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Lesson 25 S.110
A Fraction as aPercent
Lesson 25 S.110•Student Outcomes
Students write a fraction and a decimal as a percent of a whole quantity and write a percent of whole quantity as fraction or decimal.
Lesson 25 S.110
Think of two ratios that would describe the image below.Share your ratios with your neighbor.
Sam says 50% of the vehicles are cars. Give three different reasons or models that prove or disprove Sam’s statement. Models can include tape diagrams, 10 x 10 grids, double number lines, etc.Write your responses in the provided box.
Lesson 25 Example 1 continued S.110
Sam says % of the vehicles are cars. Give three different reasons or models that prove or disprove Sam’s statement.
Models can include tape diagrams, x grids, double number lines, etc.
1. are cars.
2.
3. There are more than cars.
[------------------------ ---------- Cars--------- ------------------------] [--------------Trucks ------------------------]
0 20 40 60 80 100
[------------------------ ---------- Cars--------- ------------------------] [--------------Trucks ------------------------]
Lesson 25 Example 1 continued S.110
• Another example of a possible model used is a 10 x 10 grid. It can be used to visually show that 3 out of 5 is not the same as 50 out of 100.
Lesson 25 Example 1 continued S.110
• How is the fraction of cars related to the percent? • Use a model to prove that the fraction and
percent are equivalent. • What other fractions or decimals are equal to the
same percent?
Lesson 25 Example 1 continued S.110How is the fraction of cars related to the percent?
is equal to . Since percents are out of 100, the two are the same.
Use a model to prove that the fraction and percent are equivalent.
What other fractions or decimals are equal to the same percent?
Lesson 25 Example 2 S.111
A survey was taken that asked participants whether or not they were happy with their job. An overall score was given.
of the participants were unhappy while of the participants were happy with their job. Give a part-to-whole ratio for comparing happy participants to the whole. Then write a part-to-whole ratio of the unhappy participants to the whole. What percent were happy with their job, and what percent were unhappy with their job?
Happy _____________________ ______________ Unhappy _____________________ ______________
Ratio Percent Ratio Percent
Create a model to justify your answer.
Why is it helpful to write the fraction with a denominator of 100?How would this fraction be represented as a decimal?How can you model this question using a double number line?
Lesson 25 Example 2 answer S.111Example 2
A survey was taken that asked participants whether or not they were happy with their job. An overall score was given.
of the participants were unhappy while of the participants were happy with their job. Give a part-to-whole ratio for comparing happy participants to the whole. Then write a part-to-whole ratio of the unhappy participants to the whole. What percent were happy with their job, and what percent were unhappy with their job?
Create a model to justify your answer.
Happy
Unhappy
Ratio Percent Ratio Percent
Lesson 25 Needed InfoHow do you change a fraction to a percent?Remember that percent means 100ths. How many out of 100.We can scale up or scale down to get 100 as a denominator.3 = ? 3 = ? 5 100 8 100
3 x 20 = 60 0.375 = 0.3755 x 20 100 100 37.5%
Lesson 25 Needed InfoChange the fractions to percents.1. 3/202. 9/103. 5/84. ¾5. 77/11
Lesson 25 Exercise 1 S.111Renita claims that a score of 80% is the same as the fraction . She drew the following picture in order to support her claim.
Is Renita correct? ______________ Why or why not?How could you change Renita’s picture to make it easier for Renita to see why she is correct or incorrect?
Lesson 25 Exercise 1 S.111
Renita claims that a score of is the same as the fraction . She drew the following picture in order to support her claim.
Is Renita correct?
Yes
Why or why not?
How could you change Renita’s picture to make it easier for Renita to see why she is correct or incorrect?
I could change her picture so that there is a percent scale down the right side showing 20%, 40%, etc. I could also change the picture so that there are ten strips with eight shaded.
1
2
3 4
5
Lesson 25 Exercise 2 S.112Exercise 2
Use the tape diagram to answer the following questions.
is what fraction of the whole quantity?
is what percent of the whole quantity? ̀
is what fraction of the whole quantity?
is what percent of the whole quantity?
Lesson 25 Exercise 2 answer S.112
Exercise 2
Use the tape diagram to answer the following questions.
is what fraction of the whole quantity?
is what percent of the whole quantity?
is what fraction of the whole quantity?
½ or 5/10
is what percent of the whole quantity?
1=5/5 This would be .
Lesson 25 Exercise 3 S.113
Maria completed ¾ of her workday. Create a model that represents what percent of the workday Maria has worked.
What percent of her workday does she have left?
How does your model prove that your answer is correct?
Lesson 25 Exercise 3 answer S.113
Maria completed ¾ of her workday. Create a model that represents what percent of the workday Maria has worked.
What percent of her workday does she have left?25%
How does your model prove that your answer is correct?The model shows that ¾ = 75%, and that ihe ¼ left is the same as 25%.
Lesson 25 Exercise 4 S.113
Matthew completed 5/8 of his workday. What decimal would also describe the portion of the workday he has finished?
How can you use the decimal to get the percent of the workday Matthew has completed?
Lesson 25 Exercise 4 Answer S.113
Matthew completed 5/8 of his workday. What decimal would also describe the portion of the workday he has finished?5 ÷ 8 = 0.625 or 5/8 of 100% = 62.5%How can you use the decimal to get the percent of the workday Matthew has completed?5/8 is the same as 0.625. This is 625 thousandths or 625/1000. Divide the numerator and denominator by ten. 25/1,000 = 62.5/100 = 62.5 %
Lesson 25 Exercise 5 S.114
Complete the conversions from fraction to decimal to percent.
Fraction Decimal Percent
0.35
Lesson 25 Exercise 5 answer S.114Complete the conversions from fraction to decimal to percent.
Fraction Decimal Percent
Lesson 25 Exercise 6 (Pairs) S.114Choose one of the rows from the conversion table in Exercise 5 and use models to prove your answers. (Models could included a 10x10 grid, a tape diagram, a double number line, etc.)
7/20 = 35/100 = .35 = 35%
Lesson 25 Closing
Selected pairs will display and explain their diagram from Exercise #6 showing the relationship between fractions, percents, and decimals.
Lesson 25 Summary S.115Lesson Summary
Fractions, Decimals, and Percentages are all related.
To change a fraction to a percent you can scale up or scale down so that is in the denominator.
Example:
If this is not possible, you can change the fraction to a decimal and then convert to a percent age.
Example:
Models, like tape diagrams and number lines, can also be used to model the relationships.
The diagram shows that .
Lesson 25 Exit Ticket
Show all the necessary work to support your answer.1. Convert 0.3 to a fraction and a percent. 2. Convert 9% to a fraction and a decimal. 3. Convert 3/8 to a decimal and percent.
Lesson 25 Exit Ticket answers
Show all the necessary work to support your answer.1. Convert 0.3 to a fraction and a percent. 2. Convert 9% to a fraction and a decimal. 3. Convert 3/8 to a decimal and percent.
,
,
Lesson 25 Problem Set S.115
Problem Set
1. Use the x grid to express the fraction as a percent.
2. Use a tape diagram to relate the fraction to a percent.
3. How are the diagrams related?
4. What decimal is also related to the fraction?
5. Which diagram is the most helpful for converting the fraction to a decimal? _______________ Explain why.
Lesson 25 Problem Set #1 S.115
1. Use the 10 x 10 grid to express the fraction 11/20 as a percent.
Fifty-five squares should be shaded, or divide into five sections of eleven each and shade in 11 of the 20.0 11 22 33 44 55 0 20 40 60 80 100
Lesson 25 Problem Set #2 S.115
Use a tape diagram to relate the fraction 11/20 to a percent. 0 11 22 33 44 55 0 20 40 60 80 1003. How are the diagrams related?Both show that 11/20 is the same as 55/100.4. What decimal is also related to the fraction?0.55 5. Which diagram is the most helpful for converting the fraction to a decimal? ____________ Explain why.
