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1.12 Fractions: multiplication of mixed numerals

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses multiplication of fractions. By the end of the module students should be able to understand the concept of multiplication of fractions, multiply one fraction by another, multiply mixed numbers and find powers and roots of various fractions.

Section overview

  • Multiplication of Mixed Numbers

Multiplication of mixed numbers

Multiplying mixed numbers

To perform a multiplication in which there are mixed numbers, it is convenient to first convert each mixed number to an improper fraction, then multiply.

Sample set c

Perform the following multiplications. Convert improper fractions to mixed numbers.

1 1 8 ⋅ 4 2 3 size 12{1 { {1} over {8} } cdot 4 { {2} over {3} } } {}

Convert each mixed number to an improper fraction.

1 1 8 = 8 ⋅ 1 + 1 8 = 9 8 size 12{1 { {1} over {8} } = { {8 cdot 1+1} over {8} } = { {9} over {8} } } {}

4 2 3 = 4 ⋅ 3 + 2 3 = 14 3 size 12{4 { {2} over {3} } = { {4 cdot 3+2} over {3} } = { {"14"} over {3} } } {}

9 3 8 4 ⋅ 14 7 3 1 = 3 ⋅ 7 4 ⋅ 1 = 21 4 = 5 1 4 size 12{ { { { { {9}}} cSup { size 8{3} } } over { { { {8}}} cSub { size 8{4} } } } cdot { { { { {1}} { {4}}} cSup { size 8{7} } } over { {3} cSub { size 8{1} } } } = { {3 cdot 7} over {4 cdot 1} } = { {"21"} over {4} } =5 { {1} over {4} } } {}

16 ⋅ 8 1 5 size 12{"16" cdot 8 { {1} over {5} } } {}

Convert 8 1 5 size 12{8 { {1} over {5} } } {} to an improper fraction.

8 1 5 = 5 ⋅ 8 + 1 5 = 41 5 size 12{8 { {1} over {5} } = { {5 cdot 8+1} over {5} } = { {"41"} over {5} } } {}

16 1 ⋅ 41 5 .

There are no common factors to divide out.

16 1 ⋅ 41 5 = 16 ⋅ 41 1 ⋅ 5 = 656 5 = 131 1 5 size 12{ { {"16"} over {1} } cdot { {"41"} over {5} } = { {"16" cdot "41"} over {1 cdot 5} } = { {"656"} over {5} } ="131" { {1} over {5} } } {}

9 1 6 ⋅ 12 3 5 size 12{9 { {1} over {6} } cdot "12" { {3} over {5} } } {}

Convert to improper fractions.

9 1 6 = 6 ⋅ 9 + 1 6 = 55 6 size 12{9 { {1} over {6} } = { {6 cdot 9+1} over {6} } = { {"55"} over {6} } } {}

12 3 5 = 5 ⋅ 12 + 3 5 = 63 5 size 12{"12" { {3} over {5} } = { {5 cdot "12"+3} over {5} } = { {"63"} over {5} } } {}

55 11 6 2 ⋅ 63 21 5 1 = 11 ⋅ 21 2 ⋅ 1 = 231 2 = 115 1 2 size 12{ { { { { {5}} { {5}}} cSup { size 8{"11"} } } over { { { {6}}} cSub { size 8{2} } } } cdot { { { { {6}} { {3}}} cSup { size 8{"21"} } } over { { { {5}}} cSub { size 8{1} } } } = { {"11" cdot "21"} over {2 cdot 1} } = { {"231"} over {2} } ="115" { {1} over {2} } } {}

11 8 ⋅ 4 1 2 ⋅ 3 1 8 = 11 8 ⋅ 9 3 2 1 ⋅ 10 5 3 1 = 11 ⋅ 3 ⋅ 5 8 ⋅ 1 ⋅ 1 = 165 8 = 20 5 8

Practice set c

Perform the following multiplications. Convert improper fractions to mixed numbers.

2 2 3 ⋅ 2 1 4 size 12{2 { {2} over {3} } cdot 2 { {1} over {4} } } {}

6

6 2 3 ⋅ 3 3 10 size 12{6 { {2} over {3} } cdot 3 { {3} over {"10"} } } {}

22

7 1 8 ⋅ 12 size 12{7 { {1} over {8} } cdot "12"} {}

85 1 2 size 12{"85" { {1} over {2} } } {}

2 2 5 ⋅ 3 3 4 ⋅ 3 1 3 size 12{2 { {2} over {5} } cdot 3 { {3} over {4} } cdot 3 { {1} over {3} } } {}

30
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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