Multiplying Fractions & Mixed Numbers. Essential Question: Why is the product of a fraction and...

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Multiplying Multiplying Fractions & Fractions &

Mixed NumbersMixed Numbers

Multiplying Fractions & Mixed Numbers

Essential QuestionEssential Question::Why is the product of a Why is the product of a fraction and mixed number fraction and mixed number larger than the product of larger than the product of two fractions?two fractions? Common Core Obj./Student Friendly Common Core Obj./Student Friendly TermsTerms:: (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.

VocabularyVocabulary


DifferenceNumerato

r

LCD

Like Fraction

Unlike Fraction

Mixed Number

LCM

Denominator

Quotient

Sum

Product

Real WorldReal 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


RULES for Multiplying Fractions RULES for Multiplying Fractions & Mixed Numbers& Mixed Numbers::

(1) Change Mixed Numbers to (1) Change Mixed Numbers to Improper Improper Fractions;Fractions;

(2) Multiply Numerators (Multiply (2) Multiply Numerators (Multiply Across);Across);

(3) Multiply Denominators (Multiply (3) Multiply Denominators (Multiply Across)Across)

(4) Simplify/Reduce(4) Simplify/Reduce


Example #1Example #1: : Find Find 11//22 x x 11//44

14

x 12



14

x 12

x



14

x 1 x 12 x 4

12

=

x =



14

x 1 x 12 x 4

12

=

18

=

x =


xx x x


34

x23



34

x23

x



34

x 2 x 33 x 4

23

=

x =



34

x 2 x 33 x 4

23

=

x =

612

=



34

x 2 x 33 x 4

23

= 12

=

x =

612

=


xxx

xx

Example #3Example #3: : Find Find 66 x x 11//22

12

x6



12

x6

x



12

x6

x


12

x61

=


12

x 6 x 1

1 x 2

6 =

x


12

x61

=


12

x 6 x 1

1 x 2

6 =

x =

62

=


12

x61

=

x x x x x x


12

x 6 x 1

1 x 2

6 = 3=

x =

62

=


12

x61

=

x x x x x x =

Example #4Example #4: : Find Find 33//88 x x 11 11//44

14

x38 1



14

x38 1 5

4x

38


=

x

+


14

x 3 x 58 x 4

38

=1 54

x38


=

x

+


14

x 3 x 58 x 4

38

=1 54

x38

1532

=


=

x

+


45

x23 4



45

x23 4 =


245

x23


45

x23 4 =


245

x23

= 2 x 24

3 x 5


45

x23 4 =


245

x23

= 4815

=2 x 24

3 x 5


45

x23 4 =


245

x23

= 4815

= 315

32 x 24

3 x 5

=


45

x23

153

4 =


245

x23

= 4815

= 315

32 x 24

3 x 5

=


45

x

2 x 243 x 5

23

153

4 =

=


245

x23

= 4815

= 315

32 x 24

3 x 5

=


45

x

2 x 243 x 5

23

153

4 =

==


245

x23

= 4815

= 315

32 x 24

3 x 5

=

2 x 3 x 8

3 x 5


45

x

2 x 243 x 5

23

153

4 =

==


245

x23

= 4815

= 315

32 x 24

3 x 5

=

2 x 3 x 8

3 x 5


45

x

2 x 243 x 5

23

153

4 =

= 165

=


245

x23

= 4815

= 315

32 x 24

3 x 5

=

2 x 3 x 8

3 x 5

=


45

x

2 x 243 x 5

23

153

4 =

= 165

=


245

x23

= 4815

= 315

32 x 24

3 x 5

=

2 x 3 x 8

3 x 5

= 153=

Example #6Example #6: : Find Find 33 11//33 x x 22 22//55

25

x13 23



25

x13 23 1

2

5

10 3

=


x


25

x13 23 10 x

123 x 5

=12

5

10 3

=


x


25

x13 23 10 x

123 x 5

=12

5

10 3

==


x 120

15


25

x13

=

23 10 x 12

3 x 5

=12

5

10 3

==

8


x 120

15


25

x13

=

23 10 x 12

3 x 5

=12

5

10 3

2 x 5 x 4 x 3

3 x 5

==

8


x 120

15


25

x13

=

23 10 x 12

3 x 5

=12

5

10 3

2 x 5 x 4 x 3

3 x 5

==

8


x 120

15


25

x13

=

23 10 x 12

3 x 5

=12

5

10 3

2 x 5 x 4 x 3

3 x 5

==

8


x 120

15


25

x

2 x 41

13

=

23 10 x 12

3 x 5

=12

5

10 3

2 x 5 x 4 x 3

3 x 5

=

=

=

8


x 120

15


25

x

2 x 41

13

=

81

=

23 10 x 12

3 x 5

=12

5

10 3

2 x 5 x 4 x 3

3 x 5

=

=

=

8


x 120

15


25

x

2 x 41

13

=

81

=

23 10 x 12

3 x 5

=12

5

10 3

2 x 5 x 4 x 3

3 x 5

=

=

=

8


x 120

15

=8

Independent PracticeIndependent 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


Independent PracticeIndependent Practice::Answers

(1) 3/10 (2) 5/9 (3) 4 2/3

(4) 1/4 (5) 1


Independent Practice 2Independent 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


Independent Practice 2Independent Practice 2::Answers

(1) 1 1/4 (2) 1 2/3

(3) 4 9/10 (4) 12 1/2


Real WorldReal 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


Real WorldReal 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


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Multiplying Fractions & Mixed Numbers. Essential Question: Why is the product of a fraction and...

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