Convert fractions to decimals and percents. Solve percentage problems

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

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

3. 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.

4. Fraction – Decimal – Percent - Degrees
• Fraction Decimal Percent Degrees
• ½ 0.5 50% 180°
•  0.3333… 33 % 120°
•  0.6666… 66 % 240°
• ¼ 0.25 25 % 90°
• ¾ 0.75 75 % 270°
• YOU SHOULD MEMORIZE THESE!!!
• (in other words, no calculator needed!)

5. Fraction – Decimal – Percent - Degrees
• 1/5 0.2 20% 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!

6. Fraction – Decimal – Percent - Degrees
• 1/5 0.2 20% 72°
• 2/5 0.4 40 % 144°
• 3/5 0.6 60 % 216°
• 4/5 0.8 80 % 288°
• 1/6 0.1666… 16 % 60°
• 5/6 0.8333… 83 % 300°

7. 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?

8. Fraction – Decimal – Percent - Degrees
• 1/7 0.142857… 14  % 51.4°
• 2/7 0.285714… 28 4/7 % 102.9°
• 3/7 0.428571… 42 6/7 % 154.3°
• 4/7 0.571428… 57  % 205.7°
• 5/7 0.714285… 71 3/7 % 257.1°
• 6/7 0.857142… 85 5/7 % 308.6°
• Each decimal is the same six-digit repeater,
beginning at different places.

9. 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.

10. Fraction – Decimal – Percent - Degrees
• 1/8 0.125 12½ % 45°
• 3/8 0.375 37½ % 135°
• 5/8 0.625 62½ % 225°
• 7/8 0.875 87½ % 315°
• 1/9 0.111… 11 1/9 % 40°
• 2/9 0.222… 22 2/9 % 80°
• Tenths are easy. 1/10 = 0.1 = 10%, and
so on (2/10 = 0.2 = 20%, etc).

11. F–D–P–D
• 1/11 0.090909… 9 1/11 % 32.7°
• 2/11 0.181818… 18 2/11 % 65.5°
• 3/11 0.272727… 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.

12. 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.
• abcDefghijklmnoPqrstuvwxyz
• Decimal to Percent .  2 places
• Percent to Decimal  . 2 places

13. Convert Each One
• Fraction Decimal Percent
• 13 / 16 ______ _____ %
• _____ 0.3125 _____ %
• _____ _____ 41 %
• Try these to show you’re a genius:
• _____ 0.1444444… 144/9 %
• _____ 0.633333.. 63 %

14. Convert Each One
• Fraction Decimal Percent
• 13 / 16 0.8125 81¼ %
• 5 / 16 0.3125 31¼ %
• 5 / 12 0.416666… 41 %
• Are You a genius?
• 13 / 90 0.1444444… 144/9 %
• 19 / 30 0.633333.. 63 %

15. 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.

16. 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

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

18. 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?

19. 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.

20. Round the Bill
• Bill 7x (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?

21. Round the Bill
• Bill 7x (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?

22. 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
• What would you tip in each case?

23. 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 $23.71. If you’re tipping a
dollar for every $6 you spend, that’s about
$4. So, tip is $4.29, which brings total bill
to $28.00

24. 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

25. PERCENTS
Solve Percent Problems

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

27. 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.

28. 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
• 41
• 18 correct on a 22 question quiz is what
percent correct?
• 819/11 % (81.8, rounded to nearest tenth)

29. 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.

30. Percent of Change
• Last year, we had about 1380 students.
This year, it’s about 1450. What percent
of change is that?
• Step 1: Find the difference. 1450 – 1380
is an increase of 70 students.
• Step 2: Use “Diff / Old = % / 100”
proportion, cross-multiplying & dividing.
• 100 × 70 ÷ 1380 ≈ 5.1% increase

31. What If…?
• What if we grow at 5% each year? (That’s
exponential growth, by the way!)
• How many students next year?
• Difference / 1450 = 5 / 100
• 1450 × 5 ÷ 100 =
• 72.5 … well, about 70 to 75 new students
• About 1520 to 1525 students total.
• Add about 75 to 80 the year after that…

32. “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)

33. 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
• 50 / 200 = 0.25 You save 25%

34. 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 $44.95.
• Dillards is having a sale on those same
shoes, which are discounted 20%. Their
regular price is $48.95.
• J C Penney’s sells the same shoes at
$38.95.
• Which store has the cheaper shoes?

35. Cheaper Shoes?
• Macy’s: 15% × $44.95 = $6.74 Subtract
to get price of $38.21. Dillards: 20% ×
48.95 = $9.79 Subtract to get price of
$39.16 Dillards is more expensive
• 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