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8.5 Summary of key concepts

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module reviews the key concepts from the chapter "Techniques of Estimation."

Summary of key concepts

Estimation ( [link] )

Estimation is the process of determining an expected value of a computation.

Estimation by rounding ( [link] )

The rounding technique estimates the result of a computation by rounding the numbers involved in the computation to one or two nonzero digits. For example, 512 + 896 size 12{"512 "+" 896"} {} can be estimated by 500 + 900 = 1,400 size 12{"500 "+" 900 "=" 1,400"} {} .

Cluster ( [link] )

When several numbers are close to one particular number, they are said to cluster near that particular number.

Estimation by clustering ( [link] )

The clustering technique of estimation can be used when
  1. there are more than two numbers to be added, and
  2. clustering occurs.
For example, 31 + 62 + 28 + 59 size 12{"31 "+" 62 "+" 28 "+" 59"} {} can be estimated by
( 2 ⋅ 30 ) + ( 2 ⋅ 60 ) = 60 + 120 = 180 size 12{ \( "2 " cdot " 30" \) + \( "2 " cdot " 60" \) =" 60 "+" 120 "=" 180"} {}

Distributive property ( [link] )

The distributive property is a characteristic of numbers that involves both addition and multiplication. For example,
3 ( 4 + 6 ) = 3 ⋅ 4 + 3 ⋅ 6 = 12 + 18 = 30 size 12{3 \( "4 "+" 6" \) =" 3 " cdot " 4 "+" 3 " cdot " 6 "=" 12 "+" 18 "=" 30"} {}

Estimation using the distributive property ( [link] )

The distributive property can be used to obtain exact results for a multiplication.
For example,
15 ⋅ 23 = 15 ⋅ ( 20 + 3 ) = 15 ⋅ 20 + 15 ⋅ 3 = 300 + 45 = 345 size 12{"15 " cdot " 23 "=" 15 " cdot \( "20 "+" 3" \) =" 15 " cdot " 20 "+" 15 " cdot " 3 "=" 300 "+" 45 "=" 345"} {}

Estimation by rounding fractions ( [link] )

Estimation by rounding fractions commonly rounds fractions to 1 4 size 12{ { {1} over {4} } } {} , 1 2 size 12{ { {1} over {2} } } {} , 3 4 size 12{ { {3} over {4} } } {} , 0, and 1.
For example,
5 12 + 5 16 size 12{ { {5} over {"12"} } + { {5} over {"16"} } } {} can be estimated by 1 2 + 1 4 = 3 4 size 12{ { {1} over {2} } + { {1} over {4} } = { {3} over {4} } } {}

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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