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Lesson 3

(Mixed Number) ÷ (Natural Number)

Objectives

Students will be able to:

1. Understand the calculation method for (mixed number) ÷ (natural number), and skillfully perform calculations.
2. Reduce (rename) a fraction to lowest terms.

Instructional Content and Activities

The calculation method for (mixed number) ÷ (natural number)

Based on what they have learned about dividing (proper fraction) ÷ (natural number), students now learn to divide (mixed number) ÷ (natural number). Real-life situations are used to present and reinforce the calculation principle and method.

Ted has 1 1/2 liters of water, which he divides equally between two bottles. How much water does he put into each bottle?

Be sure students understand the problem. Ted wants to divide the 1	1	L of water equally between the two bottles.
	2

Students should observe that this problem involves a mixed number and a natural number. Help them find the

expression to describe the given situation:

   

Students also should realize that dividing the water equally means putting half into each bottle, which can be

expressed as 1	1	×	1	.
	2		2

Next, teach the following calculation method:

Calculation practice and word problem

Have students practice with the problems in the textbook, using the calculation method they have learned for (mixed number) ÷ (natural number). For the word problem, remind them to use the four steps.

A wire with a length of 2 2/3 meters is divided into 4 equal pieces. What is the length of each piece?

1. Understand the problem.

   Students should realize that the problem is asking for the length of one of four equal parts of a wire whose length is given. This requires dividing the given length (2 2/3 m) by 4.

2. Find the expression.

   Help students see that a given expression can be expressed as 2	2	÷ 4 = ?
   	3

3. Perform the calculation

   			2
   2	2	÷ 4 =		8	×	1		=	2	m
   	3			3		4			3
   							1

4. Check the answer

   Each of the four pieces is	2	m. Altogether, this is	2	× 4 =	8	= 2	2	m. Since 2	2	m was the given
   	3		3		3		3		3

   length of the wire, the answer is known to be correct.

Calculate (mixed number) ÷ (natural number)

Let's calculate

5	3	÷ 4
	5

Students should perform the calculation of 5	3	÷ 4 in one of the following ways:
	5

1. Renaming to lowest equivalent terms before multiplication

   5	3	÷ 4	=	28	÷ 4
   	5			5			Mixed number		improper fraction.

    

   		7
   	=		28	×	1
   			5		4			Division		multiplication; reduce.
   						1

    

   	=	7
   		5		Perform the multiplication.

    

   	= 1	2
   		5		Improper fraction		mixed number.

    

2. Renaming to lowest equivalent terms after mulitplication

   5	3	÷ 4	=	28	÷ 4
   	5			5			Mixed number		improper fraction.

    

   	=	28	×	1
   		5		4		Division		multiplication.

    

   	=	28
   		20		Perform the multiplication.

    

   	= 1	8
   		20		Improper fraction		mixed number.

    

   	= 1	2
   		5		Express the answer in lowest terms.

Let students know that method 1, reducing (renaming) to lowest terms before multiplying, is the preferred method because it involves smaller numbers and is therefore easier.

World problem

Present students with the following problem from their books:

Three people were working together in a vegetable garden. They dug up 12 3/4 kilograms of sweet potatoes, which they want to share equally. How much will each person’s share be?

1. Understand the problem.

   Students should realize that the problem requires dividing the given weight of the sweet potatoes

   (12	3	kg) by 3.
   	4

    

2. Find the expression.

   The given situation is described by the expression 12	3	÷ 3 = ?
   	4

    

3. Perform the calculation.

   			17
   12	3	÷ 3 =		51	×	1		=	17	= 4	1	kg
   	4			4		3			4		4
   							1

    

4. Check the answer.

   4	1	× 3 =	17	× 3
   	4		4

    

   	=	51	= 12	3	kg
   		4		4

    

   Three people with 4	1	kg each makes a total of 12	3	kg. Since 12	3	kg was the given weight at the start of
   	4		4		4

   the problem, the answer is known to be correct

Instruction and Evaluation Tips

Teaching tip

• The important part of the division of mixed numbers is changing the mixed number to an improper fraction. This change was covered in the fourth grade.

Evaluation tip

• Focus on the evaluation of logical procedures, rather than simply looking at the answers.