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

Fractions and Decimals Course 2 3-7 Fractions and Decimals Warm Up Divide. 1. 63 ÷ 9 2. 27 ÷ 3 3. 102 ÷ 3 4. 225 ÷ 25 7 9 34 9

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

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

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

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. –10 –5 0 5 10 15 20 You can show –3 and 4 on a number line marked off by 1’s.

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

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 1 2 3 4 5 2 is between 2 and 3. 1 2 B. –1.4 –1.4 1 2 3 4 5 –5–4–3 –2–1 0 –1.4 is between –1 and –2.

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 1 2 3 4 5 –5 –4–3–2–1 0 is between 0 and 1. 1 4 B. –2.5 –2.5 1 2 3 4 5 –5 –4–3–2–1 0 –2.5 is between –2 and –3.

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 = –

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

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 = –

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. 0.875 7 8 0.875 = C. –4.00 4 –4.00 = –

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

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

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

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

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

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

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

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 1 2 3 4 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 4. 0.25 1 2 1 4 5 4 1 4