This document provides a lesson on writing division expressions using fractions. It discusses representing division expressions as fractions instead of using the division symbol. Students practice writing division expressions in two forms: using the division symbol and as a fraction. They learn that the dividend becomes the numerator and the divisor becomes the denominator when writing division as a fraction. Examples and exercises are provided to demonstrate this process.

1. Lesson 13: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
Lesson 13:Writing Division Expressions
Student Outcomes
 Students write numerical expressions in two forms, and , and note the
relationship between the two.
Classwork
Discussion (8 minutes)
The discussion will serve as a chance for students to show what they know about division and what division looks like.
The discussion should conclude with the overall idea that writing as is a strategic format when working
algebraically.
 How can we write or show divided by ? (You can allow students to explain or even draw examples for class
to see.
 Answers will vary. Students can draw models, arrays, use the division symbol and some may even use a
fraction.
 When working with algebraic expressions, are any of these expressions or models more efficient than others?
 Writing a fraction to show division is more efficient.
 Is the same as ?
 No, they are not the same. , while
 How would we show divided by using a fraction?

Example 1 (5minutes)
Example 1
Write an expression showing without the use of the division symbol.
 Let’s start by looking at a model of .
 We can make a bar diagram.
MP.
6

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
From the model what can we determine?
is the same as .
Example 2 (5minutes)
Example 2
Write an expression showing without the use of the division symbol.
 Here we have a variable being divided by . Let’s start by looking at a model of .
 We can make a bar diagram.
From the model what can we determine?
is the same as .
When we write division expressions using the division symbol we represent .
How would this look when we write division expressions using a fraction?
Example 3 (8 minutes)
Example 3
a. Write an expression showing without the use of the division symbol.
 How can we use what we just learned in Examples 1 and 2 to help us with this example?
 The dividend is the numerator and the divisor is the denominator.
MP.
6

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
b. Write an expression for divided by the quantity plus .
 How would this look with the division symbol?

 Now let’s rewrite this using a fraction.
c. Write an expression for the quotient of the quantity reduced by and .
 Let’s start again by writing this using a division symbol first.

 Next, we will rewrite it using the fraction bar.
Exercises 1–8 (10 minutes)
Have students use a white board or small board to practice the following questions.
Exercises
Write each expression two ways: using the division symbol and as a fraction.
1. divided by .
and
2. divided by .
and
3. divided by .
and
4. The quotient of and .
and
MP.
6

4. Lesson 13: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
5. Seven divided by the quantity plus .
and
6. divided by the quantity minus .
and
7. The sum of the quantity and divided by .
and
8. The quotient of the quantity minus and .
and
Closing (4 minutes)
 Explain to your neighbor how you would rewrite any division problem using a fraction.
 The dividend would become the numerator and the divisor would become the denominator.
Exit Ticket (5 minutes)

5. Lesson 13: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
Name Date
Lesson 13: Writing Division Expressions
Exit Ticket
Rewrite the expressions using the division symbol and as a fraction.
1. The quotient of and .
2. Five divided by the sum of and .
3. The quotient of decreased by and .

6. Lesson 13: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
Exit Ticket Sample Solutions
Rewrite the expressions using the division symbol and as a fraction.
1. The quotient of and .
and
2. Five divided by the sum of and .
and
3. The quotient of the quantity decreased by and .
and
Problem Set Sample Solutions
1. Rewrite the expressions using the division symbol and as a fraction.
a. Three divided by .
and
b. The quotient of and .
and
c. divided by the sum of and .
and
d. The quantity minus divided by .
and
2. Draw a model to show that is the same as .