# 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 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, $\text{512}+\text{896}$ can be estimated by $\text{500}+\text{900}=\text{1,400}$ .

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, $\text{31}+\text{62}+\text{28}+\text{59}$ can be estimated by
$\left(\text{2}\cdot \text{30}\right)+\left(\text{2}\cdot \text{60}\right)=\text{60}+\text{120}=\text{180}$

## Distributive property ( [link] )

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

## Estimation using the distributive property ( [link] )

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

## Estimation by rounding fractions ( [link] )

Estimation by rounding fractions commonly rounds fractions to $\frac{1}{4}$ , $\frac{1}{2}$ , $\frac{3}{4}$ , 0, and 1.
For example,
$\frac{5}{\text{12}}+\frac{5}{\text{16}}$ can be estimated by $\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$

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