Applications of Basic Mathematics Part 1:BASIC ARITHMETIC OPERATIONS

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MTH001 Elementary Mathematics

LECTURE # 15

Applications of Basic Mathematics

Part 1

OBJECTIVES

The objectives of the lecture are to learn about:

· Different course modules

· Basic Arithmetic Operations

· Starting Microsoft (MS) Excel

· Using MS Excel to carry out arithmetic operations

BASIC ARITHMETIC OPERATIONS

Five arithmetic operations provide the foundation for all mathematical operations.

These are:

Addition

Subtraction

Multiplication

Division

Exponents

Example- Addition

12 + 5 = 17

Example- Subtraction

12 - 5 = 7

Example- Multiplication

12 x 5 = 60

Example- Exponent

(4)^2 = 16

(4)^1/2 = 2

(4)^-1/2 = 1/(4)^1/2 = ½ = 0.5

MICROSOFT EXCEL IN BUSINESS MATHEMATICS & STATISTICS

Microsoft Corporation's Spreadsheet software Excel is widely used in business

mathematics and statistical applications. The latest version of this software is

EXCEL 2002 XP. This course is based on wide applications of EXCEL 2002. It is

recommended that you install EXCEL 2002 XP software on your computer. If

your computer has Windows 2000 and EXCEL 2000 even that version of

EXCEL can be used as the applications we intend to learn can be done using the

earlier version of EXCEL. Those of you who are still working with Windows 98

and have EXCEL 97 installed are encouraged to migrate to newer version of

EXCEL software.

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Starting EXCEL 2000 XP

EXCEL 2000 XP can be started by going through the following steps:

Click Start on your computer

Click All Programs

Click Microsoft Excel

The following slides show the operations:

The EXCEL window opens and a blank worksheet becomes available as shown

below:

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The slide shows a Workbook by the name book1 with three sheets: Sheet1,

Sheet2 and Sheet3. The Excel Window has Column numbers starting from A

and row numbers starting from 1. the intersection of a row and column is called a

Cell. The first cell is A1 which is the intersection of column A and row 1. All cells

in a Sheet are referenced by a combination of Column name and row number.

Example 1: B15 means cell in column B and row 15.

Example 2: A cell in row 12 and column C has reference C12.

A Range defines all cells starting from the leftmost corner where the range starts

to the rightmost corner in the last row. The Range is specified by the starting cell,

a colon and the ending cell.

Example 3: A Range which starts from A1 and ends at D15 is

referenced by A1:D15 and has all the cells in columns A to D up to and including

row 15.

A value can be entered into a cell by clicking that cell. The mouse pointer which

is a rectangle moves to the selected cell. Simply enter the value followed by the

Enter key. The mouse pointer moves to the cell below.

If you make a mistake while entering the value select the cell again (by clicking

it). Enter the new value. The old value is replaced by the new value.

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If only one or more digits are to be changed then select the cell. Then double

click the mouse. The blinking cursor appears. Either move the arrow key to move

to the digit to be changed or move the cursor to the desired position. Enter the

new value and delete the undesired value by using the Del key.

I suggest that you learn the basic operations of entering, deleting and changing

data in a worksheet.

About calculation operators in Excel

In Excel there are four different types of operators:

Arithmetic operators

Comparison operators

Text concatenation operator

Reference operators

The following descriptions are reproduced from Excel's Help file for your ready

reference. In the present lecture you are directly concerned with arithmetic

operators. However, it is important to learn that the comparison operators are

used where calculations are made on the basis of comparisons. The text

concatenation operator is used to combine two text strings. The reference

operators include ":" and "," or ; as the case maybe. We shall learn the use of

these operators in different worksheets. You should look through the Excel Help

file to see examples of these functions. Selected material from Excel Help File

relating to arithmetic operations is given in in a separate file.

The Excel arithmetic operators are as follows:

Addition. Symbol: +

(Example: =5+4 Result: 9)

Subtraction. Symbol: -

(Example: =5-4 Result: 1)

Multiplication. Symbol: *

(Example: =5*4 Result: 20)

Division. Symbol: /

(Example: =12/4 Result: 3)

Percent. Symbol: %

(Example: =20% Result: 0.2)

Exponentiation: ^

(Example: =5^2 Result: 25)

Excel Formulas for Addition

All calculations in Excel are made through formulas which are written in cells

where result is required.

Let us do addition of two numbers 5 and 10.

We wish to calculate the addition of two numbers 10 and 5. Let us see how we

can add these two numbers in Excel.

Open a blank worksheet.

Click on a cell where you would like to enter the number 10. Say cell A15.

Enter 10 in cell A15.

Click cell where you would like to enter the number 5. Say cell B15.

Click cell where you would like to get the sum of 10 and 5. Say cell C15.

Start the formula. Write equal sign = in cell C15.

After =, write "(" (left bracket) in cell C15.

Move mouse and left click on value 10 which is in cell A15. In cell C15,

the cell reference A15 is written.

Write "+" after "A15" in cell C15.

10.

Move mouse and left click on value 5 which is in cell B15. In cell C15, the

cell reference B15 is written.

11.

Write ") " (right bracket) in cell C15.

12.

Press Enter key

The answer 15 is shown in cell C15.

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If you click on cell C15, the formula "=A15+B15" is displayed the formula bar to

the right of fx in the Toolbar.

The main steps along with the entries are shown in the slide below. The

worksheet MTH302-lec-02 contains the actual entries.

The next slide shows addition of 6 numbers 5, 10, 15, 20, 30 and 40. The entries

were made in row 34. The values were entered as follows:

Cell A34: 5

Cell B34: 10

Cell C34: 15

Cell D34: 20

Cell E34: 30

Cell F34: 40

The formula was written in cell G34. The formula was:

=5+10+15+20+30+40

The answer was 120.

You can use an Excel function SUM along with the cell range A34:F34 to

calculate the sum of the above numbers. The formula in such a case will be:

=SUM(A34:F34)

You enter "=" followed by SUM, followed by "(". Click on the cell with value

5(reference: A34). Drag the mouse to cell with value 40(reference: F34) and drop

the mouse. Enter ")" and then press the Enter key.

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In the above two examples you learnt how formulas for addition are written in

Excel.

Excel Formula for Subtraction

Excel formulas for subtraction are similar to those of addition but with the minus

sign.

Let us go through the steps for subtracting 15 from 25. Enter values in row 50 as

follows:

Cell A50: 25

Cell B50: 15

Write the formula in cell C50 as follows:

=A50-B50

To write this formula, click cell C50, where you want the result. Enter "=". Click

on cell with value 25 (reference:A50). Enter "-"(minus sign). Click on cell with

value 15 (reference B50). Press enter key.

If you enter 15 first and 25 later, then the question will be to find result of

subtraction 15-25.

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Excel Formula for Multiplication

Excel formula for multiplication is also similar to the formula for addition.

Only the sign of multiplication will be used. The Excel multiplication operator is *.

Let us look at the multiplication of two numbers 25 and 15. The entries will be

made in row 60. Enter values as under:

Cell A50: 25

Cell B50: 15

The formula for multiplication is:

=A50*B50

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Click on cell C50 to write the formula in that cell. Enter "=". Click on cell

with number 25 (reference: A50). Enter "*". Click on cell with number 15

(reference: B50). Press Enter key. The answer is 375 in cell C50.

Excel Formula for Division

The formula for division is similar to that of multiplication with the

difference that the division sign "/" will be used.

Let us divide 240 by 15using Excel formula for division. Let us enter

numbers in row 75 as follows:

Cell A75: 240

Cell B75: 15

The formula for division will be written in cell C75 as under:

=A75/B75

The steps are as follows: Click the cell A75. Enter 240 in cell A75. Click

cell B75. Enter 15. Click cell C75. Enter "=". Click on cell with value 240

(reference: A75). Enter "/". Click cell with number 15 (reference: B75). Press

enter key. The answer 16 will be displayed in cell C75.

Excel Formula for Percent

The formula for converting percent to fraction uses the symbol %. To convert

20% to fraction the formula is as under:

=20%

If you enter 20 in cell A99, you can write formula for conversion to fraction by

doing the following:

Enter 2o in cell A99. In cell B99 enter "=". Click on cell A99. Enter"%". Press

Enter key. The answer 0.2 is given in cell B99.

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Excel Formula for Exponentiation

The symbol for exponentiation is ^. The formula for calculating exponents is

similar to multiplication with the difference that the carat symbol ^ will be used.

Let us calculate 16 raised to the power 2 by Excel formula for exponentiation.

The values will be entered in row 85.

The steps are:

Select Cell A85. Enter 16 in this cell.

Select cell B85 Enter 2 in this cell.

Select cell C85.

Enter"=".

Select cell with value 16 (reference:A85).

Enter "^".

Select number 2 (reference: B85)

Press Enter key.

The result 256 is displayed in cell C85.

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Recommended Homework

Download worksheet MTH302-lec-02.xls from the course web site.

Change values to see change in results.

Set up new worksheets for each Excel operator with different values.

Set up worksheets with combinations of operations.

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