Estimating Percent Mentally

1. 0 10% Step 1: Look at your cost and your percent. Do they need rounding? Estimating Percent Mentally ~ $125 is OK, but let’s round 9.9% to 10% Fee is about $12 or $13. Step 2: To find 10%, slide the decimal 1 space to the left. 5% 15% 20% 25% 50% 10%Lola borrowed $125from 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? • do the 10% trick • cut that number in half • do the 10% trick • cut that number in half • add both numbers • do the 10% trick • double that number • do 20% • + 5% • or • mentally divide the number by 4 • round your number • cut it in half

2. ≈ $60 + $30 = $90 (10%) + (5%) = (15%) about $0.05 - $0.06 (5 or 6 cents) ≈$0.40 - $0.41 (about 40 or 41 cents) ≈ $40000 + $20000 = $60,000 (10%) + (5%) = (15%) ≈ $7.00 - $7.40 ≈ $4 (10%) • = $8 = (20%) ● (2) ● (2) Estimating Percent Mentally ≈ $59 - $60 ≈ $50 00 (10%) = $10,000 (20%) ● (2) ● (2) ≈ $1000 - $1200 ≈ $2 400 00 ● 2 = $40,000 - $50,000 (10%) ● 2 = (20%) $9 000 00 or $900,000 ≈$0.08(8 cents) 4 = $.02 (2 cents) (25%) ≈ $1,6 00,000,0 00 - $2,000,000,000 (1.6 trillion to 2 trillion) ≈ $16 4 ≈ $4 - $5 (25%) ≈$.08 (or 8 cents) -->$0.08= (10%) 2 $.04 (or 4 cents) (5%) ≈$28,000 4 ≈ $7,000 (25%) --> $1 2 ≈ $1 - $1.20 (10%) = $.50 - $.60 (5%) ≈ $190 - $200 (50%) ≈$400 2 ≈ $800 (10%) -->$800 2 = $400 (5%) ≈$100,000 2 ≈ $50,000 - $55,000 (50%) ≈ $500,000 - $550,000 (50%) ≈ $.1 2 (10%) ≈ $1,000,000 2 + $.06 + (5%) = $.15 - $.20 = (15%)

3. Sales Tax Tina bought a set of golf balls sells for $20 and the sales tax is 5.75% of the price. What is the total cost of the set? 5.75% To find the sales tax, ... (price)(tax rate) as a decimal Multiplythe price and the tax rate (as a decimal) (20) (.0575) .0575 1.15 (sales tax) + 20.00 (reg price) Next, add the sales tax to the regular price. $21.15 (total cost) Answer: The total cost of the set of golf balls is $21.15

4. Tip, then Tax Linda and Bob went to dinner, received lousy service, and decided to tipthe server only 12%. If the prepared foods taxis 4.75%, and they ordered $68.19 of food and drinks, what will they pay? To find the tip, ... (price) (tip rate) as a decimal Multiplythe price and the tip rate (as a decimal). 12% (68.19) (.12) .12 8.18 Next, to find the tax Answer: Linda and Bob will pay $79.61. (price) (tax rate) Multiply the price and the tax rate. (.0475) (68.19) 4.75% .0475 3.24 68.19 + 8.18 + 3.24 Finally, add them up.

5. Discount, then Tip, then Tax 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 discount, ... (price) (discount rate) as a decimal Multiply the price and the discount rate (as a decimal) (22.57)(.15) 15% .15 3.39 Now, subtract the discount from the old price to get the new price. 22.57 - 3.39= 19.18 To find the tip, multiply the new price and the tip rate (as a decimal) (19.18)(.20) = 3.84 (19.18)(.055) = 1.05 To find the tax, multiply the new price and the tax rate (as a decimal) They paid $24.07 19.18 +3.84+1.05 Finally, add them up.

6. Converting Between Decimal and Percents DECIMAL PERCENT From a to a 0.13 = .13 = 13% …move the decimal 2 spaces to the right. 90% 0.9 = .9 0 = 0.0027 = 0.27 = 0.27% 13 00 = 1300 = 1300% • PERCENT DECIMAL From a to a 0.78 =78 = 78% • …move the decimal 2 spaces to the left. 0.05 = 5 0 = 5% 1.75 = 175 = 175% 0.000008 = 0 0.0008% • •

7. Converting Fractions to Percents To change a fraction to a percent, 7 20 • 5 35 35% = = 1. Check the denominator. • 5 100 * Can it be changed to 100? yes 2. Rewrite the fraction with a denominator of 100. 216 300 ÷ 3 72 72% = = ÷ 3 100 3. Write it as a percent. What if the denominator can’tbe changed to 100? 3 7 = 3 ÷ 7 0.4285… a. Divide 42.85 % • Change to a percent • * slide the decimal 2 to the right 42.9% c. Slap a percent sign on it. d. Round to the nearest tenth.

8. Converting Percents to Fractions 2 25 8% 8 100 ÷ 4 ÷ 4 = To change a percent to a fraction, • Re-write the percent as a • fraction over 100 11 4 275% 275 100 ÷ 25 ÷ 25 = 2. Simplify. 9_ 250 *If there’s a decimal, move it to the end. 3.6% 3.6 100 36_ 1000 ÷ 4 ÷ 4 = = … but, what you do to the numerator.. 0 • … you also do to the denominator

9. Modeling Fractions, Decimals & Percents.

10. Finding Interest 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 I = P•R•T INTEREST extra money someone pays when they borrow money. PRINCIPAL amount of money you borrow or lend. RATE interest rate written as a decimal TIME years of the loan I = P • R • T Replace the variables: ~ P with $1,500 ~ R with .04 ~ Twith 3. Why .04? All % must be written as decimals. I = 1500 • .04 • 3 Answer: Gene will earn $180 in interest in 3 years. I = 180 $ Multiply.

11. Finding Principal, Rate, or Time Joan works for West Bank, and she just made a car loan at 8.9% interest rate for 5 years. The bank will earn $5,340 in interest. How much principaldid she loan? I = P • R • T 1. Replace the variables: ~ Iwith 5340. ~ P with p ~ R with .089 ~ Twith 5. 5340= p • .089 • 5 2. Multiply (rate • time) 5340= p • .445 ------- ------- .445 .445 3. Divide to find p. Joan loaned $12,000 in principal. 12,000 = p Collette put $400 in principal in a savings account for 2 years, and she earned $7.20 in interest. 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 I = P • R • T 7.2 = 400 • R • 2 1741.25 = 3500 • 0.199 • T 7.2 = 800• R The rate is 0.009, or 0.9% 1741.25 = 699.5 • T ----- ------ 800 800 ------------ ---------- 699.5 699.5 0.009 = R It was a 30 month loan. 2.5 = T