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Page 190 #1-9 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 9 Math Learning Goal Students will understand number theory and fractions. Students will understand number theory and fractions by being able to do the following: • • • • • • • • Learn to use divisibility rules (4-1) Learn to write prime factorizations of composite numbers (4-2) Learn to find the greatest common factor (GCF) of a set of numbers (4-3) Learn to convert between decimals and fractions (4-4) Learn to write equivalent fractions (4-5) Learn to use pictures and number lines to compare and order fractions (4-6) Learn to convert between mixed numbers and improper fractions (4-7) Learn to add and subtract fractions with like denominators (4-8) • Learn to multiply fractions by whole numbers (4-9) 4-9 Multiplying Fractions by Whole Numbers Today’s Learning Goal Assignment Learn to multiply fractions by whole numbers. Course 1 4-9 Multiplying Fractions by Whole Numbers th 6 Grade Math HW Page 194 #1-13 & Finish Chop Chop Quiz! Course 1 Multiplying Fractions by 4-9 Whole Numbers Warm Up Problem of the Day Lesson Presentation Course 1 4-9 Multiplying Fractions by Whole Numbers Warm Up Multiply. 1. 15 2 30 2. 12 8 96 3. 9 16 144 4. 6 11 66 5. 8 15 120 Course 1 4-9 Multiplying Fractions by Whole Numbers Problem of the Day The length of three dowels are 13 inches, 27 inches, and 19 inches. How can you use the three dowels to mark off a length of 5 inches? 13 + 19 – 27 Course 1 4-9 Multiplying Fractions by Whole Numbers Today’s Learning Goal Assignment Learn to multiply fractions by whole numbers. Course 1 4-9 Multiplying Fractions by Whole Numbers Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 • 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method. + + 1 = __ 3 3 • __ 4 4 Course 1 = 4-9 Multiplying Fractions by Whole Numbers There is another way to multiply with fractions. Remember that a whole number can be written as an improper fraction with 1 in the denominator. 3 . So 3 = __ 1 3 1 3•1 3 __ __ ______ __ • = = 1 4 1•4 4 Course 1 Multiply numerators Multiply denominators 4-9 Multiplying Fractions by Whole Numbers Additional Example 1A: Multiplying Fractions and Whole Numbers Multiply. Write the answer in simplest form. A. 7 • 1 __ 9 7 1 7•1 __ __ ______ • = 1 9 1•9 = Course 1 7 __ 9 Write 7 as a fraction. Multiply numerators and denominators. 4-9 Multiplying Fractions by Whole Numbers Additional Example 1B: Multiplying Fractions and Whole Numbers Multiply. Write the answer in simplest form. B. 6 • 1 __ 8 6 1 6•1 __ __ ______ • = 1 8 1•8 Course 1 = 6 __ 8 = 3 __ 4 Write 6 as a fraction. Multiply numerators and denominators. Write your answer in simplest form. 4-9 Multiplying Fractions by Whole Numbers Additional Example 1C: Multiplying Fractions and Whole Numbers Multiply. Write the answer in simplest form. C. 8 • 2 __ 3 8 2 8•2 __ __ ______ • = 1 3 1•3 = Course 1 16 ___ or 3 Write 8 as a fraction. Multiply numerators and denominators. 5 1 __ 3 4-9 Multiplying Fractions by Whole Numbers Try This: Example 1A Multiply. Write the answer in simplest form. A. 4 1 • __ 5 4 1 4•1 __ __ ______ • = 1 5 1•5 = Course 1 4 __ 5 Write 4 as a fraction. Multiply numerators and denominators. 4-9 Multiplying Fractions by Whole Numbers Try This: Example 1B Multiply. Write the answer in simplest form. B. Course 1 1 __ 6 3 1 3•1 __ __ ______ • = 1 6 1•6 3 • = 3 __ 6 = 1 __ 2 Write 3 as a fraction. Multiply numerators and denominators. Write your answer in simplest form. 4-9 Multiplying Fractions by Whole Numbers Try This: Example 1C Multiply. Write the answer in simplest form. C. 9 3 • __ 4 9 3 9•3 __ __ ______ • = 1 4 1•4 = Course 1 27 ___ or 4 Write 9 as a fraction. Multiply numerators and denominators. 6 3 __ 4 4-9 Multiplying Fractions by Whole Numbers Additional Example 2A: Evaluating Fraction Expression Evaluate 4x for the value of x. Write the answer in simplest form. A. x = 1 ___ 10 4x 1 4 • ___ 10 4 4 1 __ • ___ = ___ 1 10 10 2 __ = 5 Course 1 Write the expression. Substitute 1 ___ for x. 10 Multiply. Write your answer in simplest form. 4-9 Multiplying Fractions by Whole Numbers Additional Example 2B: Evaluating Fraction Expression Evaluate 4x for the value of x. Write the answer in simplest form. B. x 3 = __ 8 Write the expression. 4x 3 4 • __ 8 4 __ 3 __ • 1 8 Course 1 Substitute 3 __ for x. 8 12 ___ Multiply. 8 3 1 __ __ = Write your answer in simplest form. ,or 1 2 2 = 4-9 Multiplying Fractions by Whole Numbers Try This: Example 2A Evaluate 3x for the value of x. Write the answer in simplest form. A. x 1 9 = __ Write the expression. 3x 1 3 • __ 9 3 __ 1 __ • 1 9 Course 1 Substitute 3 __ 9 1 __ = 3 = 1 __ for x. 9 Multiply. Write your answer in simplest form. 4-9 Multiplying Fractions by Whole Numbers Try This: Example 2B Evaluate 3x for the value of x. Write the answer in simplest form. B. 4 __ x= 7 Write the expression. 3x 4 3 • __ 7 3 __ 4 __ • 1 7 Course 1 Substitute 12 = ___ 7 5 __ = 1 7 4 __ for x. 7 Multiply. Write your answer in simplest form. 4-9 Multiplying Fractions by Whole Numbers Sometimes the denominator of an improper fraction will divide evenly into the numerator. When this happens, the improper fraction is equivalent to a whole number, not a mixed number. 12 ___ =4 3 This makes sense if you remember that the fraction bar means “divided by”. Course 1 4-9 Multiplying Fractions by Whole Numbers Additional Example 3: Application There are 25 students in the music club. Of those 3 __ students, 5 are also in the band. How many music club students are in the band? 3 of 25, multiply. To find __ 5 3 ___ 25 3 __ __ • • 25 = 5 1 5 = 75 ___ 5 = 15 There are 15 music club students in the band. Course 1 4-9 Multiplying Fractions by Whole Numbers Try This: Example 3 There are 18 saltwater fish in the aquarium. Of those 2 __ fish, 3 are blue. How many fish in the aquarium are blue? 2 __ of 18, multiply. 3 2 ___ 18 2 __ __ • • 18 = 3 1 3 To find = 36 ___ 3 = 12 There are 12 blue fish in the aquarium. Course 1 4-9 Multiplying Fractions by Whole Numbers Lesson Quiz Multiply. Write each answer in simplest form. 2 1 __ 3 1. 10 • __ 2. 6 • __ 4 5 10 5 Evaluate 6x for each value of x. Write your answer in simplest form. 1 __ 3 1 __ 3. x = __ , or 1 4 2 2 5 4. x = __ 6 5 5. Alicia spent 15 minutes making a pizza. Of those 1 were spent rolling out the crust. How many minutes __ 3 minutes did Alicia spend rolling out the crust? 5 minutes Course 1 Page 194 #1-13 ANSWERS