Percents and Rates

New York State Common Core Math Grade 6, Module 1, Lesson 25

Worksheets for Grade 6

The following diagram shows an example of fraction as a percent. Scroll down the page for more examples and solutions.

 

Lesson 25 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 Summary
Fractions, Decimals, and Percentages are all related.
To change a fraction to a percentage, you can scale up or scale down so that 100 is in the denominator.
If this is not possible, you can change the fraction to a decimal and then convert to a percentage.
Models, like tape diagrams and number lines, can also be used to model the relationships.

Lesson 25 Classwork
Example 1
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.

Example 2
A survey was taken that asked participants whether or not they were happy with their job. An overall score was given.
300 of the participants were unhappy while 700 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?

Exercise 1
Renita claims that a score 80% of is the same as the fraction 4/5. 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?

Exercise 2
Use the tape diagram to answer the following questions.
80% is what fraction of the whole quantity?
1/5 is what percent of the whole quantity?
50% is what fraction of the whole quantity?
1 is what percent of the whole quantity?

Exercise 3
Maria completed of her 3/4 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?

Exercise 4
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?

Exercise 5
Complete the conversions from fraction to decimal to percent.

Exercise 6
Choose one of the rows from the conversion table in Exercise 5 and use models to prove your answers. (Models could include a 10 x 10 grid, a tape diagram, a double number line, etc.)

• Show Step-by-step Solutions

Example 1
5 out of 20 students in the room are going to stay after school for a club.
a) Use a tape diagram to show what percentage of the students were staying after school.
b) Use a proportion to show what percentage of the students were staying after school.

Example 2
Matthew completed 5/8 of his work day. What decimal would also describe the portion of the workday that he has finished?
How can you use the decimal to the percent of the workday Matthew has completed?

• Show Step-by-step Solutions

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.

Problem Set

1. Use the 10 × 10 grid to express the fraction 11/20 as a percent.
2. Use a tape diagram to relate the fraction 11/20 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.

• Show Step-by-step Solutions

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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