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# Mathematics

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1.      Truncation of income tax rate

When a taxpayer’s tax rate is 27.8%, he would hope that this tax rate could be truncated so that the tax rate becomes 27%. This would bring a significant change in a large sum of an annual income. This is because when truncation is done, the number after the decimal point is neglected irrespective of its size. In addition, truncation is regarded as the best method when selecting the samples of tax calculations. This process ensures that truncation involving experimental data during the first period of truncation does not result into large amounts of bias. The average effects of income maintenance schemes as the one imposed in the samples is considerably large compared to those obtained by other methods. It is also the best method to use when dealing with the method of dividing earnings into indigenous variables of wages and hours worked. These results in elasticity between the times a person has worked and the wage rate or tax rate of 14 per cent in relation to non-wage income. Furthermore, truncation investigators who have not corrected it found negative wage values in equations similar to those applying truncation. Truncation is more likely to be used because it ensures that people who opt to participate in income maintenance schemes consider the hours worked. This ensures that the results of the samples are similar to those of the pre-experimental process. Consequently, it results into more accurate arrival at the amount of tax charged on earning of employees. Consequently, there is high likelihood that a person whose income tax rate is 27.8% would hope that this tax rate can be truncated to 27%.

2.       Government preferences

It has been observed that most governments prefer their taxpayers to use whole numbers when calculating the amount of tax. This has resulted in the directive to ensure that the tax rates are rounded up or rounded down. The main reason for this preference is that computers are currently being more used in processing of payments. Furthermore, these machines are only able to handle numbers effectively if they are whole numbers of five to seven digits. By using rounded up or rounded off values, return forms can be quickly processed and the refunds obtained immediately.

This preference is also applicable in calculation of the actual taxes. However, the process of rounding up or rounding down of taxes can only be done in whole dollar such as \$10.3 and \$100. 4. Rounding up or rounding down of values such as \$10 and \$100 it can result in either overpayment in case of rounding up or rounding down can result in a bill of extra tax owed.

3.       Mental Math Process

In school math curriculum, children learn mental math skills that focus on estimation and rounding up numbers that enables easy addition, subtraction, multiplication or division without the need to use papers and pencils. However, learning of these estimation skills requires constant practice and guidance from parents and teachers to ensure children are able to grasp the logic behind the use of these skills. It is therefore recommended that parents discuss the logic behind the use of these skills with their children and assist them where they have difficulties.

Children are able to apply these mental math in real life situations such as when shopping to determine if they have adequate money to buy an item or when trying to divide a number of items amongst themselves. This practice can also be applied in a grocery store, restaurant or a shopping mall while focusing on newspapers. For instance, if a person goes to the grocery with his child, he can instruct his child to round up the price of all goods bought to the nearest dollar.

Mental math skills of estimation can also be developed by training a child how much of something would be bought or used and involving the child in mental math activities of practicing these skills. For instance, when you have a bar-be-que and a total number of 15 people have been invited. Mental math would be developed by involving the child in estimating how much food, paper products and beverages would be bought based on the number of items that come in each package. At the end of the bar-be-que, it would be necessary to discuss with the child the level of estimation by looking at the leftover or items that were not enough. This assists the child in improving his mental estimation skills.

4.     Rounding off and truncation examples

There are various cases where truncation and rounding off can be applied in real life situations. These applications assist in solving problems which need decision making to arrive at a sound conclusion towards a problem.

An example of a truncation problem is when a bag weighs 56.839451 and it is necessary to know whether it is safe to put the bag in an aircraft, it would be reasonable to truncate the weight to 56 or even 50 if a single digit is required. It would be unreasonable to round up the figure to 57 pounds because it would indicate unsafe weight that can result into accidents. This is indicates that the most applicable form of estimation in this case is rounding down.

Furthermore, if one has 14 candies and wants to divide it among 3 people, each person would get 14/3 which translates to 4.66667. This problem cannot be rounded up because the fractions would still remain the same and it would be difficult to obtain a whole number value of 5. Consequently, this problem can be solved by truncation where each person is given 4 candies while you eat the remaining two. If rounding up is applied, it would be impossible to give every person 5 candies.

Rounding up can also be applied in a situation where someone visits a museum and comes across a dinosaur bone labelled 100 million years old. It is not possible to use instruments to determine the exact age of these bones due to their limitations of low accuracy. Hence, a person cannot return back to the same venue the following year and assume that the bones are 100,000,001 years. This value is too accurate to be determined by instruments for determining ages of artefacts such as carbon dating.

5.       Largest number of students that can be placed in a group

When a group of students is to be placed in groups based on certain characteristics, it is possible to determine the largest number of students with a particular characteristic that can be placed in a group. This can be calculated by finding the greatest common divisor of the number of students with different characteristics. For example, if a group of students consists of 24 boys and 18 girls, it is possible to find the largest number of students of each sex that can be placed in any group. This can be done by determining the greatest common divisor between the two numbers. In this case, the prime divisors of the two numbers are compared and the common prime factors are multiplied to obtain the greatest common divisors. The common prime factors of 24 and 18 are 2 and 3. These factors are multiplied to get 6 which give the greatest number of students that can be placed in any group.

6.      Groups from Algebra 1

It is also possible to determine the largest number of groups that can be formed from a group of students of various characteristics. For instance, if a group of students consists of 18 girls and 24 boys, it is possible to know the largest number of groups that can be formed when these numbers are used. This is obtained by determining the least common multiple of these numbers of students. Thus, the greatest number of groups that can be formed in this case is the LCM of 24 and 18, which is 72. Therefore, when groups are being created and it is necessary to know the largest number of groups that can be formed from these different groups of students. These groups accounts for the greatest number of students of a particular characteristic calculated above.