1. Fractions and Decimals
3-7
Fractions and Decimals
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Fractions and Decimals
Course 2
3-7
Fractions and Decimals
Warm Up
Divide.
1. 63 ÷ 9
2. 27 ÷ 3
÷ 3
÷ 25 7 9 34 9

3. Fractions and Decimals
Course 2
3-7
Fractions and Decimals
Problem of the Day
What three numbers between 0 and 10 can be multiplied together to make a product that matches their sum.
1, 2, and 3

4. Fractions and Decimals
Course 2
3-7
Fractions and Decimals
Learn to identify rational numbers and place them on a number line.

5. Insert Lesson Title Here
Course 2
3-7
Fractions and Decimals
Insert Lesson Title Here
Vocabulary
rational number

6. Fractions and Decimals
Course 2
3-7
Fractions and Decimals
You can show –5 and 15 on a number line marked off by 5’s.
– –
You can show –3 and 4 on a number line
marked off by 1’s.

7. Fractions and Decimals
Course 2
3-7
Fractions and Decimals
A number line can have as much detail as you want. The number line below shows that you can write numbers in many different ways. –1 1 2 1 2 2 1 2 2 – – 5 4 4 3 4 2 4 1 4 4 1 4 2 4 3 4 4 5 4 – – – – –
–1.25
–1.250
–1.00
–1.000
–0.75
–0.750
–0.50
–0.500
–0.25
–0.250
0.25
0.250
0.50
0.500
0.75
0.750
1.00
1.000
1.25
1.250

8. Additional Example 1: Graphing Numbers on a Number Line
Course 2
3-7
Fractions and Decimals
Additional Example 1: Graphing Numbers on a Number Line
Graph each number on a number line. 1 2
A. 2 2 1
–5 –4–3–2–1 0
2 is between 2 and 3. 1 2
B. –1.4
–1.4
–5–4–3 –2–1 0
–1.4 is between –1 and –2.

9. Insert Lesson Title Here
Course 2
3-7
Fractions and Decimals
Insert Lesson Title Here
Try This: Example 1
Graph each number on a number line. 1 4 A. 1 4
–5 –4–3–2–1 0
is between 0 and 1. 1 4
B. –2.5
–2.5
–5 –4–3–2–1 0
–2.5 is between –2 and –3.

10. Fractions and Decimals
Course 2
3-7
Fractions and Decimals
The numbers shown on the number lines in Example 1 are called rational numbers. Rational numbers are numbers that can be written as fractions, with integers for numerators and denominators. Integers and certain decimals are rational numbers because they can be written as fractions. 15 1 15 1 3 4 5 4
15 =
–5 = –
0.75 =
–1.25 = –

11. Fractions and Decimals
Course 2
3-7
Fractions and Decimals
The top number in a fraction is called the numerator. The bottom is called the denominator. So in the fraction , the numerator is 1 and the denominator is 2.
Remember! 1 2

12. Additional Example 2: Writing Rational Numbers as Fractions
Course 2
3-7
Fractions and Decimals
Additional Example 2: Writing Rational Numbers as Fractions
Show that each number is a rational number by writing it as a fraction.
A. –1.25 5 4
–1.25 = –
B. 0.75 3 4
0.75 =
C. –1.00 1
–1.00 = –

13. Insert Lesson Title Here
Course 2
3-7
Fractions and Decimals
Insert Lesson Title Here
Try This: Example 2
Show that each number is a rational number by writing it as a fraction.
A. –1.50 3 2
–1.50 = – B 7 8
0.875 =
C. –4.00 4
–4.00 = –

14. Additional Example 3: Earth Science Application
Course 2
3-7
Fractions and Decimals
Additional Example 3: Earth Science Application
High tide in Astoria, Oregon, on July 1 was 11:31 A.M. The graph shows how much earlier or later in minutes that high tide occurred in nearby towns.
High Tide
Time Corrections
Corrections to Astoria OR times 6 5 4 3 2 1 –1 –2
Garibaldi
St. Helens
Charleston
Vancouver
Portland

15. Additional Example 3A: Earth Science Application
Course 2
3-7
Fractions and Decimals
Additional Example 3A: Earth Science Application
A. Use a decimal to estimate how much later in minutes high tide occurred in Vancouver.
High Tide
Time Corrections
Corrections to Astoria OR times 6 5 4 3 2
The bar is about three-
fourths of the way
between 5 and 6 1 –1 –2
5.75 minutes later
Garibaldi
St. Helens
Charleston
Vancouver
Portland

16. Additional Example 3B: Earth Science Application
Course 2
3-7
Fractions and Decimals
Additional Example 3B: Earth Science Application
B. Use a fraction to estimate how much earlier in minutes high tide occurred in Charleston.
High Tide
Time Corrections
Corrections to Astoria OR times 6 5 4 3 2 1
The bar is about one-
fourth of the way
between –1 and –2. –1 –2 1 4
1 minutes earlier
Garibaldi
St. Helens
Charleston
Vancouver
Portland

17. Additional Example 3C: Earth Science Application
Course 2
3-7
Fractions and Decimals
Additional Example 3C: Earth Science Application
C. Use a fraction and a decimal to estimate the difference between the value for St. Helens and the value for Charleston represented on the graph.
High Tide
Time Corrections
Corrections to Astoria OR times 6 5 4 3
The value for St. Helens is about 3 , or 3.5, and the value for Charleston is about –1 , or –1.25. 1 2 4 2 1 –1 –2
3 –(–1 ) = 4 1 2 4 3
Garibaldi
St. Helens
Charleston
Vancouver
Portland

18. Monthly Snowfall (Above
Course 2
3-7
Fractions and Decimals
Insert Lesson Title Here
Try This: Example 3A
A. Use a decimal to
estimate how much
below average the
snowfall was in
January.
Monthly Snowfall (Above
and Below Average) 5 4 3 2
The bar is about midway between 0 and 1. 1
Inches –1 –2
0.5 inches below average –3 –4 –5
Dec Jan Feb Mar

19. Monthly Snowfall (Above
Course 2
3-7
Fractions and Decimals
Insert Lesson Title Here
Try This: Example 3B
B. Use a fraction to estimate how much more snow fell in March than the average.
Monthly Snowfall (Above
and Below Average) 5 4 3 2 1
The bar is about a
one and midway between
1 and 2.
Inches –1 –2 –3 –4
1.5 inches above average –5
Dec Jan Feb Mar

20. Monthly Snowfall (Above
Course 2
3-7
Fractions and Decimals
Insert Lesson Title Here
Try This: Example 3C
C. Use a fraction or a decimal to estimate how much less snow fell in January and February than the average.
Monthly Snowfall (Above
and Below Average) 5 4 3 2 1
January was 0.5 inches below average and February was 3 inches below average.
Inches –1 –2 –3 –4 1 2 1 2 –5 –
+ (–3) = –3
Dec Jan Feb Mar

21. Fractions and Decimals Insert Lesson Title Here
Course 2
3-7
Fractions and Decimals
Insert Lesson Title Here
Lesson Quiz
Graph each number on a number line. 1 2
–4 –3 –2–1 0 3 4 –3 –2 1 2 3 4 1 2
1. –2, 1 , –3 ,
Show that each number is a rational number by writing it as a fraction
2. 0.5
3. 1 1 2 1 4 5 4 1 4