0.40 . 6800 = 2720
Percent of increase (ex. Original amount = 100; New amount = 128)
new amount is greater than original amount (ex. Amount of increase (128-100) ÷ original amount (100) = 0.28 or 28% increase)
Percent of decrease (ex. Original amount = 100; New amount = 76 )
new amount is less than the original amount (ex. Amount of decrease (100-76) ÷ original amount (100) = 0.24 or 24% decrease)
Principal
original amount of money that is put in (deposited) or borrowed from (loan) a bank
Find a new amount - decrease
p% decrease New amount = original amount . (100% - p%) (ex. New amt = 500 . (100% - 12%) 500 . (0.88) = 440)
Find a new amount - increase
p% increase New amount = original amount . (100% + p%) (ex. New amt = 500 . (100% + 12%) .. 500 . (1.12) = 560
Annual interest rate
percent of the prinicipal earned or paid each year
Write Probability as a percent (ex. 1 out of 4 oysters have a pearl inside)
write "1 out of 4" as a fraction: 1/4 write fraction as percent: (25 . 4 = 100) 1 . 25 / 4 . 25 = 25/100 = 25%
The Percent Equation
"a is p percent of b" : a = p% . b
Percent
"per hundred" A ratio whose denominator is 100. (ex. 75/100 = 75%)
4/5 = what percent
(5 . 20 = 100) 4 . 20 / 5 . 20 = 80/100 = 80%
1/10 = what percent
1/10 = 1 . 10 / 10 . 10 = 10/100 = 10%
Find percent of a number (ex. what is 60% of 15?)
60% of 15 (60/100 = 3/5) 3/5 . 15 = 45/5 = 9
Writing fractions as percents using "equivalent fractions"
8/10? Multiply numerator and denominator by "10" 8 . 10 / 10 . 10 = 80/100 = 80%
Balance (A)
A = Interest + P or A = (Prt) + P or A = P ( 1 + rt) ..t is time in years
Discount
A decrease from the original price of an item to the sale price. (p% . OP) Calculated using percent of original price (ex. "40% off original price of $25")
Solve percent using proportions and percent bar model: "a is p percent of b"
a is part of b base and p% (p/100) or a/b = p/100
Find a "commission" (ex. Girl Scouts earn 10% on every box of $4 cookies sold. How much do they earn if they sell 1000 boxes?)
Find b = 4 . 1000 = $4000 b = 4000 p = 10% a = ? Find 10% of 4000 to get a. a = 4000 . 0.10.... a = $400 commission (400÷1000 per box. they earn 40 cents a box)
Finding simple interest (ex. P = 500, r = 0.08, t = 2 years)
I = 500 . 0.08 . 2 I = $80 (ie., if you deposit $500 into a 2 year savings bond that earns 8%, then you will earn $80 and receive $580 back in 2 years. The $80 was the Interest ("rent") the bank paid you so that they could keep your $500 for 2 years.
Simple Interest Formula
I = simple interest P = principal r = rate (percent written as decimal) t = time in years
Find Amount of increase (ex. Original Amount = 500, p% = 12%.. what is the new amount?)
New amount = Original Amount (500) + Original amount . p% (500 . 0.12) = 500 + (500 . 0.12) = 560
Sales Tax and Tips (restaurant bills)
OP (cost of food) + Sales tax (10%) + Tip (15%) = total cost of meal at restaurant OP = $40 Total = 40 + (0.10 . 40) + (0.15 . 40) ... 40 + (4) + (6) = $50
Find Compound Interest
P = 1500 r = 5% t = 6 years A = 1500 (1 + 0.05) ⁶ [order or operations] A = 1500 (1.340) .. A = $2010.14
Find Rate (r)
P = 500 A = 550 T = 6 months (since t is time in years, then t = 6/12 or 1/2) 550 = 500 (1 + r (1/2)) 550 = 500 + (500 . 0.50)r ... = 500 + 250r 550 - 550 = 250r 50 = 250r .... 0.200 = r .. r = 20%
Wholesale price (WP)
Price a retailer (shop owner) buys items from a manufacturer (factory)
Retail Price (RP)
Price a retailer sells the items to the customers
Find Original Amount
RP = $45 Markup = 75% WP = ? $45 = WP . (100% + 75%) $45 = WP . (1.75) 45/1.75 = WP ... WP = $25.71
Find retail price (RP)
Retail price = Wholesale price + Markup (wholesale price . p%) WP = $7 Markup = 150% RP = ? RP = 7 . ( 7 . 1.50) = 17.50
Find a Sale Price (SP) by multiplying OP by (100% - Discount percent)
SP = 25 . (100% - 40%) SP = 25 . (60%) ... 25 . (0.60) = $15
Find a Sale Price (SP) by subtracting discount
SP = OP - Discount (p% . OP) SP = 25 - (25 . 0.40) = $15
Find b base (ex. 6 is 30% of what number?)
a = 6 p = 0.30 b = ? 6 = b . 0.30 .... 6 ÷ 0.30 = 20 b = 20 ... "6 is 30% of 20"
Find p percent (ex. what percent of 35 is 7?)
a = 7 b = 35 p% = ? a/b = p/100 .. 7/35 = p/100 (multiply each side by 100/1) 700/35 = p p = 20 or 20% (7 is 20% of 35")
Find b base (ex. 72 is 40% of what number?)
a = 72 p = 40 b = ? 72/b = 40/100 (cross products multiply) 72 . 100 = 40 . b .... 7200 = 40b 7200/40 = b .... b = 180
Find p percent? (ex. What percent of 20 is 75?)
a = 75 b = 20 p = ? 75 = 20 . p .... 75/20 = p .... 3.75 = p p = 375% ... "75 is 375% of 20"
Find a part of a base
a = ? b = 600 p% = 60 a = 600 x 0.60 .... a = 360
Markup
increase from wholesale price of an item to the retail price
Compound Interest
interest earned on BOTH the principal plus any interest that has already been earned A = P (1 + r) ↑t (to the power of t)
