Curriculum  /  Math  /  7th Grade  /  Unit 2: Operations with Rational Numbers  /  Lesson 16

Operations with Rational Numbers

Lesson 16

Math

Unit 2

7th Grade

Lesson 16 of 18

Objective

Convert rational numbers to decimals using long division and equivalent fractions.

Common Core Standards

Core Standards

  • 7.NS.A.2.D — Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Foundational Standards

  • 5.NF.B.3
  • 6.NS.B.2

Criteria for Success

  1. Define terminating decimals as numbers with a finite number of digits after the decimal point, and define repeating decimals as numbers with an infinite number of digits after the decimal point in which a digit or group of digits repeats indefinitely.
  2. Convert fractions to decimals using long division. 
  3. Convert between decimals and fractions using place value understanding and equivalent fractions.
  4. Recognize when it is more efficient to convert fractions to decimals using equivalent fractions with denominators of powers of 10 (MP.7).
  5. Attend to precision in calculations and strategic use of place value understanding (MP.6).

Tips for Teachers

Lesson Materials

  • Calculators (1 per student)
  • Graph Paper (1 sheet per student)
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Anchor Problems

25-30 minutes

Problem 1

Using a calculator, find the decimal quotients below.

$${{1\over 2}, {1\over 3}, {1\over 4}, {1\over 5}, {1\over 6}, {1\over 7}, {1\over 8}, {1\over 9}, {1\over 10}, {1\over 11}}$$

Looking at your quotients, organize your answers into two categories. Describe your reasoning behind why you chose those two categories.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 14 — Examples 1 and 2

Grade 7 Mathematics > Module 2 > Topic B > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

a.   Write each decimal as a fraction.

  1.  $$0.35$$
  2. $$1.64$$
  3. $$2.09$$
  4. $$-3.125$$

b.   Write each rational number as a decimal.

  1. $${-{5\over 6}}$$
  2. $${9\over 16}$$
  3. $${-7\over 9}$$
  4. $${{25\over12}}$$

Guiding Questions

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Student Response

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Problem 3

Malia found a "short cut" to find the decimal representation of the fraction $${{117\over250}}$$. Rather than use long division, she noticed that because $${250 \times 4 = 1000}$$, 

$${{{117\over250}}} ={ {117 \times 4}\over {250 \times 4}} = {468\over1000} = 0.468$$

a.   For which of the following fractions does Malia's strategy work to find the decimal representation?

$${{1\over 3}, {3\over 4}, -{6\over 25}, {18\over 7}, {13\over 8}, -{113\over 40}}$$

For each one for which the strategy does work, use it to find the decimal representation.

b.   In general, for which denominators can Malia's strategy work?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Equivalent Fractions Approach to Non-Repeating Decimals

Equivalent Fractions Approach to Non-Repeating Decimals, accessed on Aug. 14, 2017, 4:14 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Problem 1

What is the decimal value of $${{20\over7}}$$?

Student Response

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Problem 2

Write two examples of fractions that have a terminating decimal equivalent, and two examples of fractions that have a repeating decimal equivalent.

Student Response

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Problem 3

Compare each pair of rational numbers using an inequality sign.

a.   $${{1{5\over 8}}}$$ ______  $${{1.6}}$$

b.   $${{1{5\over 8}}}$$ ______  $$-{{1.6}}$$

c.   $$-{{1{5\over 8}}}$$ ______ $${{1.6}}$$

d.   $$-{{1{5\over 8}}}$$ _______ $$-{{1.6}}$$

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Multiply and divide with rational numbers using properties of operations.

Lesson 17
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Adding and Subtracting Rational Numbers

Topic B: Multiplying and Dividing Rational Numbers

Topic C: Using all Four Operations with Rational Numbers

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