4-4 decimals and fractions course 1 warm up warm up problem of the day problem of the day lesson...
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4-4 Decimals and Fractions
Course 1
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
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
Course 1
4-4 Decimals and Fractions
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
Course 1
4-4 Decimals and Fractions
Learn to convert between decimals and fractions.
Course 1
4-4 Decimals and Fractions
Vocabulary
mixed numberterminating decimalrepeating decimal
Insert Lesson Title Here
Course 1
4-4 Decimals and Fractions
Course 1
4-4 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
Course 1
4-4 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
Course 1
4-4 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
Course 1
4-4 Decimals and Fractions
Check It Out: Example 1A
Write each decimal as a fraction or mixed number.
0.73
Identify the place value of the digit farthest to the right.
The 7 is in the hundredths place, so use 100 as the denominator.
0.73
100____73
Course 1
4-4 Decimals and Fractions
Check It Out: Example 1B
Write each decimal as a fraction or mixed number.
4.8
Identify the place value of the digit farthest to the right.Write the whole number, 4. The 8 is in the tenths place, so use 10 as the denominator.
4.8
10 ___ 8
4
Course 1
4-4 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
Course 1
4-4 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
Course 1
4-4 Decimals and Fractions
Additional Example 2B: Writing Fractions as Decimals
Divide 1 by 3.
Add zeros after the decimal point.
0 3 __ 1
The three 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.
Course 1
4-4 Decimals and Fractions
Check It Out: Example 2A
Write each fraction or mixed number as a decimal.
Divide 5 by 20.
Add zeros after the decimal point.
0
20____ 5
The remainder is 0.
.00- 40
.25 20
100- 100
5
0
20____ 5
= 0.25
Course 1
4-4 Decimals and Fractions
Check It Out: Example 2B
Write each fraction or mixed number as a decimal.
Divide 2 by 3.
Add zeros after the decimal point.
0
3 __ 2
The six repeats in the quotient.
.000- 18
.62 3
20- 18
6
20
=
7
- 18
6
2 3 __ 2
7 7.666… = 7.6_
Course 1
4-4 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
Common Fractions and Equivalent Decimals
0.2 0.25 0.3 0.4 0.5 0.6 0.6 0.75 0.8
13__1
5__ 1
4__ 2
5__ 1
2__ 3
5__ 2
3__ 3
4__ 4
5__
Course 1
4-4 Decimals and Fractions
Additional Example 3: Comparing and Ordering Fractions and Decimals
Order the fractions and decimals from least to greatest.
, 0.8, 7 __10
3__4
First rewrite the fractions as a decimal. = 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
Course 1
4-4 Decimals and Fractions
Check It Out: Example 3
Order the fractions and decimals from least to greatest.
, 0.35, 1 __ 4
1__2
First rewrite the fractions as decimals. = 0.5 = 0.25
Order the three decimals.
1 __ 2
0
1 __ 4
1__ 2
The numbers in order from least to greatest are , 0.35, and . 1 __ 4
1 __ 2
0.35 0.50.25
1 __ 4
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.
Insert Lesson Title Here
2.6 0.875
Course 1
4-4 Decimals and Fractions
35
__
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
Insert Lesson Title Here
Course 1
4-4 Decimals and Fraction
34__ 1
5__
23__
15__ , 0.38, 3
4__
23__