Estimating Percent Mentally 10% 10% Lola borrowed $125 from a pawn shop. She’ll have to pay back...
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Transcript of Estimating Percent Mentally 10% 10% Lola borrowed $125 from a pawn shop. She’ll have to pay back...
Estimating Percent MentallyEstimating Percent Mentally
10%10% Lola borrowed $125 from a pawn shop. She’ll have to pay
back the loan, plus the pawn shop charges an additional
9.9% fee. ≈ how much will her additional fee be?Step 1: Step 1: Look at your cost and your percent. Do they need rounding?
~ ~ $125 is OK, but let’s round 9.9% to 10%
10%10%
Step 2: To find 10%, slide the decimal 1 space to the left1 space to the left.
5%5%∞ do the
10% trick
∞ cut that number in half
15%15%∞ do the
10% trick
∞ cut that number in half
∞ add both numbers
20%20%∞ do the
10% trick
∞ double that number
25%25%∞ do 20%
+
5%
or
∞ mentally divide the number by 4
50%50%∞ round
your number
∞ cut it in half
00
Fee is Fee is about $12 about $12
or $13.or $13.
Estimating Percent MentallyEstimating Percent Mentally
about $0.05 - $0.06 (5 or 6 cents)
≈$0.40 - $0.41 (about 40 or 41 cents)
≈ $7.00 - $7.40
≈ $59 - $60
≈ $1000 - $1200
≈ $1,6 00,000,0 00 - $2,000,000,000 (1.6 trillion to 2 trillion)
≈ $1 - $1.20 (10%)
≈ $800 (10%)
≈ $60 + $30 = $90 (10%) + (5%) = (15%)
= $.02 (2 cents) (25%)
≈ $16 4
≈ $50,000 - $55,000 (50%)
-->$0.08 = (10%) 2
≈$.08 (or 8 cents)
--> $1 2
≈$0.08 (8 cents) 4
≈$28,000 4
≈ $7,000 (25%)
≈$100,000 2≈ $1,000,000 2
$9 000 00 or $900,000
$.04 (or 4 cents) (5%)
= $.50 - $.60 (5%)
≈ $40000 + $20000 = $60,000 (10%) + (5%) = (15%)
≈ $.1 2 (10%)
+ $.06+ (5%)
= $.15 - $.20= (15%)
≈ $4 (10%) •
● (2)● (2)
= $8= (20%)
≈ $50 00 (10%)
● (2)● (2)
= $10,000 (20%)
≈ $2 400 00 ● 2 = $40,000 - $50,000 (10%) ● 2 = (20%)
≈ $4 - $5 (25%)
≈ $500,000 - $550,000 (50%)
≈ $190 - $200 (50%)
≈$400 2
--> $800 2
= $400 (5%)
Tina bought a set of golf balls sells for $20 and the sales taxsales tax is 5.75% of the price. What is the total
cost of the set?To find the sales tax, ...
Next, add the sales tax to the regular price.
Answer: The Answer: The total cost total cost of the set of golf balls is of the set of golf balls is $21.15$21.15
Sales TaxSales Tax
(20)
(price)(tax rate) as a decimal
1.15 (sales tax)
+ 20.00 (reg price)
$21.15 (total cost)
MultiplyMultiply the price and the tax rate (as a decimal)
(.0575)
5.75%5.75%
.0575.0575
Linda and Bob went to dinner, received lousy service, and decided to tiptip the server only 12%. If the prepared foods taxtax is 4.75%, and they ordered $68.19 of food and
drinks, what will they pay?To find the tip, ...
Finally, add them up.
AnswerAnswer: Linda : Linda
and and Bob Bob will will pay pay
$79.61$79.61..
Tip, then Tax
(68.19)
8.18
(68.19)3.24
(price) (tip rate) as a decimal
Next, to find the tax
68.19 + 8.18 + 3.24
MultiplyMultiply the price and thetip rate (as a decimal).
(price) (tax rate)
Multiply Multiply the price and the tax rate.
(.12) 12%12% .12.12
4.75%4.75%
.0475.0475
(.0475)
Mort and Teddy receive a “15% off” coupon for Bob’s Burgers. They order $22.57 of food and drinks, decide to tip 20%, and
the food tax is 5 %. What will they pay in total?
To find the tip, multiply the new price new price and the tip rate (as a decimal)
Finally, add them up.
They paid They paid $24.07$24.07
Discount, then Tip, then Tax
(19.1819.18)(.20)
= 3.84
(19.1819.18)(.055)
= 1.05
19.1819.18 + 3.84 + 1.05
2
1
To find the discount, ...
(22.57)(.15)
3.39
Multiply the price and the discount rate (as a decimal)
22.57 - 3.39 = = 19.1819.18
(price) (discount rate) as a decimal
Now, subtract the discount from the old price to get the new pricenew price.
To find the tax, multiply the new price new price and the tax rate (as a decimal)
DECIMAL…move the decimal 2 spaces to the
right.
Converting Between Decimal and Percents
PERCENT
From a to a 0.13
= .13 13%
=
0.9 = .90=90%
0.0027
= 0.27
=0.27%
0013 = 1300 1300%
• =
DECIMAL…move the decimal 2 spaces to the
left.
PERCENT
From a to a 0.78
=78 78%=•
0.05
= 5 5%=• 1.75
= 175
175%
= 0.0008%
= 00.000008
•0
To change a fraction to a percent,1. Check the denominator.
7 20
=• 5 100• 5 35=35%35%
216 300
= ÷ 3 100 ÷ 3 72 = 72%72%
3 7
* Can it be changed to 100?
2. Rewrite the fraction with a denominator of 100.
What if the denominator can’tcan’t be changed to 100?
a. Divide
=3 ÷ 7
0.4285…
b. Change to a percent * slide the decimal 2 to the
right
42.85
d. Round to the nearest tenth.
42.9% c. Slap a percent sign on it.
%
yes
3. Write it as a percent.
To change a percent to a fraction,
1.Re-write the percent as a fraction over 100
8 100
=
2. Simplify.
8%8%
275100
÷ 4 ÷ 4
2 25
275%275% ÷ 25 ÷ 25
Converting Percents to Fractions
11 4
==
3.6100
3.6%3.6% ÷ 4 ÷ 4
9_250
== 36_ 1000
==*If there’s a decimal, move it to the end. … but, what you do to the numerator.. … you also do to the denominator
•0
Modeling Fractions, Decimals & Percents.
Gene found a bank offering a certificate of deposit that pays 4% simple interest. He has $1,500 to invest. How much interest will he earn in 3 years?To find interest, use a formula
Replace the variables:~ P with $1,500~ R with .04~ T with 3.
Multiply.Answer: Gene will earn
$180 in interest in 3 years.
Finding Interest
INTERESTINTERESTextra money
someone pays when
they borrow money.
I = P•R•T
I = 1500 • .04 • 3
I = 180
PRINCIPALPRINCIPALamount of money you borrow or
lend.
RATERATEinterest
rate written written
as a as a decimaldecimal
TIMETIMEyears of years of the loanthe loan
Why .04? All % must be written
as decimals.
$
I = P • R • T
Joan works for West Bank, and she just made a car loan at 8.9% interest rate8.9% interest rate for 5 years5 years. The bank will earn $5,340$5,340 in interestinterest. How much principalprincipal did she loan? 1. Replace the variables:
~ I with 5340. ~ P with p ~ R with .089 ~ T with 5.
Finding Principal, Rate, or Time
5340= p • .089 • 5
I = P • R • T
5340= p • .445------- -------.445 .445
12,000 = p Joan loaned $12,000 in principal.
2. Multiply (rate • time)
3. Divide to find p.
Collette put $400 in principal in a savings account for 2 years, and she earned $7.20 in interest. What interest rate What interest rate was she earning?
Ralph just finished paying off a $3500 loan. He paid an additional $1741.25 in interest on his 19.9% loan. What was the length of time on this loan?
I = P • R • T
7.2 = 400 • R • 27.2 = 800 • R----- ------ 800 800
0.009 = R
The The rate is rate is 0.009, 0.009,
or 0.9%or 0.9%
1741.25 = 699.5 • T------------ ---------- 699.5 699.5
2.5 = T
1741.25 = 3500 • 0.199 • T
It was a 30 month It was a 30 month loan.loan.
I = P • R • T