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Applications of Basic Mathematics Part 4:PERCENTAGE CHANGE

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MTH001 ­ Elementary Mathematics
LECTURE # 16
Applications of Basic Mathematics
Part 4
OBJECTIVES
The objectives of the lecture are to learn about:
·
Basic calculations of percentages, salaries and investments using
Microsoft Excel
PERCENTAGE CHANGE
Monday's Sales were Rs.1000 and grew to Rs. 2500 the next day.
Find the percent change.
METHOD
Change = Final value ­ initial value
Percentage change = (Change / initial value) x 100%
CALCULATION
Initial value =1000
Final value = 2500
Change
= 1500
% Change = (1500/1000) x 100 = 150%
The calculations using Excel are given below.
First the entries of data were made as follows:
Cell C4 = 1000
Cell C5 = 2500
In cell C6 the formula for increase was: = C5 ­ C4
The result was 1500.
In cell C7 the formula for percentage change was: = C6/C4*100
The result 150 is shown in the next slide.
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MTH001 ­ Elementary Mathematics
EXAMPLE 1
How many Percent is Next Day's sale with reference to Monday's Sale?
Monday's sale= 1000
Next day's sale= 2500
Next day's sale as % = 2500/1000 x 100 = 250 %
= Two and a half times
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MTH001 ­ Elementary Mathematics
EXAMPLE 2
In the making of dried fruit, 15kg. of fresh fruit shrinks to 3 kg of dried fruit.
Find the percentage change.
Calculation
Original fruit = 15 kg
Final fruit = 3 kg
Change = 3-15 = -12
% change = - 12/15 x 100 = - 80 %
Size was reduced by 80%
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MTH001 ­ Elementary Mathematics
Calculations in Excel were done as follows:
Data entry
Cell D19: 15
Cell D20: 3
Formulas
Formula for change in Cell D21: = D20 ­ D19
Formula for %change in Cell D22: = D21/D19*100
Results
Cell D21 = -12 kg
Cell D22 = -80 %
EXAMPLE 3
After mixing with water the weight of cotton increased from 3 kg to 15 kg. Find
the percentage change.
CALCULATION
Original weight = 3 kg
Final weight = 15 kg
Change = 15-3= 12
% change = 12/3 x 100 = 400 %
Weight increased by 400%
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MTH001 ­ Elementary Mathematics
Calculations in Excel were done as follows:
Data entry
Cell D26: 3
Cell D27: 15
Formulas
Formula for change in Cell D28: = D27 ­ D26
Formula for %change in Cell D29: = D28/D26*100
Results
Cell D28 = 12 kg
Cell D29 = 400 %
EXAMPLE 4
A union signed a three year collective agreement that provided for wage
increases of 3%, 2%, and 1% in successive years
An employee is currently earning 5000 rupees per month
What will be the salary per month at the end of the term of the contract?
Calculation
= 5000(1 + 3%)(1 + 2%)(1 + 1%)
= 5000 x 1.03 x 1.02 x 1.01
= 5306 Rs.
Calculations using Excel are shown in the following slides.
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MTH001 ­ Elementary Mathematics
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MTH001 ­ Elementary Mathematics
Calculations in Excel were done as follows:
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MTH001 ­ Elementary Mathematics
Data entry
Cell C35: 5000
Cell C36: 3
Cell C38: 2
Cell C40: 1
Formulas
Formula for salary in year 2 in Cell C37: =ROUND(C35*(1+C36/100);0)
Formula for salary year 3 in Cell C39: =ROUND(C37*(1+C38/100);0)
Formula for salary at the end of year 3 in Cell C41: =ROUND(C35
C39*(1+C39/100);0)
Results
Cell C37 = 5150 Rs.
Cell C39 = 5253 Rs.
Cell C41= 5306 Rs.
EXAMPLE 5
An investment has been made for a period of 4 years.
Rates of return for each year are 4%, 8%, -10% and 9% respectively.
If you invested Rs. 100,000 at the beginning of the term, how much will you have
at the end of the last year?
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MTH001 ­ Elementary Mathematics
Calculations in Excel were done as follows:
Data entry
Cell C46: 100000
Cell C47: 4
Cell C49: 8
Cell C51: -10
Cell C53: 9
Formulas
Formula for value in year 2 in Cell C48: = ROUND(C46*(1+C47/100);0)
Formula for value in year 3 in Cell C50: = ROUND(C48*(1+C49/100);0)
Formula for value in year 4 in Cell C52: = ROUND(C50*(1+C51/100);0)
Formula for salary end of year 4 in Cell C54: = ROUND(C52*(1+C53/100);0)
Results
Cell C48 = 104000 Rs.
Cell C50 = 112320 Rs.
Cell C52 = 101088 Rs.
Cell C54 = 110186Rs.
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Table of Contents:
  1. Recommended Books:Set of Integers, SYMBOLIC REPRESENTATION
  2. Truth Tables for:DE MORGAN’S LAWS, TAUTOLOGY
  3. APPLYING LAWS OF LOGIC:TRANSLATING ENGLISH SENTENCES TO SYMBOLS
  4. BICONDITIONAL:LOGICAL EQUIVALENCE INVOLVING BICONDITIONAL
  5. BICONDITIONAL:ARGUMENT, VALID AND INVALID ARGUMENT
  6. BICONDITIONAL:TABULAR FORM, SUBSET, EQUAL SETS
  7. BICONDITIONAL:UNION, VENN DIAGRAM FOR UNION
  8. ORDERED PAIR:BINARY RELATION, BINARY RELATION
  9. REFLEXIVE RELATION:SYMMETRIC RELATION, TRANSITIVE RELATION
  10. REFLEXIVE RELATION:IRREFLEXIVE RELATION, ANTISYMMETRIC RELATION
  11. RELATIONS AND FUNCTIONS:FUNCTIONS AND NONFUNCTIONS
  12. INJECTIVE FUNCTION or ONE-TO-ONE FUNCTION:FUNCTION NOT ONTO
  13. SEQUENCE:ARITHMETIC SEQUENCE, GEOMETRIC SEQUENCE:
  14. SERIES:SUMMATION NOTATION, COMPUTING SUMMATIONS:
  15. Applications of Basic Mathematics Part 1:BASIC ARITHMETIC OPERATIONS
  16. Applications of Basic Mathematics Part 4:PERCENTAGE CHANGE
  17. Applications of Basic Mathematics Part 5:DECREASE IN RATE
  18. Applications of Basic Mathematics:NOTATIONS, ACCUMULATED VALUE
  19. Matrix and its dimension Types of matrix:TYPICAL APPLICATIONS
  20. MATRICES:Matrix Representation, ADDITION AND SUBTRACTION OF MATRICES
  21. RATIO AND PROPORTION MERCHANDISING:Punch recipe, PROPORTION
  22. WHAT IS STATISTICS?:CHARACTERISTICS OF THE SCIENCE OF STATISTICS
  23. WHAT IS STATISTICS?:COMPONENT BAR CHAR, MULTIPLE BAR CHART
  24. WHAT IS STATISTICS?:DESIRABLE PROPERTIES OF THE MODE, THE ARITHMETIC MEAN
  25. Median in Case of a Frequency Distribution of a Continuous Variable
  26. GEOMETRIC MEAN:HARMONIC MEAN, MID-QUARTILE RANGE
  27. GEOMETRIC MEAN:Number of Pupils, QUARTILE DEVIATION:
  28. GEOMETRIC MEAN:MEAN DEVIATION FOR GROUPED DATA
  29. COUNTING RULES:RULE OF PERMUTATION, RULE OF COMBINATION
  30. Definitions of Probability:MUTUALLY EXCLUSIVE EVENTS, Venn Diagram
  31. THE RELATIVE FREQUENCY DEFINITION OF PROBABILITY:ADDITION LAW
  32. THE RELATIVE FREQUENCY DEFINITION OF PROBABILITY:INDEPENDENT EVENTS