4-6 Mixed Numbers and Improper Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson

4-6 Mixed Numbers and Improper Fractions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpOrder the fractions from least to greatest.

1.

2.

3.

2

9 __ 1

6 __ 2

3__

7

12__ 5

6__2

3 __

5

8__ 1

2__ 4

11__

, ,

, ,

, , 5

8__1

2__4

11__ , ,

2

3__ 5

6__7

12__ , ,

2

9__ 2

3__1

6__ , ,


Problem of the Day

Two numbers have a product of 48. When the larger number is divided by the smaller, the quotient is 3. What are the numbers?4 and 12


Learn to convert between mixed numbers and improper fractions.


Vocabulary

improper fractionproper fraction


An improper fraction is a fraction in which the numerator is greater than or equal to the denominator such as .11

4__

is read as “eleven-fourths.”

Reading Math

114

___


Whole numbers can be written as improper fractions. The whole number is the numerator, and the denominator is 1. For example, 7 = .

When the numerator is less than the denominator, the fraction is called a proper fraction.

71__


You can write an improper fraction as a mixed number.


Additional Example 1: Application

Ella hiked for hours yesterday. Write as a mixed number.

9

4__9

4__

Method 1: Use a model.

Draw squares divided into fourth sections. Shade 9 of the fourth sections.

14

14

14

14

1

4__There are 2 whole squares and 1 fourth square, or 2

squares, shaded.

14

14

14

14

14

14

14

14

1 2 1

4__


Additional Example 1 Continued

Method 2: Use division.

1

4__

Divide the numerator by the denominator.

To form the fraction part of the quotient, use the remainder as the numerator and the divisor as the denominator.

4 9- 8

2

1

Ella hiked for 2 hours.1

4__


Check It Out: Example 1

Arnold biked for hours yesterday. Write

as a mixed number.

7

4__7

4__


Draw squares divided into fourth sections. Shade 7 of the fourth sections.

14

14

14

14

3

4__There is 1 whole square and 3 fourth squares, or 1

squares, shaded.

14

14

14

14

1 3

4__


Check It Out: Example 1 Continued

Method 2: Use division.

3

4__

Divide the numerator by the denominator.

To form the fraction part of the quotient, use the remainder as the numerator and the divisor as the denominator.

4 7- 4

1

3

Arnold biked for 1 hours.3

4__


Additional Example 2: Writing Mixed Numbers as Improper Fractions

Write 3 as an improper fraction.2

3__


You can draw a diagram to illustrate the whole and fractional parts.

There are 11 thirds or .

11

3__ Count the thirds in the diagram.


Additional Example 2 Continued

Method 2: Use multiplication and addition.

When you are changing a mixed number to an improper fraction, spiral clockwise as shown in the picture. The order of operations will help you remember to multiply before you add.

2

3__

3 =(3 • 3) + 2__________

3Multiply the whole number by the denominator and add the numerator.

Keep the same denominator.

= 9 + 2_____

3

= 11

3__

First Multiply.

Then add.

233


Check It Out: Example 2

Write 4 as an improper fraction.1

3__


You can draw a diagram to illustrate the whole and fractional parts.

There are 13 thirds, or .

13

3__ Count the thirds in the diagram.


Check It Out: Example 2 Continued

Method 2: Use multiplication and addition.

When you are changing a mixed number to an improper fraction, spiral clockwise as shown in the picture. The order of operations will help you remember to multiply before you add.

1

3__

4 =(3 • 4) + 1__________

3Multiply the whole number by the denominator and add the numerator.

Keep the same denominator.

= 12 + 1______3

= 13

3__

13__4

Multiply.

Then add.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson QuizWrite each mixed number as an improper fraction.

1. Janet watches hours of television per day.

Write as a mixed number.

2. 3 3. 6

4. 10 5. 4

3

5__ 1

9__

1

2__ 1

8__

7

4__

7

4__

55

9__18

5__

21

2__ 33

8__

3

4__1


1. Veronica attended hours of piano classes

in a week. Which of the following expresses

as a mixed number?

A. C.

B. D.



2. Which of the following expresses as an

improper fraction?

A. C.

B. D.




improper fraction?

A. C.

B. D.




improper fraction?

A. C.

B. D.


Documents

4-6 Mixed Numbers and Improper Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson