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

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

3. Course 2 3-7 Fractions and Decimals You can show –5 and 15 on a number line marked off by 5’s. –10 –5 0 5 10 15 20 You can show –3 and 4 on a number line marked off by 1’s.

4. 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. –1.25 –1.250 –1.00 –1.000 –0.75 –0.750 –0.50 –0.500 –0.25 –0.250 0.25 0.250 0 0.50 0.500 0.75 0.750 1.00 1.000 1.25 1.250 5454 – 4 – 2 – –1–1 3 4 – 2 4 – 1 2 – 1 4 – 0 4 0 2 0 1 4 2 4 1 2 3 4 2 0 5 4

5. Graph each number on a number line. Additional Example 1: Graphing Numbers on a Number Line Course 2 3-7 Fractions and Decimals A. 2 1212 –5 –4–3–2–1 01 2 3 4 5 2 is between 2 and 3. 1212 B. –1.4 1 2 3 4 5 –5–4–3 –2–1 0 –1.4 is between –1 and –2. 2 1212 –1.4

6. Try This: Example 1 Insert Lesson Title Here Course 2 3-7 Fractions and Decimals Graph each number on a number line. A. 1414 1 2 3 4 5 –5 –4–3–2–1 0 is between 0 and 1. 1414 B. –2.5 1 2 3 4 5 –5 –4–3–2–1 0 –2.5 is between –2 and –3. 1414 –2.5

7. 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 = 15 1 –15 = – 15 1 0.75 = 3434 –1.25 = – 5454

8. 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! 1212

9. Show that each number is a rational number by writing it as a fraction. Additional Example 2: Writing Rational Numbers as Fractions Course 2 3-7 Fractions and Decimals A. –1.25 –1.25 = – 5454 B. 0.75 0.75 = 3434 C. –1.00 –1.00 = 1111 –

10. Try This: Example 2 Insert Lesson Title Here Course 2 3-7 Fractions and Decimals Show that each number is a rational number by writing it as a fraction. A. –1.50 –1.50 = – 3232 B. 0.875 0.875 = 7878 C. –4.00 –4.00 = – 4444

11. Additional Example 3: Earth Science Application Course 2 3-7 Fractions and Decimals 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 –2 –1 0 1 2 3 4 5 6 Garibaldi St. Helens Charleston Vancouver Portland Corrections to Astoria OR times

12. Additional Example 3A: Earth Science Application Course 2 3-7 Fractions and Decimals A. Use a decimal to estimate how much later in minutes high tide occurred in Vancouver. High Tide Time Corrections –2 –1 0 1 2 3 4 5 6 Garibaldi St. Helens Charleston Vancouver Portland Corrections to Astoria OR times 5.75 minutes later The bar is about three- fourths of the way between 5 and 6

13. Course 2 3-7 Fractions and Decimals B. Use a fraction to estimate how much earlier in minutes high tide occurred in Charleston. High Tide Time Corrections –2 –1 0 1 2 3 4 5 6 Corrections to Astoria OR times 1 minutes earlier The bar is about one- fourth of the way between –1 and –2. 1414 Garibaldi St. Helens Charleston Vancouver Portland Additional Example 3B: Earth Science Application

14. Course 2 3-7 Fractions and Decimals 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 –2 –1 0 1 2 3 4 5 6 Corrections to Astoria OR times Garibaldi St. Helens Charleston Vancouver Portland 3 –(–1 ) = 4 1212 1414 3434 Additional Example 3C: Earth Science Application The value for St. Helens is about 3, or 3.5, and the value for Charleston is about –1, or –1.25. 1212 1414

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

16. Try This: Example 3B Insert Lesson Title Here 1.5 inches above average The bar is about a one and midway between 1 and 2. Course 2 3-7 Fractions and Decimals B. Use a fraction to estimate how much more snow fell in March than the average. Monthly Snowfall (Above and Below Average) Dec Jan Feb Mar 0 1 3 4 –1 –2 –3 2 5 –4 –5 Inches

17. Try This: Example 3C Insert Lesson Title Here Course 2 3-7 Fractions and Decimals 1 2 January was 0.5 inches below average and February was 3 inches below average. C. Use a fraction or a decimal to estimate how much less snow fell in January and February than the average. + (–3) = –3 1 2 – Monthly Snowfall (Above and Below Average) Dec Jan Feb Mar 0 1 3 4 –1 –2 –3 2 5 –4 –5 Inches

18. Lesson Quiz Graph each number on a number line. Insert Lesson Title Here Course 2 3-7 Fractions and Decimals 1. –2, 1, –3, 1212 3434 1212 Show that each number is a rational number by writing it as a fraction 2. 0.5 3. 1 4. 0.25 1212 5454 1414 1414 –4 –3 –2–1 0 1 2 3 4 3434 –3 –2 1212 1212 1