6th Grade Math Unit 6 - Percents, Fractions, Decimals

0.625 = 62.5% (move decimal 2 places to the right)

At the football game, 0.625 of the fans bought food from the snack bar. What percent of the fans bought food from the snack bar? A) 62.5% B) 625%

240/2000 ÷ 10/10 = 24/200 ÷2/2 = 12/100 = 12% teachers 100% - 12% = 88% students

Of the 2,000 people at a concert, 240 are teachers. The rest are students. What percentage of the people at the concert are students?

A) 32/400 ÷ 4/4 = 8/100 = 8% monkeys B) 100% - 8% = 92% not monkeys

Of the 400 animals in a zoo, 32 were monkeys. A) What percent of the animals were monkeys? B) What percent of the animals were not monkeys?

3/5 = 6/10 = 0.6 2/10 = 0.2 0.645 13% = 0.13 So: 0.13, 0.2, 0.6, 0.645 or 13%, 2/10, 3/5, 0.645

Order from least to greatest: 3/5, 2/10, 0.645, 13%

40% = 0.4 10/20 = 5/10 = 0.5 18% = 0.18 0.082 So: 0.082, 0.18, 0.4, 0.5 or 0.082, 18%, 40%, 10/20

Order from least to greatest: 40%, 10/20, 18%, 0.082

12/20 x 5/5 = 60/100 = 60% incorrect 100% - 60% = 40% correct

Out of 20 questions, Jordan answered 12 of them incorrectly. What percent of the questions did he answer correctly?

14/25 x 4/4 = 56/100 = 56% of chairs of brown

Out of 25 chairs, 14 are brown. What percent of the chairs are brown?

11/25 x 4/4 = 44/100 = 44%

Out of 25 doors, 11 of them are brown. What percent of the doors are brown?

65/500 ÷ 5/5 = 13/100 = 13%

Out of a total of 500 flowers, 65 are roses. What percent of the flowers are roses?

340/100 ÷ 10/10 = 34/10 ÷ 2/2 = 17/5 = 3 and 2/5

Over the past 3 years, a company's stock increased 340%. What is 340% expressed as a fraction or mixed number in simplest form? A) 5/17 B) 3 and 2/5

8-2 = 6 6/8 = 3/4 x 25/25 = 75/100 = 75%

2 out of 8 puppies are brown. What percent of the puppies are not brown? A) 25% B) 75%

6 %

0.06 = _____ %

50 %

0.5 = ______ %

52.3 %

0.523 = _______ %

95 %

0.95 = ______ %

65 = 125 x 100 6500 = 125x x = 6500 ÷ 125 = 52

125% of a number is 65. Find the number.

1. is/of = %/100 or part/whole = %/100 2. is = 180 of = x % = 15 3. 180 = 15 x 100 4. 18000 = 15x 5. 18000 ÷ 15 = x 6. x = 1200 6. 15% of 1200 = 180

15% of a number is 180. Find the number.

0.16

16% = _____.____

17 out of 100 17/100 17 squares out of 100 squares

17% means

1. is/of = percent/100 2. is = 18 of = ? percent = 75 100 is given 3. 18 = 75 x 100 4. 1800 = 75x 5. 1800 ÷ 75 = x 6. x = 24 7. So, 18 is 75% of 24

18 is 75% of what number? Use the part/whole = %/100 ratio method to solve. A) 24 B) 13.5

44 = 22 x 100 4400 = 22x x = 4400 ÷ 22 = 200

22% of a number is 44. Find the number.

25% + 35% + 30% = 90%, so 10% chose PC. 1. is/of = %/100 2. x = 10 300 100 3. 3000 = 100x 4. 3000 ÷ 100 = x 5. x = 30 students chose PC or 300 x 0.10 = 30

300 students were surveyed about their favorite video game system. 25% chose Nintendo, 35% chose PlayStation, 30% chose Xbox. The rest chose PC. How many students chose PC? A) 210 B) 30

0.343

34.3% = _____._____

0.04

4% = ____.____

1. is/of = percent / 100 2. is = 75 percent = 50% 100 is given of = ? or x (our variable) 3. 75 = 50 cross multiply x 100 4. 7500 = 50x (50x = 50 times a # that is represented by x) 5. 7500 ÷ 50 = x 6. x = 150 7. So 50% of 150 = 75

50% of what number is 75?

.064

6.4% = _____._____

hundred, 100

8% means 8 per ___________ or 8 out of _________

100

A 10-by-10 square grid has __________ squares

a) 350/1400 = 0.25 = 25% to his brother b) 1400 - 350 = 1050 1050/1400 = 0.75 = 75%

Harold had 1,400 stamps. He gave 350 of them to his brother and the rest to his sister. a) What percent of the stamps did he give to his brother? b) What percent of the stamps did he give to his sister?

To convert 3/8 to a decimal with long division, i t should be 3 ÷ 8 not 8 ÷ 3 or 8√3 instead of 3√8

Ellen is writing 3/8 as a decimal by hand, using long division. Please find and describe the error in Ellen's work.

5.25% = 0.0525 (move decimal 2 places to the left) $40 x 0.0525 = $2.10

Emma's county charges 5.25% sales tax. What is the sales tax on a $40 purchase? A) $21 B) $2.10

8%

Express 0.08 as a percent

3/4 x 25/25 = 75/100 = 75%

Express 3/4 as a percent

4/5 x 20/20 = 80/100 = 80%

Express 4/5 as a percent

9/100 = 0.09

Express 9% as a decimal

2%

Express each decimal as a percent. 0.02

63%

Express each decimal as a percent. 0.63

0.46

Express each percent as a decimal. 46%

0.09

Express each percent as a decimal. 9%

46/100 ÷ 2/2 = 23/50

Express each percent as a fraction in simplest form. 46%

8.8/100 ÷ 4/4 = 2.2/25

Express each percent as a fraction in simplest form. 8.8%

24% = 24/100 ÷ 2/2 = 12/50 ÷ 2/2 = 6/25

Express the percent as a fraction or mixed number in simplest form: 24%

1. is/of = %/100 2. is = 20 of = x % = 5 100 is given 3. 20 = 5 x 100 4. 2000 = 5x 5. x = 2000 ÷ 5 = 400 people were surveyed

Favorite Type of Music Rock 25% Rap 40% Pop 30% Country 5% If 20 people chose country music, how many total people were surveyed? Use the part/whole = %/100 ratio method to solve. A) 500 B) 400

500 kg x 0.35 = 175 kg

Find the quantity represented by each percent. 35% of 500 kilograms

$2800 x 0.68 = $1,904

Find the quantity represented by each percent. 68% of $2,800

move the decimal two places to the right and add a percent sign ex - 0.715 = 71.5%

How to write a decimal as a percent

1) change the mixed number to an improper fraction 2) change the fraction to a decimal using division 3) multiply the decimal by 100 and add the % sign ex - 1 and 5/9 = 14/9 = 1.5555 x 100 = 155.55 %

How to write a mixed number as a percent

move the decimal two spaces to the left and take away the percent sign

How to write a percent as a decimal

write the percent as a fraction with a denominator of 100, then simplify ex - 75% = 75/100 = 3/4

How to write a percent as a fraction

re-write the percent as a fraction with a denominator of 100 simplify and write the improper fraction as a mixed number ex - 125% = 125/100 = 1 and 1/4 or 1.25

How to write a percent greater than 100 as a mixed number

$900 x 0.22 = $198 for the mobile phone

Iris had $900. She spent 22% of this amount on a mobile phone. How much did she pay for the mobile phone?

Jalen used the wrong multiplier to convert 25 to 100, thus he also multiplied 8 by the wrong multiplier. He should have multiplied 8/25 x 4/4 = 32/100 = 32%

Jalen is expressing the fraction as a percent. Please find and describe the error in his work below.

1. is/of = %/100 or part/whole = %/100 2. is = 520 of = x % = 40 3. 520 = 40 x 100 4. 52,000 = 40x 5. 52,000 ÷ 40 = x 6. x = 1,300 biscuits

Jenny made 520 walnut biscuits. This is 40% of the total number of biscuits that she made. How many biscuits did she make in all?

1.40 = 140% (move decimal two places to the right)

Morton at 1.4 pizzas. What is 1.4 written as a percent? A) 140% B) 14%

4.2% = 0.042 (move decimal 2 places to the left)

Natasha got a 4.2% raise. What is this number written as a decimal? A) 0.042 B) 0.42

0.7

Write 70% as a decimal

3/10 = 0.3 = 30%

Write as a decimal and percent: 3/10

3/4 = 0.75 0.5 = 0.5 80% = 0.80 0.82 = 0.82 So: 0.5, 0.75, 0.80, 0.82 = 0.5, 3/4, 80%, 0.82

Put in order from least to greatest: 3/4, 0.5, 80%, 0.82

1. is/of = %/100 or part/whole = %/100 2. is = 1,500 of = x % = 20 3. 1500 = 20 x 100 4. 150,000 = 20x 5. 150,000 ÷ 20 = x 6. x = $7,500 total savings before buying the computer

Ray spends 20% of his savings to buy a $1500 computer. How much did he have before he bought the computer?

1. is/of = %/100 or part/whole = %/100 2. is = 352 of = x percent = 80 3. 352 = 80 x 100 4. 35200 = 80x 5. 35200 ÷ 80 = x 6. x = 440 miles

So far, Kayla has driven 352 miles, which is 80% of her final distance. What is the total distance Kayla is going to drive? A) 281.6 miles B) 440

1. is/of = percent/100 2. is = 160 of = ? or x percent = 125% 100 is given 3. 160 = 125 x 100 4. 16000 = 125x 5. 16000 ÷ 125 = x 6. X = 128 people attended the reunion last year

The attendance at a family reunion was 160 people. This was 125% of last year's attendance. How many people attended the reunion last year?

3%

The model represents the part of the US population that are twins. What percent of the US population are twins? A) 3% B) 0.03%

6/30 ÷ 3/3 = 2/10 = 0.2 = 20%

Write as a decimal and percent: 6/30

1. is/of = percent/100 2. is = 714 of = 1295 percent = ? or x 100 is given 3. 714 = x 1295 100 4. 71400 = 1295x 5. 71400 ÷ 1295 = 55.14 = 55% of students are women

There are 1,295 students attending a small university. There are 714 women enrolled. What percentage of students are women?

15 girls + 25 boys = 40 total 15/40 = 0.375 = 37.5%

There were 15 girls and 25 boys in the Science club. What percent of the members were girls?

45 adults x 0.60 = 27 were women

There were 45 adults on a bus. 60% of them were women. How many women were on the bus?

1. Write the ratio in fraction form 2. Use equivalent fractions to make the denominator 100 (multiply or divide) 3. Then the numerator is your percentage

To calculate the percent of something out of a number other than 100:

right

To convert a decimal to a percent, you move the decimal two spaces to the __________

left

To convert a percent to a decimal, you move the decimal two spaces to the __________

True (28 = 28)

True/False - 70% of 40 = 40% of 70

False (70%)

True/False - The decimal 0.7 expressed as a percent is 7%.

$2,800 x 0.07 = $196.00 in sales tax Total = $2,800 + $196 = $2,996

Tyrone paid $2,800 plus 7% sales tax on mountain bikes for a bike club. How much did Tyrone pay in total for the mountain bikes?

1. is/of = %/100 2. is = ? of = 550 kg % = 12 3. x = 12 550 100 4. 100x = 6600 5. 6600 ÷ 100 = x 6. x = 66 kg

What is 12% of 550 kg?

120%

What percent is modeled here? A) 12% B) 120%

1. is/of = percent/100 2. is = 18 of = 90 percent = ? or x (variable) 100 is given 3. 18 = x 90 100 4. 1800 = 90x 5. 1800 ÷ 90 = x 6. x = 20 7. So 20% of 90 is 18

What percent of 90 is 18?

B) 2 places to the right

When changing a decimal to a percent, you move your decimal point how many places? A) 2 places to the left B) 2 places to the right C) 3 places to the left d) 3 places to the right

A) 2 places to the left

When changing a percent to a decimal, you move your decimal point how many places? A) 2 places to the left B) 2 places to the right C) 3 places to the left d) 3 places to the right

is/of = percent/100

When solving percent problems using proportions, use the proportion __________ = __________

6%

Write 0.06 as a percent

46%

Write 0.46 as a percent

70%

Write 0.7 as a percent

12/100 ÷ 4/4 = 3/25

Write 12% as a fraction in simplest form

18/100 ÷ 2/2 = 9/50

Write 18% as a fraction in simplest form

0.02

Write 2% as a decimal

45/100 ÷ 5/5 = 9/20

Write 45% as a fraction in simplest form

0.543

Write 54.3% as a decimal

hundred

a percent means per __________

percent

a ratio of a number to 100

proportion

an equation stating that two ratios are equal

part/whole = percent/100

because the ratios part to whole and percent to 100 are equal the form the proportion: __________

multiply denominators to find a common denominator

cross products are the numerators that result if you __________

cross products

proportions can be solved using _______