chapter 5 equivalents and percents. percent percent means “per centum” or “per hundred” or...

Chapter 5Chapter 5

Equivalents and PercentsEquivalents and Percents

PercentPercent

Percent means “per centum” or “per Percent means “per centum” or “per hundred” or /100.hundred” or /100.

28 28 = 28%, = 28%, 396396 = 396%, = 396%, .9.9 = .9 % = .9 %

100 100 100

1. Write 1. Write 156156 as a percent as a percent 100 100

2. Write 2. Write 7171 as a percent. as a percent. 100 100

3. Change 3. Change 17.617.6 to a percent. to a percent. 100 100

How do you change a percent How do you change a percent to a decimal?to a decimal?

Going from Percent to DecimalGoing from Percent to Decimal

Move the decimal point 2 places to the left Move the decimal point 2 places to the left then drop the % signthen drop the % sign

72% = .7272% = .72 .25% = .0025.25% = .0025 124% = 1.24124% = 1.24 2% = .022% = .02

4. Change 53.7% to a 4. Change 53.7% to a decimal.decimal.

5. Change 0.76% to a 5. Change 0.76% to a decimal.decimal.

6. Change 134% to a decimal.6. Change 134% to a decimal.

How do you change a decimal How do you change a decimal to a percent?to a percent?

Going from Decimal to PercentGoing from Decimal to Percent

Move the decimal point 2 places to the Move the decimal point 2 places to the right then add the % sign (move to the % right then add the % sign (move to the % sign)sign)

.24 = 24%.24 = 24% .024 = 2.4%.024 = 2.4% .0024 = .24%.0024 = .24% 1.25 = 125%1.25 = 125%

7. Write 0.36 as a percent.7. Write 0.36 as a percent.

8. Write 7.3 as a percent.8. Write 7.3 as a percent.

9. Write 0.0072 as a percent.9. Write 0.0072 as a percent.

How do you change a percent How do you change a percent to a fraction?to a fraction?

Changing a Percent to a FractionChanging a Percent to a Fraction

Change to a decimal first, then write as a Change to a decimal first, then write as a fraction and simplify.fraction and simplify.

37% = .37 = 37% = .37 = 3737 , 75% = , 75% = 7575 = = 33

100 100 4100 100 4

43.5% = .435 = 43.5% = .435 = 435435 = = 8787

1000 200 1000 200

325% = 3.25 = 3 325% = 3.25 = 3 2525 = 3 = 3 11

100 4100 4

10. Change 2% to a fraction. 10. Change 2% to a fraction. Reduce to lowest terms.Reduce to lowest terms.

11. Change 0.7% to a 11. Change 0.7% to a fraction. Reduce to lowest fraction. Reduce to lowest terms.terms.

12. Change 225% to a 12. Change 225% to a fraction. Reduce to lowest fraction. Reduce to lowest terms.terms.

Changing a Percent to a FractionChanging a Percent to a Fraction

If the percent contains a mixed number, If the percent contains a mixed number, change the mixed number into an change the mixed number into an improper fraction and multiply by 1/100. improper fraction and multiply by 1/100. Simplify.Simplify.

3 3/8% = 27/8 x 1/100 = 27/8003 3/8% = 27/8 x 1/100 = 27/800

16 7/8% = 135/8 x 1/100 = 135/800 = 16 7/8% = 135/8 x 1/100 = 135/800 = 27/10027/100

13. Change 3 1/5% to a 13. Change 3 1/5% to a fraction.fraction.

14. Change 7 5/8 % to a 14. Change 7 5/8 % to a fraction.fraction.

How do we change a fraction How do we change a fraction to a percent?to a percent?

Changing a Fraction to a PercentChanging a Fraction to a Percent

Change the fraction to a decimal, then Change the fraction to a decimal, then change the decimal to a percent.change the decimal to a percent.

.375.375 3/8 = 8 3.000 .375 = 37.5%3/8 = 8 3.000 .375 = 37.5% 2424 6060 5656 4040 4040 00

Changing a Fraction to a PercentChanging a Fraction to a Percent

Change the fraction to a decimal, then Change the fraction to a decimal, then change the decimal to a percent.change the decimal to a percent.

7/40 = .175 = 17.5%7/40 = .175 = 17.5%39/50 = .78 = 78%39/50 = .78 = 78%

If a decimal repeats infinitely, round off to If a decimal repeats infinitely, round off to nearest hundredth of a percent.nearest hundredth of a percent.

1/6 = .16666… 1/6 = .16666… ≈ .1667 = 16.67%≈ .1667 = 16.67%

15. Change 15. Change 88 to a percent. to a percent. 15 15

16. Change 16. Change 55 to a percent. to a percent. 16 16

EquivalentsEquivalents

Change from fraction to Change from fraction to decimal to percent, given one decimal to percent, given one formform

17. Change 27.5% to an equivalent 17. Change 27.5% to an equivalent

A) fraction reduced to lowest A) fraction reduced to lowest termsterms

B) decimalB) decimal

18. Change 0.825 to an equivalent 18. Change 0.825 to an equivalent

A) fraction reduced to lowest A) fraction reduced to lowest termsterms

B) percentB) percent

19.19. Change 9/5 to an equivalentChange 9/5 to an equivalent

A) decimalA) decimal

B) percentB) percent

20. Change to a common value 20. Change to a common value and put in order from smallest and put in order from smallest to largest. to largest.

3/16 .17 20% 3/16 .17 20%

21. Change to a common value 21. Change to a common value and put in order from smallest to and put in order from smallest to largest. largest.

15/25 59/100 61 2/3% .6215/25 59/100 61 2/3% .62

Solving Percent Problems with the Solving Percent Problems with the Equation MethodEquation Method

Note the Note the mathematical mathematical equivalent for the equivalent for the following words.following words.

ofof Multiply (X)Multiply (X)

isis ==

whatwhat NN

findfind N=N=

Solving Percent Problems with the Solving Percent Problems with the Equation MethodEquation Method

What is 5% of 19?What is 5% of 19?N = 5% x 19N = 5% x 19N = .05 x 19N = .05 x 19N = .95N = .95 Find 160% of 500Find 160% of 500N = 160% x 500N = 160% x 500N = 1.60 x 500N = 1.60 x 500N = 800N = 800

Solving Percent Problems with the Solving Percent Problems with the Equation MethodEquation Method

12 is 0.6% of what?12 is 0.6% of what?12 = 0.6% x N12 = 0.6% x N12 = .006 x N12 = .006 x N 1212 = = .006 x N.006 x N.006 .006.006 .0062000 = N2000 = N What percent of 5000 is 3.8?What percent of 5000 is 3.8?N x 5000 = 3.8N x 5000 = 3.8N x 5000N x 5000 = = 3.83.8 5000 50005000 5000N = .00076N = .00076N = .076%N = .076%

22. 160% of what number 22. 160% of what number is 152? is 152?

23. Find 0.6% of 45.23. Find 0.6% of 45.

24. What percent of 40 24. What percent of 40 is 160?is 160?

Solving Percent Problems with Solving Percent Problems with Proportion MethodProportion Method a/b = p/100a/b = p/100

a = amounta = amount

b = baseb = base

p = percent number p = percent number

Note “a” is associated with “is” It’s on the topNote “a” is associated with “is” It’s on the top

“ “b” is associated with “of.” It’s on the b” is associated with “of.” It’s on the bottom. Remember a, e, i, o, u: i before obottom. Remember a, e, i, o, u: i before o

Solving Percent Problems with Solving Percent Problems with Proportion MethodProportion Method

Note “a” is associated with “is”Note “a” is associated with “is”

“ “b” is associated with “of”b” is associated with “of”

What is 52% of 300?What is 52% of 300?

isis = = pp

of 100of 100

NN = = 5252

300 100300 100

Identify p b aIdentify p b a

25. What is 60% of 7025. What is 60% of 70

26. 68 is what percent of 72?26. 68 is what percent of 72?

27. 354 is 40% of what number?27. 354 is 40% of what number?

28. What percent of 40 is 8?28. What percent of 40 is 8?

29. 12% of what number 29. 12% of what number is 15? is 15?

30. What is 25% of 92 ?30. What is 25% of 92 ?