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
Multiplying Fractions & Mixed Numbers
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
Multiplying Fractions & Mixed Numbers
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
Multiplying Fractions & Mixed Numbers
Example #1Example #1: : Find Find 11//22 x x 11//44
14
x 12
Multiplying Fractions & Mixed Numbers
Example #1Example #1: : Find Find 11//22 x x 11//44
14
x 12
x
Multiplying Fractions & Mixed Numbers
Example #1Example #1: : Find Find 11//22 x x 11//44
14
x 1 x 12 x 4
12
=
x =
Multiplying Fractions & Mixed Numbers
Example #1Example #1: : Find Find 11//22 x x 11//44
14
x 1 x 12 x 4
12
=
18
=
x =
Multiplying Fractions & Mixed Numbers
xx x x
Example #2Example #2: : Find Find 22//33 x x 33//44
34
x23
Multiplying Fractions & Mixed Numbers
Example #2Example #2: : Find Find 22//33 x x 33//44
34
x23
x
Multiplying Fractions & Mixed Numbers
Example #2Example #2: : Find Find 22//33 x x 33//44
34
x 2 x 33 x 4
23
=
x =
Multiplying Fractions & Mixed Numbers
Example #2Example #2: : Find Find 22//33 x x 33//44
34
x 2 x 33 x 4
23
=
x =
612
=
Multiplying Fractions & Mixed Numbers
Example #2Example #2: : Find Find 22//33 x x 33//44
34
x 2 x 33 x 4
23
= 12
=
x =
612
=
Multiplying Fractions & Mixed Numbers
xxx
xx
Example #3Example #3: : Find Find 66 x x 11//22
12
x6
Multiplying Fractions & Mixed Numbers
Example #3Example #3: : Find Find 66 x x 11//22
12
x6
x
Multiplying Fractions & Mixed Numbers
Example #3Example #3: : Find Find 66 x x 11//22
12
x6
x
Multiplying Fractions & Mixed Numbers
12
x61
=
Example #3Example #3: : Find Find 66 x x 11//22
12
x 6 x 1
1 x 2
6 =
x
Multiplying Fractions & Mixed Numbers
12
x61
=
Example #3Example #3: : Find Find 66 x x 11//22
12
x 6 x 1
1 x 2
6 =
x =
62
=
Multiplying Fractions & Mixed Numbers
12
x61
=
x x x x x x
Example #3Example #3: : Find Find 66 x x 11//22
12
x 6 x 1
1 x 2
6 = 3=
x =
62
=
Multiplying Fractions & Mixed Numbers
12
x61
=
x x x x x x =
Example #4Example #4: : Find Find 33//88 x x 11 11//44
14
x38 1
Multiplying Fractions & Mixed Numbers
Example #4Example #4: : Find Find 33//88 x x 11 11//44
14
x38 1 5
4x
38
Multiplying Fractions & Mixed Numbers
=
x
+
Example #4Example #4: : Find Find 33//88 x x 11 11//44
14
x 3 x 58 x 4
38
=1 54
x38
Multiplying Fractions & Mixed Numbers
=
x
+
Example #4Example #4: : Find Find 33//88 x x 11 11//44
14
x 3 x 58 x 4
38
=1 54
x38
1532
=
Multiplying Fractions & Mixed Numbers
=
x
+
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x23 4
Multiplying Fractions & Mixed Numbers
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x23 4 =
Multiplying Fractions & Mixed Numbers
245
x23
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x23 4 =
Multiplying Fractions & Mixed Numbers
245
x23
= 2 x 24
3 x 5
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x23 4 =
Multiplying Fractions & Mixed Numbers
245
x23
= 4815
=2 x 24
3 x 5
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x23 4 =
Multiplying Fractions & Mixed Numbers
245
x23
= 4815
= 315
32 x 24
3 x 5
=
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x23
153
4 =
Multiplying Fractions & Mixed Numbers
245
x23
= 4815
= 315
32 x 24
3 x 5
=
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x
2 x 243 x 5
23
153
4 =
=
Multiplying Fractions & Mixed Numbers
245
x23
= 4815
= 315
32 x 24
3 x 5
=
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x
2 x 243 x 5
23
153
4 =
==
Multiplying Fractions & Mixed Numbers
245
x23
= 4815
= 315
32 x 24
3 x 5
=
2 x 3 x 8
3 x 5
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x
2 x 243 x 5
23
153
4 =
==
Multiplying Fractions & Mixed Numbers
245
x23
= 4815
= 315
32 x 24
3 x 5
=
2 x 3 x 8
3 x 5
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x
2 x 243 x 5
23
153
4 =
= 165
=
Multiplying Fractions & Mixed Numbers
245
x23
= 4815
= 315
32 x 24
3 x 5
=
2 x 3 x 8
3 x 5
=
Example #5Example #5: : Find Find 22//33 x x 44 44//55
45
x
2 x 243 x 5
23
153
4 =
= 165
=
Multiplying Fractions & Mixed Numbers
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
Multiplying Fractions & Mixed Numbers
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
25
x13 23 1
2
5
10 3
=
Multiplying Fractions & Mixed Numbers
x
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
25
x13 23 10 x
123 x 5
=12
5
10 3
=
Multiplying Fractions & Mixed Numbers
x
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
25
x13 23 10 x
123 x 5
=12
5
10 3
==
Multiplying Fractions & Mixed Numbers
x 120
15
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
25
x13
=
23 10 x 12
3 x 5
=12
5
10 3
==
8
Multiplying Fractions & Mixed Numbers
x 120
15
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
25
x13
=
23 10 x 12
3 x 5
=12
5
10 3
2 x 5 x 4 x 3
3 x 5
==
8
Multiplying Fractions & Mixed Numbers
x 120
15
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
25
x13
=
23 10 x 12
3 x 5
=12
5
10 3
2 x 5 x 4 x 3
3 x 5
==
8
Multiplying Fractions & Mixed Numbers
x 120
15
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
25
x13
=
23 10 x 12
3 x 5
=12
5
10 3
2 x 5 x 4 x 3
3 x 5
==
8
Multiplying Fractions & Mixed Numbers
x 120
15
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
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
Multiplying Fractions & Mixed Numbers
x 120
15
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
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
Multiplying Fractions & Mixed Numbers
x 120
15
Example #6Example #6: : Find Find 33 11//33 x x 22 22//55
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
Multiplying Fractions & Mixed Numbers
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
Multiplying Fractions & Mixed Numbers
Independent PracticeIndependent Practice::Answers
(1) 3/10 (2) 5/9 (3) 4 2/3
(4) 1/4 (5) 1
Multiplying Fractions & Mixed Numbers
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
Multiplying Fractions & Mixed Numbers
Independent Practice 2Independent Practice 2::Answers
(1) 1 1/4 (2) 1 2/3
(3) 4 9/10 (4) 12 1/2
Multiplying Fractions & Mixed Numbers
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
Multiplying Fractions & Mixed Numbers
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
Multiplying Fractions & Mixed Numbers