Chapter 3: Rational and Real Numbers Regular Math Section 3.1: Rational Numbers пЃ¬ A rational number is any number that can be written as a fraction. пЃ¬ Relatively prime numbers have no common factors other than 1. Example 1: Simplifying Fractions пЃ¬ Simplify. 6 9 21 25 пЂ 24 32 пЃ¬ Try these on your ownвЂ¦ 5 10 16 80 пЂ18 29 Example 2: Writing Decimals as Fractions пЃ¬ пЃ¬ Write each decimal as a fraction in simplest form. вЂў 0.5 вЂў -2.37 вЂў 0.8716 Try these on your ownвЂ¦ вЂў вЂў вЂў -0.8 вЂў -4/5 5.37 вЂў 5 37/100 0.622 вЂў 311/500 Example 3: Writing Fractions as Decimals пЃ¬ Write each fraction as a decimal. вЂў вЂў пЃ¬ Try these on your ownвЂ¦ 5/4 вЂў 1.25 вЂў 11/9 вЂў 7/20 1/6 вЂў 0.16666 вЂў 1.22222 вЂў 0.35 Section 3.2: Adding and Subtracting Rational Numbers пЃ¬ Example 1: In the 2001 World Championships 100-meter dash, it took Maurice Green 0.132 seconds to react to the starter pistol. His total race time, including this reaction time, was 9.82 seconds. How long did it take him to run the actual 100 meters? Try this one on your ownвЂ¦ пЃ¬ In August 2001 at the World University Games in Beijing, China, Jimyria Hicks ran the 200-meter dash in 24.08 seconds. Her best time at the U.S. Senior National Meet in June of the same year was 23.35 seconds. How much faster did she run in June? вЂў She ran 0.73 seconds faster in June. Example 2: Using a Number Line to Add Rational Numbers пЃ¬ -0.4 + 1.3 пЃ¬ Try these on your ownвЂ¦ вЂў 0.3 +(-1.2) пЃ¬ -5/8 + (-7/8) вЂў -0.9 вЂў 1/5 + 2/5 вЂў 3/5 Example 3: Adding and Subtracting Fractions with Like Denominators пЃ¬ Add or Subtract. вЂў 6/11 + 9/11 пЃ¬ Try these on your ownвЂ¦ вЂў -2/9 вЂ“ 5/9 вЂў -7/9 вЂў -3/8 вЂ“ 5/8 вЂў 6/7 + (-3/7) вЂў 3/7 Example 4: Evaluating Expressions with Rational Numbers пЃ¬ Try these on your ownвЂ¦ вЂў 12.1 вЂ“ x for x = -0.1 вЂў 12.2 вЂў 7/10 + m for m = 3 1/10 вЂў3 пЃ¬ 4/5 Evaluate each expression for the given value of the variable. вЂў 23.8 + x for x = -41.3 вЂў -1/8 + t for t = 2 5/8 Section 3.3: Multiplying Rational Numbers Example 1: Multiplying a Fraction and an Integer пЃ¬ Multiply. Write each answer in simplest form. вЂў 6 (2/3) вЂў -4 (2 пЃ¬ Try these on your ownвЂ¦ вЂў -8(6/7) вЂў -6 6/7 вЂў 2(5 3/5) 1/3) вЂў 10 2/3 Example 2: Multiplying Fractions пЃ¬ Multiply. Write each answer in simplest form. пЂ1 пѓ¦ пЂ 3 пѓ¶ пѓ§ пѓ· 2пѓЁ 5 пѓё 5 пѓ¦ 12 пѓ¶ пѓ§пЂ пѓ· 12 пѓЁ 5 пѓё 2пѓ¦ 7 пѓ¶ 6 пѓ§ пѓ· 3 пѓЁ 20 пѓё пЃ¬ Try these on your ownвЂ¦ 1пѓ¦6пѓ¶ пѓ§ пѓ· 8пѓЁ7пѓё 2пѓ¦9пѓ¶ пЂ пѓ§ пѓ· 3пѓЁ 2пѓё 3пѓ¦1пѓ¶ 4 пѓ§ пѓ· 7пѓЁ2пѓё Example 3: Multiplying Decimals пЃ¬ Multiply. вЂў -2.5(-8) вЂў -0.07(4.6) пЃ¬ Try these on your ownвЂ¦ вЂў 2(-0.51) вЂў -1.02 вЂў (-0.4)(-3.75) вЂў 1.5 Example 4: Evaluating Expressions with Rational Numbers пЃ¬ Evaluate -5 1/2t for each value of t. вЂў t = -2/3 пЃ¬ Try these one on your ownвЂ¦ вЂў Evaluate -3 1/8x for each value of x. вЂў t=8 вЂў x=5 вЂў -15 5/8 вЂў x = 2/7 вЂў -25/28 Section 3.4: Dividing Rational Numbers пЃ¬ A number and its reciprocal have a product of 1. Example 1: Dividing Fractions пЃ¬ Try these on your ownвЂ¦ 5 1 п‚ё 11 2 3 2 п‚ё2 8 пЃ¬ Divide. Write each answer in simplest forms. 7 2 п‚ё 12 3 1 3 п‚ё4 4 Example 2: Dividing Decimals пЃ¬ Divide. вЂў 2.92 / 0.4 вЂў 7.3 пЃ¬ Try this one on your ownвЂ¦ вЂў 0.384 / 0.24 вЂў 1.6 Example 3: Evaluating Expressions with Fractions and Decimals пЃ¬ Evaluate each expression for the given value of the variable. вЂў 7.2/n for n = 0.24 вЂў M / (3/8) for M = 7 1/2 Try these on your ownвЂ¦ пЃ¬ Evaluate each expression for the given value of the variable. вЂў 5.25/n for n = 0.15 вЂў 35 вЂў K / (4/5) for K = 5 вЂў6 1/4 Example 4: Problem Solving пЃ¬ You pour 2/3 cup of sports drink into a glass. The serving size is 6 ounces, or Вѕ cup. How many servings will you consume? How many calories will you consume? Calories 50 Total Fat 0g 0% Sodium 110mg 5% Potassium 30mg 1% Total Carbs 0g 5% Sugar 14g 5% Protein 0g 0% Try this one on your ownвЂ¦ пЃ¬ A cookie recipe calls for ВЅ cup of oats. You have Вѕ cup of oats. How many batches of the cookies can you bake? вЂў You can bake 1 ВЅ batches of the cookies. Section 3.5: Adding and Subtracting with Unlike Denominators пЃ¬ Add or subtract. вЂў 2/3 + 1/5 пЃ¬ Try these on your ownвЂ¦ вЂў 1/8 + 2/7 вЂў 23/56 вЂў 3 2/5 + (-3 ВЅ) вЂў 1 1/6 + 5/8 вЂў1 19/24 Example 2: Evaluating Expressions with Rational Numbers пЃ¬ Evaluate n вЂ“ 11/16 for n = -1/3. пЃ¬ Try this one on your ownвЂ¦ вЂў Evaluate t вЂ“ 4/5 for t = 5/6. вЂў 1/30 Example 3: Consumer Application пЃ¬ A folkloric dance skirt pattern calls for 2 2/5 yards of 45-inch-wide material to make the ruffle and 9 1/3 yards to make the skirt. The material for the skirt and ruffle will be cut from a bolt that is 15 ВЅ yards long. How many yards will be left on the bolt? Try this one on your ownвЂ¦ пЃ¬ Two dancers are making necklaces from ribbon for their costumes. They need pieces measuring 13 Вѕ inches and 12 7/8 inches How much ribbon will be left over after the pieces are cut from 36inch length? вЂў There will be 9 3/8 inches left. Section 3.6: Solving Equations with Rational Numbers пЃ¬ Example 1: Solving Equations with Decimals вЂў Solve. вЂў y вЂ“ 12.5 = 17 вЂў -2.7p = 10.8 вЂў t/7.5 = 4 Try these on your ownвЂ¦ пЃ¬ Solve. вЂў M + 4.6 = 9 вЂў M = 4.4 вЂў 8.2p = -32.8 вЂў p = -4 вЂў x/1.2 = 15 вЂў x = 18 Example 2: Solving Equations with Fractions пЃ¬ Solve. вЂў x + 1/5 = -2/5 пЃ¬ Try these on your ownвЂ¦ вЂў n + 2/7 = -3/7 вЂў n = -5/7 вЂў x вЂ“ Вј = 3/8 вЂў y вЂ“ 1/6 = 2/3 вЂў y = 5/6 вЂў 5/6(x) = 5/8 вЂў 3/5(w) = 3/16 вЂў x = 3/4 Example 3: Solving Word Problems Using Equations пЃ¬ Try this one on your ownвЂ¦ вЂў Mr. Rios wants to prepare a casserole that requires 2 ВЅ cups of milk. If he makes the casserole, he will have only Вѕ cup of milk left for his breakfast cereal. How much milk does Mr. Rios have? вЂў Mr. Rios has 3 Вј cups of milk. пЃ¬ In 1668 the Hope diamond was reduced from its original weight by 45 1/6 carats to a diamond weighing 67 1/8 carat. How many carats was the original diamond? Section 3.7: Solving Inequalities with Rational Numbers пЃ¬ Solving Inequalities with Decimals пЃ¬ Try these on your ownвЂ¦ 0.5x п‚і 0.5 0.4 x п‚Ј 0.8 t пЂ 7.5 пЂѕ 30 y пЂ 3.8 пЂј 11 Example 2: Solving Inequalities with Fractions пЃ¬ Solve. 1 пЂј1 2 xпЂ« пЂ3 пЃ¬ 1 y п‚і 10 3 Try these on your ownвЂ¦ xпЂ« 2 пЂѕ 2 3 пЂ2 1 nп‚Ј9 4 Example 3: Problem Solving Application пЃ¬ With first-class mail, there is an extra cost in any of these cases: вЂў The length is greater than 11 ВЅ inches. вЂў The height is greater than 6 1/8 inches. вЂў The thickness is greater than Вј inch. вЂў The length divided by the height is less than 1.3 or greater than 2.5 пЃ¬ The height of an envelope is 4.5 inches. What are the minimum and maximum lengths to avoid an extra charge? Try this one on your ownвЂ¦ пЃ¬ With first-class mail, there is an extra cost in any of these cases: вЂў вЂў вЂў вЂў пЃ¬ The length is greater than 11 ВЅ inches. The height is greater than 6 1/8 inches. The thickness is greater than Вј inch. The length divided by the height is less than 1.3 or greater than 2.5 The height of an envelope is 3.8 inches. What are the minimum and maximum lengths to avoid an extra charge. вЂў The length of the envelope must be between 4.94 inches and 9.5 inches to avoid extra charges. Section 3.8: Squares and Square Roots пЃ¬ The principal square root is the nonnegative square root. пЃ¬ A perfect square is a number that has integers as its square roots. Example 1: Finding the Positive and Negative Square Roots of a Number вЂў Find the two square roots of each number. вЂў 64 вЂў1 вЂў 121 Try these on your ownвЂ¦ пЃ¬ Find the two square roots of each number. вЂў 49 вЂў + or - 7 вЂў 100 вЂў + or - 10 вЂў 225 вЂў + or - 15 Example 2: Computer Application пЃ¬ The square computer icon (pg. 147) contains 676 pixels. How many pixels tall is the icon? пЃ¬ Try this one on your ownвЂ¦ вЂў A square window has an area of 169 square inches. How wide is the window? вЂў The window is 13 inches wide. Example 3: Evaluating Expressions Involving Square Roots пЃ¬ Evaluate each expression. 2 16 пЂ« 5 9 пЂ« 16 пЂ« 7 пЃ¬ Try these on your ownвЂ¦ 3 36 пЂ« 7 21пЂ 5 пЂ« 9 Section 3.9: Finding Square Roots пЃ¬ Estimating Square Roots of NumbersвЂ¦ 30 пЂ 150 пЃ¬ Try these on your ownвЂ¦ 55 пЂ 90 Example 2: Problem Solving Application пЃ¬ You want to install a square skylight that has an area of 300 square inches. Calculate the length of each side and the length of trim you will need, to the nearest tenth of an inch. Try this one on your ownвЂ¦ пЃ¬ You want to sew a fringe on a square tablecloth with an area of 500 square inches. Calculate the length of each side of the tablecloth and the length of fringe you will need to the nearest tenth of an inch. вЂў The length of each side of the table is about вЂў 22.4 inches. You will need about 89.6 inches of fringe. Example 3: Using a Calculator to Estimate the Value of a Square Root пЃ¬ Use a calculator to 300 find . Round to the nearest tenth. пЃ¬ Try this one on your ownвЂ¦ вЂў Use a calculator to find 500 . Round to the nearest tenth. вЂў 22.4 Section 3.10: The Real Numbers пЃ¬ Irrational numbers can only be written as decimals that do not terminate or repeat. пЃ¬ The set of real numbers consists of the set of rational numbers and the set of irrational numbers. пЃ¬ The Density Property of real numbers states that between any two real numbers is another real number. Example 1: Classifying Real Numbers пЃ¬ Write all the names that apply to each number. пЃ¬ Try these on your ownвЂ¦ 5 3 пЂ 56.85 9 3 пЂ 12.75 16 2 Example 2: Determine the Classification of All Numbers пЃ¬ Try these on your ownвЂ¦ 15 0 3 пЃ¬ State if the number is rational, irrational, or not a real 10 number. 3 0 пЂ9 4 9 1 4 пЂ 17 Example 3: Applying the Density Property of Real Numbers пЃ¬ Find a real number between 2 1/3 and 2 2/3. пЃ¬ Try this one on your ownвЂ¦ вЂў Find a real number between 3 2/5 and 3 3/5. вЂў3ВЅ

1/--страниц