1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up 1. 2. 3. Order the fractions from least to greatest. , , , ,9 __ 1 6 __
, , 2 3 __ 2 9 __ 3 1 6
, , 2 3 __ 7 12 __
, , 5 6 __ 2 3 __ 5 6 7 12
, , 5 8 __ 1 2 __
, , 4 11 __ 5 8 __ 1 2 4 11
, ,

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

4. Learn to convert between mixed numbers and improper fractions.

5. Vocabulary
improper fraction
proper fraction

6. 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 11 4
___

7. Whole numbers can be written as improper fractions
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. 7 1 __

8. You can write an improper fraction as a mixed number.

9. Additional Example 1: Application9 4 __ 9 4 __
Ella hiked for hours yesterday. Write as a mixed number.
Method 1: Use a model.
Draw squares divided into fourth sections. Shade 9 of the fourth sections. 1 4 1 4 1 4 1 2 1 4 __ 1 4 __
There are 2 whole squares and 1 fourth square, or squares, shaded.

10. Additional Example 1 Continued
Method 2: Use division. 1 4 __ 2 4 9
Divide the numerator by the denominator.
- 8
To form the fraction part of the quotient, use the remainder as the numerator and the divisor as the denominator. 1 1 4 __
Ella hiked for 2 hours.

11. Arnold biked for hours yesterday. Write as a mixed number.
Check It Out: Example 1 7 4 __ 7 4 __
Arnold biked for hours yesterday. Write
as a mixed number.
Method 1: Use a model.
Draw squares divided into fourth sections. Shade 7 of the fourth sections. 1 4 1 4 3 4 __ 1 3 4 __
There is 1 whole square and 3 fourth squares, or squares, shaded.

12. Check It Out: Example 1 Continued
Method 2: Use division. 3 4 __ 1 4 7
Divide the numerator by the denominator.
- 4
To form the fraction part of the quotient, use the remainder as the numerator and the divisor as the denominator. 3 3 4 __
Arnold biked for 1 hours.

13. Additional Example 2: Writing Mixed Numbers as Improper Fractions
Write 3 as an improper fraction. 2 3 __
Method 1: Use a model.
You can draw a diagram to illustrate the whole and fractional parts. 11 3 __
There are 11 thirds or .
Count the thirds in the diagram.

14. 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) + 2
__________
Then add. =
Multiply the whole number by the denominator and add the numerator. 3 3 2 3
9 + 2
_____ = 3 11 3 __ =
Keep the same denominator.
First Multiply.

15. Write 4 as an improper fraction.
Check It Out: Example 2
Write 4 as an improper fraction. 1 3 __
Method 1: Use a model.
You can draw a diagram to illustrate the whole and fractional parts. 13 3 __
There are 13 thirds, or .
Count the thirds in the diagram.

16. 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 __
(3 • 4) + 1
__________
Then add. 4 =
Multiply the whole number by the denominator and add the numerator. 3 __ 1 3
12 + 1
______ 4 = 3 13 3 __ =
Keep the same denominator.
Multiply.

17. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

18. Write each mixed number as an improper fraction.
Lesson Quiz
Write each mixed number as an improper fraction.
1. Janet watches hours of television per day Write as a mixed number. 7 4 __ 7 4 __ 3 4 __ 1 3 5 __ 18 5 __ 1 9 __ 55 9 __ 1 2 __ 21 2 __ 1 8 __ 33 8 __

19. Lesson Quiz for Student Response Systems
Veronica attended hours of piano classes in a week. Which of the following expresses as a mixed number?
A C.
B D.

20. Lesson Quiz for Student Response Systems
2. Which of the following expresses as an improper fraction?
A C.
B D.

21. Lesson Quiz for Student Response Systems
3. Which of the following expresses as an improper fraction?
A C.
B D.

22. Lesson Quiz for Student Response Systems
4. Which of the following expresses as an improper fraction?
A C.
B D.