KNOW YOUR NUMBERS! Factors, Multiples, Fractions, Percents, Estimates, Change From a Dollar, Tips

FRACTIONS, DECIMALS, PERCENTS, & ANGLES Convert from one to any of the other three… with or without a calculator!

Purpose Know your numbers! In this case, understand how to convert fractions to decimals, percents, or pieces of a circle. Get a “feel” for each. Estimate a fraction based on the decimal. Create a circle graph given a percent or a fraction. Circle has 360 degrees. Multiply fraction, decimal, or percent times 360.

Fraction – Decimal – Percent - Degrees FractionDecimalPercentDegrees ½ %180°  … 33  % 120°  … 66  %240° ¼ %90° ¾ % 270° YOU SHOULD MEMORIZE THESE!!! (in other words, no calculator needed!)

Fraction – Decimal – Percent - Degrees 1/50.220%72° 2/5________ %___° 3/5________ %___° 4/5________ %___° 1/6____ ____ %___° 5/6________ %___° Why didn’t I include 2/6, 3/6, and 4/6? Simplified: 1/3, ½, and 2/3. You have ‘em!

Fraction – Decimal – Percent - Degrees 1/50.220%72° 2/ %144° 3/ %216° 4/ %288° 1/ …16  %60° 5/ …83  %300°

Fraction – Decimal – Percent - Degrees 7 is not a factor of 360, so round the percents and degrees to 1 decimal place. Write decimal to six places, however. 1/7 ___________ %____° 2/7 ___________ %____° 3/7 ___________ %____° 4/7 ___________ %____° 5/7 ___________ %____° 6/7 ______ _____ %____° What patterns do you notice?

Fraction – Decimal – Percent - Degrees 1/ …14  %51.4° 2/ …28 4 / 7 %102.9° 3/ …42 6 / 7 %154.3° 4/ …57  %205.7° 5/ …71 3 / 7 %257.1° 6/ …85 5 / 7 %308.6° Each decimal is the same six-digit repeater, beginning at different places.

Fraction – Decimal – Percent - Degrees 1/8 __________ %____° 3/8 __________ %____° 5/8 __________ %____° 7/8 _____ _____ %____° Again, what patterns do you notice? Do the ninths (1/9, 2/9, etc.) and find the easy pattern for them.

Fraction – Decimal – Percent - Degrees 1/ ½ %45° 3/ ½ %135° 5/ ½ %225° 7/ ½ %315° 1/ … 11 1/9 %40° 2/90.222…22 2/9 %80° Tenths are easy. 1/10 = 0.1 = 10%, and so on (2/10 = 0.2 = 20%, etc).

F – D – P – D 1/ …9 1 / 11 %32.7° 2/ …18 2 / 11 %65.5° 3/ …27 3 / 11 %98.2° You should be able to see the pattern for the remaining elevenths. Now you do the twelfths. You should be able to convert any fraction to a decimal or percent.

Converting Back & Forth To convert any fraction or decimal to a percent, multiply by 100. To convert any percent to a fraction or decimal, divide by 100. abc D efghijklmno P qrstuvwxyz Decimal to Percent.  2 places Percent to Decimal . 2 places

Convert Each One FractionDecimalPercent 13 / 16___________ % _____0.3125_____ % __________41  % Try these to show you’re a genius: _____ …14 4 / 9 % _____  %

Convert Each One FractionDecimalPercent 13 / ¼ % 5 / ¼ % 5 / …41  % Are You a genius? 13 / …14 4 / 9 % 19 /  %

Estimate the Fraction Suppose you have a percent, and need to “think” of it as a relatively simple fraction, involving halves, thirds, fourths, fifths, etc. Round the percent to one that matches a fraction that you know. Example: 43.7% is a tad more than 40%, which is 2/5. So, if 43.7% voted for Candidate X, then about 2 out of every 5 voters voted for him.

Estimate the Fraction 35% is a bit more than …. One third 72% is just a hair less than… Three fourths 83% is almost exactly… Five sixths 60% is exactly… Three fifths

Estimate the Fraction 38.7% About 2/5 th 13% About 1/8 th 14.5% About 1/7 th 17% About 1/6 th

Tip? Granted, most of you don’t even think about tipping the server (waiter/waitress), but most adults do! “Standard” tip is about 15 to 18%. Think about these fractions & percents: 1/7 = 14.3% 1/6 = 16.7% 1/5 = 20% What would you tip for average, good, or super service on a $21.97 bill?

Tip on $21.97? If you tip $1 for every $7 you spend, that’s a bit more than 14%. For every $6 you spend, that’s almost 17%. For every $5 you spend, that’s 20%. A $3 tip (3 × 7 = 21) is less than 15%, but a $4 tip is about 18%. Round the bill to the nearest multiple of 7, 6, or 5, based on your tipping percentage.

Round the Bill Bill7x (14.3%) 6x (16.7%) 5x (20%) $34.83$35$36$35 $17.12$14$18$15 $22.75____________ $47.29____________ $27.33____________ $8.93____________ What would you tip in each case?

Round the Bill Bill7x (14.3%) 6x (16.7%) 5x (20%) $34.83$35$36$35 $17.12$14$18$15 $22.75$21$24$20/25 $47.29$49$48$45/50 $27.33$28$24/30$25/30 $8.93$7$6/12$5/10 What would you tip in each case?

Round the Bill Bill(14.3%)(16.7%) (20%) $34.83$5$6$75 $17.12$2$3$3 or 4 $22.75$3$4$4 or 5 $47.29$7$8$9 or 10 $27.33$4$4 or 5$5 or 6 $8.93$1$1 or 2$1 or 2 Tip is rounded to nearest dollar.

Tip: Cash or Plastic? If you’re leaving cash on the table, you probably leave whole dollars, or maybe dollars and a couple of quarters. But, if you’re using plastic, what’s typical? Suppose bill is $ If you’re tipping a dollar for every $6 you spend, that’s about $4. (24 is a multiple of 6) So, tip is $4.29, which brings total bill to $28.00

Change From A Dollar If you’re paying in cash, don’t you want correct change? Of course! What’s the change back from a dollar : $.53$.82$.67$.39 $.47$.18$.33$.61 Can you do this quickly, in your head? $.34$.29$.58$.74 $.66$.71$.42$.26

PERCENTS Solve Percent Problems

Three Typical Problems What number is 20% of 30?x 30 is 20% of what number?y 20 out of 30 is what percent? z All three have 20 & 30, but different answers. Answers: x = 6 y = 150 z = 66  % Note that only one answer has a %

Percent Proportion Use this proportion to solve percent problems. IS Percent = OF 100

Solving Percent Problems Use the “IS over OF equals Percent Over One Hundred” proportion. When the problem calls for a percent of increase (growth) or decrease (decline), use “Difference” as the “IS” and “OLD” as the “OF.” Difference = New – Old.

Solve What is 33 1/3 % of 123? Hint: 33 1/3% is one-third! Just divide by 3, or, set up proportion: is / of = 1 / 3 ? =

Solve 18 correct on a 22 question quiz is what percent correct? 18 ? = × 100 ÷ 22= ? 81 9 / 11 % (81.8, rounded to nearest tenth)

Solve 13,500 voters represent 25% of the eligible voting population. How many people are eligible to vote? 13,500 = “IS” 25% out of 100 is ¼, so you could just multiply by 4. 13,500 / x = 25 / 100  13,500 / x = 1 / 4 Total population (the “OF”) = 54,000.

As Seen on TV… “Four out of five doctors” recommend Tylenol to their patients. What percent is that? IS = 4 OF = 5 4 / 5 = % / % By the way, the makers of Tylenol give loads of free samples to doctors, so they give ‘em out! Thus, the ad…

Percent of Change (New – Old) Percent of Change = Old 100 It’s the same “IS over OF” ratio, but the “IS” is the difference between the old value and the new one. Old…Original...Of (How to remember?)

Percent of Change In , we had about 1320 students. Next year, it was about What percent of change is that? Step 1: Find the difference – 1320 is an increase of 80 students. Step 2: Use “Diff / Old = % / 100” proportion, cross-multiplying & dividing. 100 × 80 ÷ 1320 ≈ 6.1% increase

“B O G O” Many stores have “BOGO” sales. “Buy One, Get One” or sometimes “Buy Two, Get One,” and so on. What percent do you save? Example: “Buy one, get one free” is a 50% savings, since 1 free out of 2 is ½. Ex: “Buy two, get one free” is a 33 1/3% savings. (1 out of 3 is free)

BOGO Suppose you see: “Buy one, get second half off.” What percent is savings? Think: If you had to pay full price for two, that’s the equivalent of 200%. You pay 100% for the first one, but 50% for the second. So you pay 150% vs. 200%. 200 – 150 = 50. You save 50 out of / 200 = 0.25 You save 25%

Which is Cheaper? Macy’s is having a sale, where everything in the store is 15% off. Their regular price of a pair of shoes is $ Dillards is having a sale on those same shoes, which are discounted 20%. Their regular price is $ J C Penney sells the same shoes at $ Which store has the cheapest shoes?

Where are the Cheapest Shoes? Macy’s: 15% × $44.95 = $6.74 Subtract to get price of $ Dillards: 20% × = $9.79 Subtract to get price of $39.16 Dillards costs more. All prices within a dollar and change of each other, Macy’s slightly cheaper. Alternate method: 100% – 15% = 85% Multiply $44.95 × 85% = $38.21