6-2 Fractions, Decimals, and Percents Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

6-2 Fractions, Decimals, and Percents

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpWrite each fraction in the simplest form.

1. 410

850

2.

3. 75100

4. 1236

5. 6. 1848

25

34

13

35

38

425

915


Problem of the DayUse the clues to find the mystery percent.

1. The product of its digits is 24.

12

3. The sum of its digits is a prime number.

83%

2. It is greater than .


Prep for MA.7.A.1.2 Solve percent problems, including problems involving discounts, simple interest, taxes, tips, and percents of increase or decrease.Rev. MA.6.A.5.1Rev. MA.6.A.5.2

Sunshine State Standards


The students at Westview Middle School are collecting cans of food for the local food bank. Their goal is to collect 2,000 cans in one month. After 10 days, they have 800 cans of food. What percent of their goal have they reached?


0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000

0 15

25

35

45

55

00 0.2 0.4 0.6 0.8 1.0

0 20% 40% 60% 80% 100%

The model shows that 800 out of 2,000 can be written as , ,

0.4, or 40%. The students have reached 40% of their goal.

8002000

25


Write 0.7 as a percent.

Additional Example 1: Writing Decimals as Percents

Method 1: Use pencil and paper.

0.7 = 70100

= 70%

Write the decimal as a fraction with a denominator of 100.

Write the numerator with a percent sign.

710

=



Additional Example 1 Continued

Method 2: Use mental math.

0.70 =

= 70%

Move the decimal point two places to the right and add a percent sign.

70%



Check It Out: Example 1


0.3 = 30100

= 30%

Write the decimal as a fraction with a denominator of 100.

Write the numerator with a percent sign.

310

=



Check It Out: Example 1 Continued


0.30 =

= 30%

Move the decimal point two places to the right and add a percent sign.

30%


Write as a percent.58

58

= 5 ÷ 8

= 0.625

= 62.5%

Use division to write the fraction as a decimal.

Write the decimal as a percent.

Additional Example 2: Writing Fractions as Decimals


To divide 5 by 8, use long division and place a decimal point followed by a zero after the 5.

8 5.00

Remember!

.625


5 ● 12.5 8 ● 12.5

Write an equivalent fraction with a denominator of 100.

=




62.5 100

Write the numerator with a percent sign.= 62.5%



35

= 3 ÷ 5

= 0.60

= 60%

Use division to write the fraction as a decimal.





3 • 20 5 • 20

Write an equivalent fraction with a denominator of 100.

=




60 100

Write the numerator with a percent sign.= 60%


Order 17%, 0.25, , 0.1, , and 20% from least to greatest.

Additional Example 3: Ordering Rational Numbers

Step 1: Write the numbers as decimals with the same number of decimal places.

17% = 0.17

45

34

0.25 = 0.25 34 = 0.75

0.1 = 0.10 45 = 0.80 20% = 0.20




Step 2: Graph the numbers on the number line.

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

0.10 < 0.17 < 0.20 < 0.25 < 0.75 < 0.80

45

34

Step 3: Compare the decimals.

From least to greatest, the numbers are: 0.1, 17%,

20%, 0.25, , .34

45




Step 1: Write the numbers as decimals with the same number of decimal places.

12% = 0.20

34

12

0.20 = 0.20 12 = 0.50

0.8 = 0.80 34 = 0.75 40% = 0.40




Step 2: Graph the numbers on the number line.

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

0.12 < 0.20 < 0.40 < 0.50 < 0.75 < 0.80

34

12

Step 3: Compare the decimals.

From least to greatest, the numbers are: 12%, 0.20, 40%, , , 0.8.1

234


Decide whether using pencil and paper, mental math, or a calculator is most useful when solving the following problem. Then solve.

27 out of 50 =

Using pencil and paper is the best method.

Think: 27 ÷ 50 divides evenly.


Additional Example 4: Choosing a Method of Computation

If 27 out of 50 people have the newspaper delivered to their home, what percent of these people have the newspaper delivered to their home?

2750

= 0.54

= 54%54% of the people have the newspaper delivered to their home.


10 out of 50 =

Mental math or pencil and paper is the best method.

Think: The denominator is a multiple of 100.



If 10 out of 50 students have blue backpacks, what percent of the students have blue backpacks?

1050

= 0.20

= 20%

20% of the students have blue backpacks.

20100

=



Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

60%

1. Write 0.65 as a percent.

2. Write as a percent.

65%

610

3. Order , 0.8, 73%, and 0.57 from least to

greatest.


Lesson Quiz: Part II


Calculator; 45%

4. If 36 out of 80 people surveyed have been on a boat, what percent of these people have been on a boat?


1. Which of the following represents 0.52 as a percent?

A. 52%

B. 26%

C. 13%

D. 4%



2. Which of the following represents 0.08 as a percent?

A. 80%

B. 40%

C. 28%

D. 8%



3. Which of the following represents as a percent?

A. 7%

B. 17%

C. 70%

D. 77%


7 10



2 5

4. Order 0.2, 14%, 0.63, and in order from least to greatest.

A. 0.2, 14%, , 0.63 C. 14%, 0.2, , 0.63

B. 14%, 0.2, 0.63, D. 0.63, , 0.2, 14%

2 5

2 5

2 5

2 5


5. Choose the most useful method of computation and then solve.

If 45 out of 90 students surveyed prefer Algebra to Geometry, what percent of these students prefer Algebra?

A. calculator; 30%

B. calculator; 50%

C. mental math; 30%

D. mental math; 50%


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6-2 Fractions, Decimals, and Percents Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson