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Lesson Plans and Worksheets for Grade 8

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More Lessons for Grade 8

Common Core For Grade 8

Examples, solutions, and videos to help Grade 8 students learn when a fraction has a denominator that is the product of 2’s and/or 5’s then it is a finite decimal equivalent otherwise it has an infinite decimal equivalent.

### New York State Common Core Math Grade 8, Module 7, Lesson 6

• Students know that when a fraction has a denominator that is the product of 2’s and/or 5’s, it has a finite decimal expansion because the fraction can then be written in an equivalent form with a denominator that is a power of 10.

Lesson 6 Classwork

Opening Exercises 1–5

1. Use long division to determine the decimal expansion of 54/20.

2. Use long division to determine the decimal expansion of 7/8.

3. Use long division to determine the decimal expansion of 8/9.

4. Use long division to determine the decimal expansion of 22/7.

5. What do you notice about the decimal expansions of Exercises 1 and 2 compared to the decimal expansions of Exercises 3 and 4?

Example 1

Consider the fraction 5/8. Is it equal to a finite decimal? How do you know?

Example 2

Consider the fraction 17/125. Is it equal to a finite or infinite decimal? How do you know?

Exercises 6–10

Show your steps, but use a calculator for the multiplications.

6. Convert the fraction 7/8 to a decimal.

a. Write the denominator as a product of 2’s or 5’s. Explain why this way of rewriting the denominator helps to find the decimal representation of 7/8.

b. Find the decimal representation of 7/8. Explain why your answer is reasonable.

7. Convert the fraction 43/64 to a decimal.

8. Convert the fraction 29/125 to a decimal.

9. Convert the fraction 19/34 to a decimal.

10. Identify the type of decimal expansion for each of the numbers in Exercises 6–9 as finite or infinite. Explain why their decimal expansion is such.

Example 3

Write 7/80 as a decimal. Will it be finite or infinite? Explain.

Example 4

Write 3/160 as a decimal. Will it be finite or infinite? Explain.

Exercises 11–13

Show your steps, but use a calculator for the multiplications.

11. Convert the fraction 37/40 to a decimal.

a. Write the denominator as a product of 2’s and/or 5’s. Explain why this way of rewriting the denominator helps to find the decimal representation of 37/40.

b. Find the decimal representation of 37/40. Explain why your answer is reasonable.

12. Convert the fraction 3/250 to a decimal.

13. Convert the fraction 7/1,250 to a decimal.

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

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, solutions, and videos to help Grade 8 students learn when a fraction has a denominator that is the product of 2’s and/or 5’s then it is a finite decimal equivalent otherwise it has an infinite decimal equivalent.

Download Worksheets for Grade 8, Module 7, Lesson 6

Lesson 6 Student Outcomes

• Students know that every number has a decimal expansion (i.e., is equal to a finite or infinite decimal).• Students know that when a fraction has a denominator that is the product of 2’s and/or 5’s, it has a finite decimal expansion because the fraction can then be written in an equivalent form with a denominator that is a power of 10.

Lesson 6 Summary

Fractions with denominators that can be expressed as products of 2’s and/or 5’s have decimal expansions that are finite.Lesson 6 Classwork

Opening Exercises 1–5

1. Use long division to determine the decimal expansion of 54/20.

2. Use long division to determine the decimal expansion of 7/8.

3. Use long division to determine the decimal expansion of 8/9.

4. Use long division to determine the decimal expansion of 22/7.

5. What do you notice about the decimal expansions of Exercises 1 and 2 compared to the decimal expansions of Exercises 3 and 4?

Example 1

Consider the fraction 5/8. Is it equal to a finite decimal? How do you know?

Example 2

Consider the fraction 17/125. Is it equal to a finite or infinite decimal? How do you know?

Exercises 6–10

Show your steps, but use a calculator for the multiplications.

6. Convert the fraction 7/8 to a decimal.

a. Write the denominator as a product of 2’s or 5’s. Explain why this way of rewriting the denominator helps to find the decimal representation of 7/8.

b. Find the decimal representation of 7/8. Explain why your answer is reasonable.

7. Convert the fraction 43/64 to a decimal.

8. Convert the fraction 29/125 to a decimal.

9. Convert the fraction 19/34 to a decimal.

10. Identify the type of decimal expansion for each of the numbers in Exercises 6–9 as finite or infinite. Explain why their decimal expansion is such.

Write 7/80 as a decimal. Will it be finite or infinite? Explain.

Example 4

Write 3/160 as a decimal. Will it be finite or infinite? Explain.

Exercises 11–13

Show your steps, but use a calculator for the multiplications.

11. Convert the fraction 37/40 to a decimal.

a. Write the denominator as a product of 2’s and/or 5’s. Explain why this way of rewriting the denominator helps to find the decimal representation of 37/40.

b. Find the decimal representation of 37/40. Explain why your answer is reasonable.

12. Convert the fraction 3/250 to a decimal.

13. Convert the fraction 7/1,250 to a decimal.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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