4-5 Decimals and Fractions
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
4-5 Decimals and Fractions
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
4-5 Decimals and Fractions
Problem of the Day
Write the day of the month as the product of two factors.
Possible answer: 12th of the month, 6 2
4-5 Decimals and Fractions
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
4-5 Decimals and Fractions
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
4-5 Decimals and Fractions
Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers
Write each decimal as a fraction or mixed number.
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
4-5 Decimals and Fractions
Check It Out: Example 1A
Write each decimal as a fraction or mixed number.
0.24
100____24
25____6or
4-5 Decimals and Fractions
Check It Out: Example 1B
Write each decimal as a fraction or mixed number.
3.07
100 ___ 7
3
4-5 Decimals and Fractions
Check It Out: Example 1C
Write each decimal as a fraction or mixed number.
0.5
10__5
2__1or
4-5 Decimals and Fractions
Check It Out: Example 1D
Write each decimal as a fraction or mixed number.
4.8
10____8
5____4or
4
4
4-5 Decimals and Fractions
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
4-5 Decimals and Fractions
To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6
Writing Math
4-5 Decimals and Fractions
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_
Write each fraction or mixed number as a decimal.
4-5 Decimals and Fractions
Check It Out: Example 2A
Write each fraction or mixed number as a decimal.
20____ 5
0
.00- 40
.2
5 20
100- 100
5
0
20__ 5 = 0.25
4-5 Decimals and Fractions
Check It Out: Example 2B
Write each fraction or mixed number as a decimal.
8 __ 13
.000- 8
1 8
20- 16
0.125
40
=
- 400
8 __ 1
3 3.125
4-5 Decimals and Fractions
Check It Out: Example 2C
Write each fraction or mixed number as a decimal.
9 __ 7
0.777
.000- 63
7 9
70- 63
70
=
- 637
9 __ 7
0.7
4-5 Decimals and Fractions
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__
4-5 Decimals and Fractions
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
4-5 Decimals and Fractions
Check It Out: Example 3A
Order the fractions and decimal from least to greatest.
, 0.35, 1 __ 4
1__2
1 __ 4
1 __ 2
, 0.35 ,
4-5 Decimals and Fractions
Check It Out: Example 3B
Order the fractions and decimal from least to greatest.
0.3, 3__5
, 0.53
0.3, 0.53, __53
4-5 Decimals and Fractions
Check It Out: Example 3C
Order the fractions and decimal from least to greatest.
9__10
, 0.89 , 0.90
0.89 ,__10 9
, 0.90
4-5 Decimals and Fractions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
4-5 Decimals and Fractions
Lesson Quiz: Part I
Write each decimal as a fraction or mixed number.
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
__
4-5 Decimals and Fractions
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__
4-5 Decimals and Fractions
1. Which of the following represents the given decimal as a fraction?
0.26
A. C.
B. D.
Lesson Quiz for Student Response Systems
4-5 Decimals and Fractions
2. Which of the following represents the given decimal as a mixed number?
5.25
A. C.
B. D.
Lesson Quiz for Student Response Systems
4-5 Decimals and Fractions
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
Lesson Quiz for Student Response Systems
4-5 Decimals and Fractions
4. Which of the following represents the given fraction as a decimal?
A. 0.2565 C. 0.5625
B. 0.5256 D. 0.6525
Lesson Quiz for Student Response Systems