LESSON NOTES ON FRACTIONS
SUBJECT: NUMBER THEORY
TOPIC: FRACTIONS
LESSON: Meaning of fraction, Types of fractions, Addition or Subtraction of fractions
PREVIOUS KNOWLEDGE: Students can peel and share an orange into parts among themselves, they can also add, or subtract integers.
OBJECTIVES: By the end of the lesson, students should be able to ; define a fraction, identify the different types of fractions, state parts of a fraction, add and subtract fractions.
TEACHING AIDS: An Orange Fruit, Chalk Board, A chart showing peeled orange shared in parts.
TEACHING METHOD: Demonstration, Questioning, Group discussion an Assignment.
GRADE LEVEL: 7 (Form 2)
DURATION: 45 Minutes
DATE: 3/4/19
INTRODUCTION
An orange is peeled and separated into 6 parts. It is shared to Paul, Jane, and Ben as follows: Paul receives 1 part out the 6, Jane receives 2 parts out of the 6 and Ben 3 out of the 6. The parts of orange received by each of the children are called the fraction. Each of the parts received as fractions are1/6, 2/6, 3/6. Note: 1/6 represents 1 part out of 6. 2/6 represents 2 parts out of 6. 2/6 Represents 3 parts out of 6.
PRESENTATION
Definition: A fraction is a small or tiny part, amount or proportion of something. It is the result of dividing an integer by another. Example: 1/6, 3/7, 4/11, 0.25 etc. The number above each of the fractions is called the numerator while the one below is called the denominator.
Fractions are used to describe situations in life such as election results, percentage pass in an examination, percentage of a population infected by a certain disease or displaced by war, portion of a man’s land handed to his son etc.
>TYPES OF FRACTIONS.
They are i) proper fractions; numerator is less than denominator eg 3/5. ii) Improper fractions eg 7/4, iii) mixed fractions 53/8 and iv) Decimal fractions eg 0.25 or 25/100 or 25%.
>ADDITION OR SUBTRACTION OF FRACTIONS.
i) Adding or Subtracting Fractions with the same denominator.
Example: Evaluate and simplify your answer in each of the following.
3/5 +1/5, b) 1/8+3/8, c) 3/4- - 1/4 d) 3/7 - 1/7
Solution
Simply add the numerators and maintain the denominator.
i)3/5+ 1/5= 4/5
ii)1/8+ 3/8= 4/8
iii)3/4- - 1/4= 2/4
iv)3/7 - 1/7=2/( 7)
ii) Adding or Subtracting Fractions with different denominators.
Example: Evaluate and simplify your answer in each of the following
a), 3/4+2/5 , b) 5/6+2/3 , c) 3/4+2/3 , d) 3/4 - 1/3 , e) 6/7 - 3/8 , f) 13/4 -2/3
Solution
When the denominators are different, use their lowest common multiple to evaluate the fractions. The lowest common multiple is usually the product of the denominators.
a)3/4 + 2/5 =(15+8)/20
3/4 + 2/5 =23/20
3/4 +2/5 =13/20
b)5/6 + 2/3 = (5+4)/6
5/6 + 2/3 =9/6
5/6 + 2/3 =13/6
5/6 + 2/3 =11/2
c)13/4 + 2/3 = 7/4 + 2/3
=(21+8)/12
=29/( 12)
13/4 + 2/3 = 25/12
d ) 3/4 - 1/3 =(9-4)/12
3/4 - 1/3 = 5/12
f) 6/7 - 3/8 = (48-21)/56
6/7 - 3/8 = 27/56
g) 13/4 - 2/3 = 7/4 -2/3
13/4 - 2/3 = (21-8)/12
13/4 - 2/3 = 13/12
13/4 - 2/3 = 13/12
EVALUATION
Evaluate and simplify each of the following fractions
a) 3/7 + 4/7 =7/7 =1
b) 4/7 - 2/( 7) = 2/7
c) 3/8 + 2/5 =(15+16)/40 =31/40
d) 2/11 - 1/3 =(6-11)/33 =(-5)/33 e) 32/3 +21/5 = 11/3 + 11/5= (55+33)/15=88/15=513/88
f) 32/3 - 21/5 = 11/3 - 11/5=(55-33)/15 = 22/15 = 17/15
SUMMARY
A fraction is made up of two parts; the numerator and denominator. In 2/5 , 2 is the numerator while 5 is the denominator.
When adding or subtracting fractions with the same denominators, add or subtract ONLY the numerators
When adding or subtracting fractions with different denominators find the lowest common multiple and simplify as explained in the examples above.
CONCLUSION
Assignment: Evaluate the following simplifying your answer as far as possible.
a)3/5 + 1/5 , b) 5/(9 ) - 2/9 , c) 6/7 +1/8 , d) 2/3 - ( 1)/6 , e) 13/4 + 3/5 , f) 31/2 - 1/5
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