Multiplying Fractions & Mixed Numbers. Essential Question: Why is the product of a fraction and mixed number larger than the product of two fractions?

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Presentation transcript:

Multiplying Fractions & Mixed Numbers

Essential Question: Why is the product of a fraction and mixed number larger than the product of two fractions? Common Core Obj./Student Friendly Terms: ( 6.NS.1) Students will be able to multiply fractions and mixed numbers with one and two digit like and unlike denominators with at least 80% accuracy.

Vocabulary Multiplying Fractions & Mixed Numbers Difference Numerator LCD Like Fraction Unlike Fraction Mixed Number LCM Denominator Quotient Sum Product

Real World: Carlos won 4 / 5 of the games for which he was the pitcher last season. If Carlos pitched in 30 games last season, how many of those games did he win? 4 / 5 of 30= 4 / 5 x 30= 4 / 5 x 30 / 1 Multiplying Fractions & Mixed Numbers

RULES for Multiplying Fractions & Mixed Numbers: (1) Change Mixed Numbers to Improper Fractions; (2) Multiply Numerators (Multiply Across); (3) Multiply Denominators (Multiply Across) (4) Simplify/Reduce Multiplying Fractions & Mixed Numbers

Example #1: Find 1 / 2 x 1 / x Multiplying Fractions & Mixed Numbers

Example #1: Find 1 / 2 x 1 / x x Multiplying Fractions & Mixed Numbers

Example #1: Find 1 / 2 x 1 / x 1 x 1 2 x = x = Multiplying Fractions & Mixed Numbers

Example #1: Find 1 / 2 x 1 / x 1 x 1 2 x = = x = Multiplying Fractions & Mixed Numbers x xxx

Example #2: Find 2 / 3 x 3 / x 2323 Multiplying Fractions & Mixed Numbers

Example #2: Find 2 / 3 x 3 / x 2323 x Multiplying Fractions & Mixed Numbers

Example #2: Find 2 / 3 x 3 / x 2 x 3 3 x = x= Multiplying Fractions & Mixed Numbers

Example #2: Find 2 / 3 x 3 / x 2 x 3 3 x = x= 6 12 = Multiplying Fractions & Mixed Numbers

Example #2: Find 2 / 3 x 3 / x 2 x 3 3 x = 1212 = x= 6 12 = Multiplying Fractions & Mixed Numbers x x x xx

Example #3: Find 6 x 1 / x 6 Multiplying Fractions & Mixed Numbers

Example #3: Find 6 x 1 / x 6 x Multiplying Fractions & Mixed Numbers

Example #3: Find 6 x 1 / x 6 x Multiplying Fractions & Mixed Numbers 1212 x 6161 =

Example #3: Find 6 x 1 / x 6 x 1 1 x 2 6 = x Multiplying Fractions & Mixed Numbers 1212 x 6161 =

Example #3: Find 6 x 1 / x 6 x 1 1 x 2 6 = x = 6262 = Multiplying Fractions & Mixed Numbers 1212 x 6161 = xxxxxx

Example #3: Find 6 x 1 / x 6 x 1 1 x 2 6 = 3 = x = 6262 = Multiplying Fractions & Mixed Numbers 1212 x 6161 = xxxxxx =

Example #4: Find 3 / 8 x 1 1 / x Multiplying Fractions & Mixed Numbers

Example #4: Find 3 / 8 x 1 1 / x x 3838 Multiplying Fractions & Mixed Numbers = x +

Example #4: Find 3 / 8 x 1 1 / x 3 x 5 8 x = x 3838 Multiplying Fractions & Mixed Numbers = x +

Example #4: Find 3 / 8 x 1 1 / x 3 x 5 8 x = x = Multiplying Fractions & Mixed Numbers = x +

Example #5: Find 2 / 3 x 4 4 / x Multiplying Fractions & Mixed Numbers

Example #5: Find 2 / 3 x 4 4 / x = Multiplying Fractions & Mixed Numbers 24 5 x 2323

Example #5: Find 2 / 3 x 4 4 / x = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = 2 x 24 3 x 5

Example #5: Find 2 / 3 x 4 4 / x = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = = 2 x 24 3 x 5

Example #5: Find 2 / 3 x 4 4 / x = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = = x 24 3 x 5 =

Example #5: Find 2 / 3 x 4 4 / x = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = = x 24 3 x 5 =

Example #5: Find 2 / 3 x 4 4 / x 2 x 24 3 x = = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = = x 24 3 x 5 =

Example #5: Find 2 / 3 x 4 4 / x 2 x 24 3 x = = = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = = x 24 3 x 5 = 2 x 3 x 8 3 x 5

Example #5: Find 2 / 3 x 4 4 / x 2 x 24 3 x = = = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = = x 24 3 x 5 = 2 x 3 x 8 3 x 5

Example #5: Find 2 / 3 x 4 4 / x 2 x 24 3 x = = 16 5 = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = = x 24 3 x 5 = 2 x 3 x 8 3 x 5 =

Example #5: Find 2 / 3 x 4 4 / x 2 x 24 3 x = = 16 5 = Multiplying Fractions & Mixed Numbers 24 5 x 2323 = = x 24 3 x 5 = 2 x 3 x 8 3 x 5 = =

Example #6: Find 3 1 / 3 x 2 2 / x Multiplying Fractions & Mixed Numbers

Example #6: Find 3 1 / 3 x 2 2 / x = Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x x 12 3 x 5 = = Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x x 12 3 x 5 = = = Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x 1313 = x 12 3 x 5 = = = 8 Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x 1313 = x 12 3 x 5 = x 5 x 4 x 3 3 x 5 = = 8 Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x 1313 = x 12 3 x 5 = x 5 x 4 x 3 3 x 5 = = 8 Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x 1313 = x 12 3 x 5 = x 5 x 4 x 3 3 x 5 = = 8 Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x 2 x = x 12 3 x 5 = x 5 x 4 x 3 3 x 5 = = = 8 Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x 2 x = 8181 = x 12 3 x 5 = x 5 x 4 x 3 3 x 5 = = = 8 Multiplying Fractions & Mixed Numbers x

Example #6: Find 3 1 / 3 x 2 2 / x 2 x = 8181 = x 12 3 x 5 = x 5 x 4 x 3 3 x 5 = = = 8 Multiplying Fractions & Mixed Numbers x = 8

Independent Practice: Simplify (1) 1 / 2 x 3 / 5 (2) 5 / 6 x 2 / 3 (3) 2 / 3 x 7 (4) 1 / 3 x 3 / 4 (5) 5 / 6 x 6 / 5 Multiplying Fractions & Mixed Numbers

Independent Practice: Answers (1) 3 / 10 (2) 5 / 9 (3) 4 2 / 3 (4) 1 / 4 (5) 1 Multiplying Fractions & Mixed Numbers

Independent Practice 2: Simplify (1) 3 / 8 x 3 1 / 3 (2) 2 / 3 x 2 1 / 2 (3) 1 3 / 4 x 2 4 / 5 (4) 2 x 6 1 / 4 Multiplying Fractions & Mixed Numbers

Independent Practice 2: Answers (1) 1 1 / 4 (2) 1 2 / 3 (3) 4 9 / 10 (4) 12 1 / 2 Multiplying Fractions & Mixed Numbers

Real World: The state of Rhode Island has an area of 1,545 square miles. Water makes up about 1 / 3 of the total area of the state. About how many square miles of water does the state of Rhode Island have? 515 miles Multiplying Fractions & Mixed Numbers

Real World: Mr. Williams is baking 4 ½ batches of brownies for the school bake sale. If each batch requires 2 ¾ cups of brownie mix, how much brownie mix will he need? * Since each batch uses 2 ¾ cups, multiply 2 ¾ by 4 ½. 4 ½ x 2 ¾ = 9 / 2 x 11 / 4 = 99 / 8 = 12 3 / 8 Multiplying Fractions & Mixed Numbers

HOMEWORK p.218 #24-36, even