(7.1) Number, operation, and quantitative reasoning.

The student represents and uses rational numbers in a variety of equivalent forms.

The student is expected to:(B) convert between fractions, decimals, whole numbers, and

percents mentally, on paper, or with a calculator.

7.1B STUDENT ACTIVITY #1

Part I: How do I convert ½ to a decimal?

Divide the ___________ by the ___________ . The quotient is ___________ . Therefore, ___________ is the decimal equivalent to

½.Write a decimal equivalent for the fraction in each box.

For each fraction converted to a decimal, divide the ___________ by the ___________ .

The quotient is the ___________ ___________ of the fraction.

numerator denominator

0.5

0.5

= 0.___ = 0.___ = 0.___ = 0.___3 5

2 8

4 5

1 8 = 0.___2

3

23

230.0.6

-182

00

Top In Bottom Out

6

Part I: How do I convert ½ to a decimal?

Divide the ___________ by the ___________ . The quotient is ___________ . Therefore, ___________ is the decimal equivalent to

½.Write a decimal equivalent for the fraction in each box.

For each fraction converted to a decimal, divide the ___________ by the ___________ .

The quotient is the ___________ ___________ of the fraction.

numerator denominator

0.5

0.5

= 0.___2 3 = 0.___ = 0.___ = 0.___67 3

52 8

4 5 = 0.___1

8

18

180.0.1

-82002

-164

005Top In Bottom Out

Part I: How do I convert ½ to a decimal?

Divide the ___________ by the ___________ . The quotient is ___________ . Therefore, ___________ is the decimal equivalent to

½.Write a decimal equivalent for the fraction in each box.

For each fraction converted to a decimal, divide the ___________ by the ___________ .

The quotient is the ___________ ___________ of the fraction.

numerator denominator

0.5

0.5

= 0.___2 3 = 0.___ = 0.___ = 0.___67 125 3

52 8

1 8 = 0.___4

5

45

450.0.8

-400

Top In Bottom Out

Part I: How do I convert ½ to a decimal?

Divide the ___________ by the ___________ . The quotient is ___________ . Therefore, ___________ is the decimal equivalent to

½.Write a decimal equivalent for the fraction in each box.

For each fraction converted to a decimal, divide the ___________ by the ___________ .

The quotient is the ___________ ___________ of the fraction.

numerator denominator

0.5

0.5

= 0.___2 3 = 0.___ = 0.___ = 0.___67 125 8 3

54 5

1 8 = 0.___2

8

28

280.0.2

-164

005

-40

Top In Bottom Out

Part I: How do I convert ½ to a decimal?

Divide the ___________ by the ___________ . The quotient is ___________ . Therefore, ___________ is the decimal equivalent to

½.Write a decimal equivalent for the fraction in each box.

For each fraction converted to a decimal, divide the ___________ by the ___________ .

The quotient is the ___________ ___________ of the fraction.

numerator denominator

0.5

0.5

= 0.___2 3 = 0.___ = 0.___ = 0.___67 125 8 252

84 5

1 8 = 0.___3

5

35

350.0.6

-300

Top In Bottom Out

Part I: How do I convert ½ to a decimal?

Divide the ___________ by the ___________ . The quotient is ___________ . Therefore, ___________ is the decimal equivalent to

½.Write a decimal equivalent for the fraction in each box.

For each fraction converted to a decimal, divide the ___________ by the ___________ .

The quotient is the ___________ ___________ of the fraction.

numerator denominator

0.5

0.5

numerator denominator

decimal equivalent

= 0.___2 3 = 0.___ = 0.___ = 0.___ = 0.___67 125 8 25 63

52 8

4 5

1 8

Part II: How do I convert 0.25 to a fraction?Use ________ as the denominator because it is the ________

________ of the digit farthest to the right of the ________ point.

Use ________ as the numerator because they are the ________ to the ________ of the ________ point.

Therefore, ___________ is the fraction equivalent to 0.25. Write a fraction equivalent for the decimal in each box.

For each decimal converted to a fraction, use the _________ _________ of the digit farthest to the right of the _________ _________ as the denominator. Then use the _________ to the right of the _________ _________ as the _________.

100 placevalue decimal

25 digitsright decimal

_25_100

0.75 = 0.5 = 0.4 = 0.625 = 0.375 =

0

ones

tent

hshu

ndre

dths

thou

sand

ths

.

75. 10075

Part II: How do I convert 0.25 to a fraction?Use ________ as the denominator because it is the ________

________ of the digit farthest to the right of the ________ point.

Use ________ as the numerator because they are the ________ to the ________ of the ________ point.

Therefore, ___________ is the fraction equivalent to 0.25. Write a fraction equivalent for the decimal in each box.

For each decimal converted to a fraction, use the _________ _________ of the digit farthest to the right of the _________ _________ as the denominator. Then use the _________ to the right of the _________ _________ as the _________.

100 placevalue decimal

25 digitsright decimal

_25_100

0.75 = 75100 0.5 = 0.4 = 0.625 = 0.375 =

0

ones

tent

hshu

ndre

dths

thou

sand

ths

.

5. 105

Part II: How do I convert 0.25 to a fraction?Use ________ as the denominator because it is the ________

________ of the digit farthest to the right of the ________ point.

Use ________ as the numerator because they are the ________ to the ________ of the ________ point.

Therefore, ___________ is the fraction equivalent to 0.25. Write a fraction equivalent for the decimal in each box.

For each decimal converted to a fraction, use the _________ _________ of the digit farthest to the right of the _________ _________ as the denominator. Then use the _________ to the right of the _________ _________ as the _________.

100 placevalue decimal

25 digitsright decimal

_25_100

0.75 = 75100 0.5 = 5

10 0.4 = 0.625 = 0.375 =

0

ones

tent

hshu

ndre

dths

thou

sand

ths

.

4. 104

Part II: How do I convert 0.25 to a fraction?Use ________ as the denominator because it is the ________

________ of the digit farthest to the right of the ________ point.

Use ________ as the numerator because they are the ________ to the ________ of the ________ point.

Therefore, ___________ is the fraction equivalent to 0.25. Write a fraction equivalent for the decimal in each box.

For each decimal converted to a fraction, use the _________ _________ of the digit farthest to the right of the _________ _________ as the denominator. Then use the _________ to the right of the _________ _________ as the _________.

100 placevalue decimal

25 digitsright decimal

_25_100

0.75 = 75100 0.5 = 5

10 0.4 = 0.625 = 0.375 = 410

0

ones

tent

hshu

ndre

dths

thou

sand

ths

.

62. 1000625

5

Part II: How do I convert 0.25 to a fraction?Use ________ as the denominator because it is the ________

________ of the digit farthest to the right of the ________ point.

Use ________ as the numerator because they are the ________ to the ________ of the ________ point.

Therefore, ___________ is the fraction equivalent to 0.25. Write a fraction equivalent for the decimal in each box.

For each decimal converted to a fraction, use the _________ _________ of the digit farthest to the right of the _________ _________ as the denominator. Then use the _________ to the right of the _________ _________ as the _________.

100 placevalue decimal

25 digitsright decimal

_25_100

0.75 = 75100 0.5 = 5

10 0.4 = 0.625 = 0.375 = 6251000

410

0

ones

tent

hshu

ndre

dths

thou

sand

ths

.

37. 1000375

5

Part II: How do I convert 0.25 to a fraction?Use ________ as the denominator because it is the ________

________ of the digit farthest to the right of the ________ point.

Use ________ as the numerator because they are the ________ to the ________ of the ________ point.

Therefore, ___________ is the fraction equivalent to 0.25. Write a fraction equivalent for the decimal in each box.

For each decimal converted to a fraction, use the _________ _________ of the digit farthest to the right of the _________ _________ as the denominator. Then use the _________ to the right of the _________ _________ as the _________.

100 placevalue decimal

25 digitsright decimal

_25_100

place valuedecimal point

digitsdecimal point numerator

0.75 = 75100 0.5 = 5

10 0.4 = 0.625 = 0.375 = 3751000

6251000

410

Part III: How do I convert 0.75 to a percent?

Move the ________ ________ two places to the ________.Put a ________ sign after the number to replace the ________

point.Therefore, ________ is the percent equivalent to 0.75.

Write a percent equivalent for the decimal in each box.

For each decimal converted to a percent, ________ the decimal by ________. Place a ________ sign after the product.

decimal point rightpercent decimal

75%

0.6 = ___%66 0.35 = ___%35 0.25 = ___%25 0.625 = ____% 0.80 = ___%

066%

Part III: How do I convert 0.75 to a percent?

Move the ________ ________ two places to the ________.Put a ________ sign after the number to replace the ________

point.Therefore, ________ is the percent equivalent to 0.75.

Write a percent equivalent for the decimal in each box.

For each decimal converted to a percent, ________ the decimal by ________. Place a ________ sign after the product.

decimal point rightpercent decimal

75%

0.6 = ___%66 0.35 = ___% 0.25 = ___% 0.625 = ____% 0.80 = ___%

035%

Part III: How do I convert 0.75 to a percent?

Move the ________ ________ two places to the ________.Put a ________ sign after the number to replace the ________

point.Therefore, ________ is the percent equivalent to 0.75.

Write a percent equivalent for the decimal in each box.

For each decimal converted to a percent, ________ the decimal by ________. Place a ________ sign after the product.

decimal point rightpercent decimal

75%

0.6 = ___%66 0.35 = ___%35 0.25 = ___% 0.625 = ____% 0.80 = ___%

025%

Part III: How do I convert 0.75 to a percent?

Move the ________ ________ two places to the ________.Put a ________ sign after the number to replace the ________

point.Therefore, ________ is the percent equivalent to 0.75.

Write a percent equivalent for the decimal in each box.

For each decimal converted to a percent, ________ the decimal by ________. Place a ________ sign after the product.

decimal point rightpercent decimal

75%

0.6 = ___%66 0.35 = ___%35 0.25 = ___%25 0.625 = ____% 0.80 = ___%

062 %5

Part III: How do I convert 0.75 to a percent?

Move the ________ ________ two places to the ________.Put a ________ sign after the number to replace the ________

point.Therefore, ________ is the percent equivalent to 0.75.

Write a percent equivalent for the decimal in each box.

For each decimal converted to a percent, ________ the decimal by ________. Place a ________ sign after the product.

decimal point rightpercent decimal

75%

0.6 = ___%66 0.35 = ___%35 0.25 = ___%25 0.625 = ____%62.5 0.80 = ___%

080%

Part III: How do I convert 0.75 to a percent?

Move the ________ ________ two places to the ________.Put a ________ sign after the number to replace the ________

point.Therefore, ________ is the percent equivalent to 0.75.

Write a percent equivalent for the decimal in each box.

For each decimal converted to a percent, ________ the decimal by ________. Place a ________ sign after the product.

decimal point rightpercent decimal

75%

multiply100 percent

0.6 = ___%66 0.35 = ___%35 0.25 = ___%25 0.625 = ____%62.5 0.80 = ___%80

Part IV: How do I convert ¾ to a percent?Convert the ________ to a ________.Divide the ________ by the __________. The quotient is ______.Therefore, ________ is the decimal equivalent to ¾.Then, convert the ________ to a ________.Move the ________ ________ two places to the ________.Put a ________ sign after the number. The decimal point can

be omitted if it is to the right of all the digits.Therefore, ________ is the percent equivalent to 0.75, and

therefore is the percent equivalent to the fraction ________.

Write a percent equivalent for the fraction in each box.

For each fraction converted to a percent, ________ the ________ by the __________.Convert the ________ to a percent by multiplying by ________ and writing a ________ sign after the product.

= ___%1 3 = ___% = ___% = ___% = ____%33 75 40 50 87.57

84 8

2 5

3 4

fraction decimalnumerator denominator 0.75

0.75decimal percent

decimal point rightpercent

75%¾

dividenumerator denominator

decimal100 percent

13

130.0.3

-91

00033%

3Top In Bottom Out

34

340.0.7

-282

00075%

5Top In Bottom Out

25

250.0.4

-200

040%

Top In Bottom Out

48

480.0.5

-400

050%

Top In Bottom Out

78

780.0.8

-646

00087 %

7

-56

0

4

05

5

Top In Bottom Out

Part V: How do I convert 6.75 to a percent?

Move the ________ ________ two places to the ________.Put a ________ sign after the number.Therefore, ________ is the percent equivalent to 6.75.

Write a percent equivalent for the mixed decimal in each box.

For each decimal I converted to a percent, I move the ________ ________ two places to the ________.Then I put a ________ sign after the number.If the decimal point is to the ________ of the digits, I do not have to write it in the percent number. ________ is the only one of these percents above that I must write the decimal point.

decimal point rightpercent

675%

3.35 = ___%335 12.08 = ____%1208 1.20 = ___%120 3.63 = ____%363 9.091 = _____%909.1

decimal point rightpercent

right909.1

335%

208%1

120%

363%

909 %1

(7.1) Number, operation, and quantitative reasoning.

The student represents and uses rational numbers in a variety of equivalent forms.

The student is expected to:(B) convert between fractions, decimals, whole numbers, and

percents mentally, on paper, or with a calculator.

7.1B STUDENT ACTIVITY #2

Part I: How do I convert 3.275 to a mixed fraction?

I use ________ as the ________ ________ part of the ________ because it is to the ________ of the ________ point.

I use ________ as the denominator because it is the ________ ________ of the digit farthest to the right of the ________ point.

I use ________ as the numerator because they are the ________ to the ________ of the ________ point.

Therefore, ________ is the mixed fraction equivalent to 3.275.

Write a mixed fraction equivalent for the decimal in each box.

For each decimal number I convert to a mixed number, I use the ________ ________ of the digit farthest to the right of the ________ ________ as the denominator. I then use the ________ to the right of the ________ ________ as the ________.Finally, I use any ________ to the left of the decimal point as the ________-number part of the ________ fraction.

21.5 = _____ 33.2 = _____ 8.75 = _____ 1.25 = _____ 87.4 = _____

3 whole number fractionleft decimal

1000 placevalue decimal

275 digitsright decimal

3 2751000

place valuedecimal point

digits decimal pointnumerator

digitswhole mixed

21 33 8 1 87510

210

75100

25100

410

21 5. 105on

este

nths

hund

redt

hsth

ousa

ndth

s

.tens

21

33 2. 102on

este

nths

hund

redt

hsth

ousa

ndth

s

.tens

33

8 75. 10075on

este

nths

hund

redt

hsth

ousa

ndth

s

.tens

8

1 25. 10025on

este

nths

hund

redt

hsth

ousa

ndth

s

.tens

1

87 4. 104on

este

nths

hund

redt

hsth

ousa

ndth

s

.tens

87

Part II: How do I convert 4.5% to a decimal?

Move the ________ ________ two places to the ________,Place a leading ________ before the number. Drop the

________ sign after the number.Therefore, ________ is the decimal equivalent to 4.5%.

Write a decimal equivalent for the percent in each box.

For each percent converted to a decimal, move the ________ ________ two places to the ________.Then drop the ________ sign after the number.

25% = _____ 3.7% = _____ 9% = _____ 32.8% = ______ 5.5% = _____

0.045

decimal point leftpercent

0.25 0.037 0.09 0.328 0.055

decimal point leftpercent

zero

025%

037%0

009%

328%0

055%0

Part III: How do I convert 75% to a fraction?

Express the ________ as a ________ with a denominator of ________.

Therefore, ________ is the fraction equivalent to 75%.

Write a percent equivalent for the decimal in each box.

For each percent converted to a fraction, express the percent as a fraction with a denominator of ________. Then simplify the fraction if needed.

20% = ____ 10% = ____ 45% = ____ 30% = ____ 25% = ____

percent fraction100 75

100

100

20100

10100

45100

30100

25100

20%100

10%100

45%100

30%100

25%100

Part IV: How do I convert 145 percent to a fraction?

Express the ________ as a ________ with a denominator of ________.

The percent is greater than ________%, so it may be expressed as a ________ fraction.

Therefore, ________ is the fraction equivalent to 145% and ________ is the ________ fraction equivalent of 145%.

Write a fraction or mixed fraction equivalent for the percent in each box.

For each percent converted to a fraction, express the ________ as a ________ with a denominator of ________.If the percent is greater than ________%, express the fraction equivalent as a ________ ________.

150% = 555% = 272% = 37.1% = 87.4% =

percent fraction100

100mixed

145100

145

100 mixed

percent fraction100

100mixed fraction

50100

55100

72100

87.4100

37.11001 5 2

50%10011

55%10055

72%10022

37.2%100

1%10

3737 .on

este

nths

hund

redt

hsth

ousa

ndth

s

.tens

87.4%100

4%10

8787 .on

este

nths

hund

redt

hsth

ousa

ndth

s

.tens

Part V: Simeon answered 21 out of 25 questions correctly on his quiz. What percent of the quiz questions did he

answer correctly?

The fraction of questions Simeon answered correctly is

Convert the decimal to a percent by moving the decimal point _____ places to the _____.The decimal _____ is equivalent to _____ %.Simeon answered _____ % of the quiz questions correctly.

2125

Convert this fraction to a decimal by dividing _____ by _____.

21 25

The fraction is equivalent to the decimal ______.2125

0.84

2125 .08

-20010

0

0

4

-1000

two right0.84 84

84

0.

Part V: At a school football game 45% of the people watching the game were

middle school students. What fraction of the people watching the game were

middle school students?

Convert ________ to a decimal. Move the decimal point _____ places to the _____.

Of the people watching the game, were middle school students.

______% = ______

Rewrite the decimal 0.45 as a fraction.

Simplify the fraction.

percent twoleft

45 0.45

.45 =10045

10045

209=

209