1. Decimals and Fractions
4-4
Decimals and Fractions
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Decimals and Fractions
Course 1
4-4
Decimals and Fractions
Warm Up
Find the GCF of each set of numbers.
1. 15, 24
2. 30, 60
3. 54, 102
4. 12, 16, 24 3 30 6 4

3. Decimals and Fractions
Course 1
4-4
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. Decimals and Fractions
Course 1
4-4
Decimals and Fractions
Learn to convert between decimals and fractions.

5. Insert Lesson Title Here
Course 1
4-4
Decimals and Fractions
Insert Lesson Title Here
Vocabulary
mixed number
terminating decimal
repeating decimal

6. 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. __ 3 4
Mixed numbers 14 12 34 __ 4 1 1 __ 2 1 __ 4 3 2 __ 4 1 2 __ 1

7. Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers
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.
A. 0.67
0.67
Identify the place value of the digit farthest to the right.
100
____ 67
The 7 is in the hundredths place, so use 100 as the denominator.
Remember!
Ones
Tenths
Hundredths
Thousandths
Place Value

8. Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers
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.
B. 5.9
5.9
Identify the place value of the digit farthest to the right. 10
___ 9 5
Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator.

9. Decimals and Fractions
Course 1
4-4
Decimals and Fractions
Try This: Example 1A
Write each decimal as a fraction or mixed number.
A. 0.73
0.73
Identify the place value of the digit farthest to the right.
100
____ 73
The 7 is in the hundredths place, so use 100 as the denominator.

10. Decimals and Fractions
Course 1
4-4
Decimals and Fractions
Try This: Example 1B
Write each decimal as a fraction or mixed number.
B. 4.8
4.8
Identify the place value of the digit farthest to the right. 10
___ 8 4
Write the whole number, 4. The 8 is in the tenths place, so use 10 as the denominator.

11. Additional Example 2A: Writing Fractions as Decimals
Course 1
4-4
Decimals and Fractions
Additional Example 2A: Writing Fractions as Decimals
Write each fraction or mixed number as a decimal. 20
____ 3 A. .1 5
Divide 3 by 20. 20 3
.00
Add zeros after the decimal point.
- 20
100
- 100
The remainder is 0. 20
____ 3 =
0.15

12. Decimals and Fractions
Course 1
4-4
Decimals and Fractions
Writing Math
To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6

13. Additional Example 2B: Writing Fractions as Decimals
Course 1
4-4
Decimals and Fractions
Additional Example 2B: Writing Fractions as Decimals
Write each fraction or mixed number as a decimal. 3 __ 1 A. 6 .3 3 3
Divide 1 by 3. 3 1
.000
Add zeros after the decimal point.
- 9 10
The three repeats in the quotient.
- 9 10
- 9
6.333… = 6.3 _ 1 3 __ 1 6 =

14. Decimals and Fractions
Course 1
4-4
Decimals and Fractions
Try This: Example 2A
Write each fraction or mixed number as a decimal. 20
____ 5 A. .2 5
Divide 5 by 20. 20 5
.00
Add zeros after the decimal point.
- 40
100
- 100
The remainder is 0. 20
____ 5 =
0.25

15. Decimals and Fractions
Course 1
4-4
Decimals and Fractions
Try This: Example 2B
Write each fraction or mixed number as a decimal. 3 __ 2 B. 7 .6 6 6
Divide 2 by 3. 3 2
.000
Add zeros after the decimal point.
- 18 20
The six repeats in the quotient.
- 18 20
- 18
7.666… = 7.6 _ 2 3 __ 2 7 =

16. Common Fractions and Equivalent Decimals
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
0.75
0.8 1 5 __ 1 4 __ 1 3 __ 2 5 __ 1 2 __ 3 5 __ 2 3 __ 3 4 __ 4 5 __

17. Additional Example 3: Comparing and Ordering Fractions and Decimals
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. __ 3 __ 7
, 0.8, 4 10 3 __ 4 __ 10 7
First rewrite the fractions as a decimal. = = 0.7
Order the three decimals. 7 __ 10 3 __ 4
0.7
0.75
0.8
The numbers in order from least to greatest are , , and 0.8. 7 10 3 4

18. Decimals and Fractions
Course 1
4-4
Decimals and Fractions
Try This: Example 3
Order the fractions and decimals from least to greatest. __
, 0.35, 1 1 __ 4 2 1 __ 2 1 __ 4
First rewrite the fractions as decimals = = 0.25
Order the three decimals. 1 __ 4 1 __ 2
0.25
0.35
0.5 1 __ 4
The numbers in order from least to greatest are , 0.35, and 1
__ . 2

19. Decimals and Fractions Insert Lesson Title Here
Course 1
4-4
Decimals and Fractions
Insert Lesson Title Here
Lesson Quiz: Part 1
Write each decimal as a fraction or mixed number.
Write each fraction or mixed number as a decimal. 6 25
____ 6 3 4 __ 3 5 __
2.6 7 __
0.875 8

20. Insert Lesson Title Here
Course 1
4-4
Decimals and Fraction
Insert Lesson Title Here
Lesson Quiz: Part 2
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. 3 4 __ 1 5 __ 1 5 __
, 0.38, 3 4 __ 2 3 __ 2 3 __
0.13, , 0.87