4-5 Decimals and Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

4-5 Decimals and Fractions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpFind the GCF of each set of numbers.

1. 15, 24

2. 30, 60

3. 54, 102

4. 12, 16, 24

3

30

6

4


Problem of the Day

Write the day of the month as the product of two factors.

Possible answer: 12th of the month, 6 2


Vocabulary

mixed numberterminating decimalrepeating decimal


A number that contains both a whole number greater than 0 and a fraction, such as 1 , is called a mixed number.

34

__

__41

1 1__21

1 __43

2 __41

2 __21

Mixed numbers12

14

34

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5


Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers

Write each decimal as a fraction or mixed number.

0.67

Identify the place value of the digit farthest to the right.

The 7 is in the hundredths place, so use 100 as the denominator.

0.67

100____67 Remember!

One

s

Ten

ths

Hun

dred

ths

Tho

usan

dths

Place Value


Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers


5.9

Identify the place value of the digit farthest to the right.Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator.

5.9

10 ___ 9

5


Check It Out: Example 1A


0.24

100____24

25____6or


Check It Out: Example 1B


3.07

100 ___ 7

3


Check It Out: Example 1C


0.5

10__5

2__1or


Check It Out: Example 1D


4.8

10____8

5____4or

4

4


Additional Example 2A: Writing Fractions as Decimals

Write each fraction or mixed number as a decimal.

Divide 3 by 20.

Add zeros after the decimal point.

0 20____ 3

The remainder is 0.

.00- 20

.1320

100- 100

5

0

20____ 3

= 0.15


To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6

Writing Math


Additional Example 2B: Writing Fractions as Decimals

Divide 1 by 3.

Add zeros after the decimal point.

0 3 __ 1

The 3 repeats in the quotient.

.000- 9

.31 3

10- 9

3

10

=

6

- 9

3

1 3 __ 1

6 6.333… = 6.3_





20____ 5

0

.00- 40

.2

5 20

100- 100

5

0

20__ 5 = 0.25




8 __ 13

.000- 8

1 8

20- 16

0.125

40

=

- 400

8 __ 1

3 3.125




9 __ 7

0.777

.000- 63

7 9

70- 63

70

=

- 637

9 __ 7

0.7


A terminating decimal, such as 0.75, has a finite number of decimal places. A repeating decimal, such as 0.666…, has a block of one or more digits that repeat continuously

0.80.750.60.60.50.40.30.250.2

Common Fractions and Equivalent Decimals1

3__1

5__ 1

4__ 2

5__ 1

2__ 3

5__ 2

3__ 3

4__ 4

5__


Additional Example 3: Comparing and Ordering Fractions and Decimals

Order the fractions and decimal from least to greatest.

, 0.8, 7 __10

3__4

First rewrite the fractions as decimals. = 0.75 = 0.7

Order the three decimals.

3 __ 4

0

7 __10

__107

3 __ 4

0.75 0.80.7

The numbers in order from least to greatest are , , and 0.8. 710

3 4




, 0.35, 1 __ 4

1__2

1 __ 4

1 __ 2

, 0.35 ,




0.3, 3__5

, 0.53

0.3, 0.53, __53




9__10

, 0.89 , 0.90

0.89 ,__10 9

, 0.90


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I


1. 0.24

2. 6.75

Write each fraction or mixed number as a

decimal.

3. 2 4.

2.6 0.87535

__

8__7

625

____

6 34

__


Lesson Quiz: Part II

5. Order the fractions and decimals from least to

greatest.

0.38, ,

6. Jamal ran the following distances on three

different days: 0.87 mile, mile, and 0.13 mile.

Order the distances from least to greatest.

0.13, , 0.87

34__ 1

5__

23__

15__ , 0.38, 3

4__

23__


1. Which of the following represents the given decimal as a fraction?

0.26

A. C.

B. D.



2. Which of the following represents the given decimal as a mixed number?

5.25

A. C.

B. D.



3. Which of the following represents the given mixed number as a decimal?

A. 2.3 C. 3.5

B. 3.4 D. 5.2



4. Which of the following represents the given fraction as a decimal?

A. 0.2565 C. 0.5625

B. 0.5256 D. 0.6525



5. Which of the following represents the given fractions and decimals ordered from least to greatest?

A. C.

B. D.


Documents

4-5 Decimals and Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes