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Page 133 #14-26 ANSWERS Student Learning Goal Chart Lesson Reflections Pre-Algebra Learning Goal Students will understand rational and real numbers. Students will understand rational and real numbers by being able to do the following: • Learn to write rational numbers in equivalent forms (3.1) • Learn to add and subtract decimals and rational numbers with like denominators (3.2) • Learn to add and subtract fractions with unlike denominators (3.5) • Learn to multiply fractions, decimals, and mixed numbers (3.3) 3-3 Multiplying Rational Numbers Today’s Learning Goal Assignment Learn to multiply fractions, decimals, and mixed numbers. Pre-Algebra 3-3 Multiplying Rational Numbers Pre-Algebra HW Page 124 #33-64 all Pre-Algebra 3-3 3-3 Multiplying MultiplyingRational RationalNumbers Numbers Warm Up Problem of the Day Lesson Presentation Pre-Algebra Pre-Algebra 3-3 Multiplying Rational Numbers Warm Up Write each number as an improper fraction. 1. 2 1 3 7 3 2. 1 7 8 15 8 4. 6 2 3 20 3 5. 5 3 8 43 8 Pre-Algebra 3. 3 2 17 5 5 3-3 Multiplying Rational Numbers Problem of the Day The sum of three consecutive integers is 168. What are the three integers? 55, 56, and 57 Pre-Algebra 3-3 Multiplying Rational Numbers Today’s Learning Goal Assignment Learn to multiply fractions, decimals, and mixed numbers. Pre-Algebra 3-3 Multiplying Rational Numbers Kendall invited 36 people to a party. She needs to triple the recipe for a dip, or multiply the amount of each ingredient by 3. Remember that multiplication by a whole number can be written as repeated addition. Repeated addition 1 1 1 3 = + + 4 4 4 4 Multiplication 1 =3•1 = 3 3 4 4 4 Notice that multiplying a fraction by a whole number is the same as multiplying the whole number by just the numerator of the fraction and keeping the same denominator. Pre-Algebra 3-3 Multiplying Rational Numbers RULES FOR MULTIPLYING TWO RATIONAL NUMBERS If the signs of the factors are the same, the product is positive. (+) • (+) = (+) or (–) • (–) = (+) If the signs of the factors are different, the product is negative. (+) • (–) = (–) or (–) • (+) = (–) Pre-Algebra 3-3 Multiplying Rational Numbers Additional Example 1A: Multiplying a Fraction and an Integer Multiply. Write the answer in simplest form. A. –8 6 7 Helpful Hint –8 • 6 7 –48 = Multiply 7 6 = –6 Simplify 7 number, divide: = Pre-Algebra To write 12 5 12 5 as a mixed = 2 R2 2 =2 5 3-3 Multiplying Rational Numbers Additional Example 1B: Multiplying a Fraction and an Integer Multiply. Write the answer in simplest form. B. 2 5 13 =2 = 16 3 32 3 = 10 Pre-Algebra 1 53 5(3) + 1 = 3 Multiply 2 3 Simplify = 16 3 3-3 Multiplying Rational Numbers Try This: Example 1A Multiply. Write the answer in simplest form. A. –3 5 8 –3 • 5 = 8 –15 = 8 7 = –1 8 Pre-Algebra Multiply Simplify 3-3 Multiplying Rational Numbers Try This: Example 1B Multiply. Write the answer in simplest form. B. 4 9 2 5 47 =4 5 2 9(5) + 2 47 9 = = 5 5 5 188 = 5 Multiply = 37 3 5 Simplify Pre-Algebra 3-3 Multiplying Rational Numbers 3 5 • 2 3 A model of is shown. Notice that to multiply fractions, you multiply the numerators and multiply the denominators. 3 5 • • 2 3 = 6 15 = If you place the first rectangle on top of the second, the number of green squares represents the numerator, and the number of total squares represents the denominator. Pre-Algebra 3-3 Multiplying Rational Numbers To simplify the product, rearrange the six green squares into the first two columns. You can see that this is 25 . = 6 15 = 2 5 Helpful Hint A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors. Pre-Algebra 3-3 Multiplying Rational Numbers Additional Example 2A: Multiplying Fractions Multiply. Write the answer in simplest form. A. 1 6 8 7 1(6) = 8(7) Multiply numerators. Multiply denominators. 3 1(6) = 8(7) Look for common factors: 2. 4 = Pre-Algebra 3 28 Simplest form 3-3 Multiplying Rational Numbers Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form. B. 2 9 – 3 2 –2(9) = 3(2) –1 3 –2(9) = 3(2) Multiply numerators. = –3 Simplest form 1 Pre-Algebra Multiply denominators. Look for common factors: 2, 3. 1 3-3 Multiplying Rational Numbers Additional Example 2C: Multiplying Fractions Multiply. Write the answer in simplest form. C. 3 4 7 1 2 43 1 2 7 = 31 1 7 2 Write as an improper fraction. 31(1) = 7(2) Multiply numerators. Multiply denominators. 31 3 = or 2 14 14 31 ÷ 14 = 2 R3 Pre-Algebra 3-3 Multiplying Rational Numbers Try This: Example 2A Multiply. Write the answer in simplest form. A. 3 5 5 8 3(5) = 5(8) Multiply numerators. Multiply denominators. 1 3(5) = 5(8) Look for common factors: 5. 3 = 8 Simplest form 1 Pre-Algebra 3-3 Multiplying Rational Numbers Try This: Example 2B Multiply. Write the answer in simplest form. B. – 7 4 8 7 –7(4) = 8(7) –1 1 –7(4) = 8(7) 2 1 =– 2 Pre-Algebra Multiply numerators. Multiply denominators. Look for common factors: 4, 7. 1 Simplest form 3-3 Multiplying Rational Numbers Try This: Example 2C Multiply. Write the answer in simplest form. C. 2 3 7 5 9 23 5 7 9 = 13 7 5 13(7) = 5(9) = Pre-Algebra 91 1 or 2 45 45 9 Write as an improper fraction. Multiply numerators. Multiply denominators. 91 ÷ 45 = 2 R 1 3-3 Multiplying Rational Numbers Additional Example 3: Multiplying Decimals Multiply. A. 2(–0.51) 2 • (–0.51) = –1.02 Product is negative with 2 decimal places. B. (–0.4)(–3.75) Product is (–0.4) • (–3.75) = 1.500 positive with 3 decimal places. = 1.500 You can drop the zeros after the decimal point. Pre-Algebra 3-3 Multiplying Rational Numbers Try This: Example 3 Multiply. A. 3.1 (0.28) 3.1 • (0.28) = 0.868 Product is positive with 3 decimal places. B. (–0.4)(–2.53) (–0.4) • (–2.53) = 1.012 Product is positive with 3 decimal places. Pre-Algebra 3-3 Multiplying Rational Numbers Additional Example 4A: Evaluating Expressions with Rational Numbers Evaluate –3 A. x = 5 1 x for the value of x. 8 1 –3 8 x 1 = –3 8 (5) Substitute 5 for x. –25 = (5) 8 Write as an improper fraction. –125 = 8 = –15 5 8 Pre-Algebra –125 ÷ 8 = –15 R5 3-3 Multiplying Rational Numbers Additional Example 4B: Evaluating Expressions with Rational Numbers Continued Evaluate –3 B. x = 2 7 1 x for the value of x. 8 1 –3 8 x 1 2 7 = –3 8 = = –25 • 2 1 4 8•7 =– Pre-Algebra 2 7 –25 8 25 28 Substitute 2 7 for x. Write as an improper fraction. Look for common factors: 2. 3-3 Multiplying Rational Numbers Try This: Example 4A 3 Evaluate –5 y for the value of y. 5 A. y = 6 7 –5 3 5 y = –5 = 3 5 6 7 –4–28 • 6 = 5•71 Pre-Algebra 24 5 6 7 for x. Write as an improper fraction. –28 6 7 5 =– Substitute Look for common factors: 7. , or – 4 45 3-3 Multiplying Rational Numbers Try This: Example 4B 3 Evaluate –5 y for the value of y. 5 B. y = 3 3 –5 5 y = –5 35 (3) Substitute 3 for y. Write as an (3) = –28 5 improper fraction. = –84 5 = –16 Pre-Algebra 4 5 –84 ÷ 5 = –16 R4 3-3 Multiplying Rational Numbers Lesson Quiz: Part 1 Multiply. 1 1. 9 7 2 5 2. – 8 3 2 17 5 –12 3. –0.47(2.2) –1.034 1 4. Evaluate 2 2 (x) for x = 4. 5 2 Pre-Algebra 3-3 Multiplying Rational Numbers Lesson Quiz: Part 2 5. Teri is shopping for new shoes. Her mom has agreed to pay half the cost (and all the sales tax). The shoes that Teri likes are normally $30 a pair but are on sale for 13 off. How much money does Teri need to buy the shoes? $10 Pre-Algebra