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4-6 Mixed Numbers and Improper Fractions
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
4-6 Mixed Numbers and Improper Fractions
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__ , ,
4-6 Mixed Numbers and Improper Fractions
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
4-6 Mixed Numbers and Improper Fractions
Learn to convert between mixed numbers and improper fractions.
4-6 Mixed Numbers and Improper Fractions
Vocabulary
improper fractionproper fraction
4-6 Mixed Numbers and Improper Fractions
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
___
4-6 Mixed Numbers and 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.
71__
4-6 Mixed Numbers and Improper Fractions
You can write an improper fraction as a mixed number.
4-6 Mixed Numbers and Improper Fractions
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__
4-6 Mixed Numbers and Improper Fractions
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__
4-6 Mixed Numbers and Improper Fractions
Check It Out: Example 1
Arnold biked for hours yesterday. Write
as a mixed number.
7
4__7
4__
Method 1: Use a model.
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__
4-6 Mixed Numbers and Improper Fractions
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__
4-6 Mixed Numbers and Improper Fractions
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.
There are 11 thirds or .
11
3__ Count the thirds in the diagram.
4-6 Mixed Numbers and Improper Fractions
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
4-6 Mixed Numbers and Improper Fractions
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.
There are 13 thirds, or .
13
3__ Count the thirds in the diagram.
4-6 Mixed Numbers and Improper Fractions
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.
4-6 Mixed Numbers and Improper Fractions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
4-6 Mixed Numbers and Improper Fractions
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
4-6 Mixed Numbers and Improper Fractions
1. Veronica attended hours of piano classes
in a week. Which of the following expresses
as a mixed number?
A. C.
B. D.
Lesson Quiz for Student Response Systems
4-6 Mixed Numbers and Improper Fractions
2. Which of the following expresses as an
improper fraction?
A. C.
B. D.
Lesson Quiz for Student Response Systems
4-6 Mixed Numbers and Improper Fractions
3. Which of the following expresses as an
improper fraction?
A. C.
B. D.
Lesson Quiz for Student Response Systems
4-6 Mixed Numbers and Improper Fractions
4. Which of the following expresses as an
improper fraction?
A. C.
B. D.
Lesson Quiz for Student Response Systems