Fractions continued: Addition and subtraction of fractions
Subject :
Mathematics
Term :
First Term
Week:
Week 8
Class :
Jss 1
Previous lesson :
The pupils have previous knowledge of Review of the first half term’s work and periodic test
Topic :
Table of Contents
Fractions continued: Addition and subtraction of fractions
Behavioural objectives :
At the end of the lesson, the pupils should be able to
 add up fractions that are of the same denominators
 sum up fractions that are of different denominators
 increase a fraction by another fraction
 calculate the difference between fractions
 take away a certain fraction from another one
 solve word problem questions on fractions
Instructional Materials :
 Wall charts
 Pictures
 Related Online Video
 Flash Cards
Methods of Teaching :
 Class Discussion
 Group Discussion
 Asking Questions
 Explanation
 Role Modelling
 Role Delegation
Reference Materials :
 Scheme of Work
 Online Information
 Textbooks
 Workbooks
 9 Year Basic Education Curriculum
 Workbooks
Content :
WEEK EIGHT
TOPIC : ADDITION AND SUBTRACTION OF FRACTIONS
CONTENT
i. Introduction
ii. Addition of Fractions
iii. Subtraction of Fractions
iv. Further Examples.
I. Introduction
Two or more fractions can be added or subtracted immediately if they both possess the same denominator, in which case we add or subtract the numerators and divide by the common denominator . For example
2/5 + 1/5 = 2 + 1 = 3/5
5
If they do not have the same denominator they must be rewritten in equivalent form so that they do have the same denominator – called the common denominator e.g
2/7 + 1/5 = 10/35 + 7/35 = 10 + 7 = 17
35 35.
The common denominator of the equivalent fraction is the LCM of the two original denominator that is,
2/7 + 1/5 = 5 x 2 + 7 x 1 = 10 + 7 = 10 + 7 = 17
5 x 7 7 x 5 35 35 35 35
From the explanation, the above example has its LCM = 35.
Can you try this,
5/8 + 1/6 ?
the correct answer is 19/24
Summary
If fractions have different denominators:
 Find a common denominator by expressing each fractions as an equivalent fraction
 Add or subtract their numerators.
II. Addition of Fractions
Example: Simplify the following fractions
(a) ¼ + ½ (b) 2/3 + 5/6 (c) 2/5 + ½ + ¼
Solution
a. ¼ + ½ = ¼ + 2 x 1 = ¼ + 2 = 1+ 2 = 3
2 x 2 4 4 4
(b) 2 + 5 = 2 x 2 + 5 = 4 + 5 = 4 + 5 = 9 = 1 ^{3}/6
3 6 3 x 2 6 6 6 6 6
= 1 ½ mixed fraction
(c ) 2 + ½ + ¼ = 2 x 4 + 1 x 10 + 1 x 5
5 5 x 4 2 x 10 4 x 5
= 8/20 10/20 + 5/20 = 8 + 10 + 5 = 23/24 = 1 3/20
20.
Example 2:Simplify the following fractions.
 1 ¾ + 2 ^{2}/3 + ½
 3 ¾ + ^{5}/8 1 ^{7}/12
 5 ^{4}/9 +7 ^{1}/3 + ^{1}/12
Solution.
1 ¾ + 2 ^{2}/3 + ½
convert to improper fractions
^{7}/4 +^{8}/3 + ½
7 x 3 + 8 x 4 + 1 x 6
4 x 3 3x 4 2 x 6
^{21}/12 +^{ 32}/12 +^{ 6}/12
= 21+ 32 + 6
12
= ^{59}/ 12
4 ^{11}/12
b. 3 ¾ +^{ 5}/8 + 1 ^{7}/12
convert to improper fractions
^{15}/4 + ^{5}/ 8 +^{19}/ 12
15 x 6 + 5 x 3 + 19 x 2
4 x 6 8 x 3 12 x 12
= ^{90}/24 +^{15}/ 24 + ^{38}/24
= 90 + 15 + 38
24
143
24
5 ^{23}/24
c. 5^{ 4}/9 +7^{ 1}/3 + ^{1}/12
convert to improper fractions
^{49}/9 + ^{22}/2 + ^{1}/12
= 49 x 4 + 22 x 12 + 1 x 3
9 x 4 3 x 12 12 x 3
^{196}/36 +^{264}/36 +^{ 3}/36
196 + 264 + 3
36
463
36
= 12
EVALUATION
Simplify the following:
a. 3 ^{7}/8 + 2 ^{3}/4
b. 1 ½ + 2 ^{1}/3 + 3 ¼
c. 5 + 1 ¾ + 2 ^{2}/3
READING ASSIGNMENT
1. Essential Mathematics for JSS 1 by AJS Oluwasanmipg 32 – 45
2. New General Mathematics for JSS1 by M.F. Macraepg 32 – 33.
III. Subtraction of Fractions
Example 1: simplify the following:
a. ^{2}/3 – ¼ b. ¾ – ^{5}/8 c. 5 ¾ – 2 ^{4}/5
Solution
^{2}/3 – ¼
= 2 x 4 – 1 x 3
3 x 4 4 x 3
= 8 – 3
12 12
8 – 3
12
5
12.
b. ¾ – ^{5}/8
3 x 2 – 5
4 x 2 8
6 – 5
8 8
6 – 5
8
1
8
c. 5 ¾ – 2 ^{4}/5
convert to improper fraction,
23/4 –^{14}/5 = 23 x 5 – 14 x 4
4 x 5 5 x 4
= 115 56
20 20
= 115 – 56
20
59
20 = 2 ^{19}/20.
Example 2: simplify the following :
a. 5 ^{1}/_{6} – 3^{ 2}/_{3} + 6 ^{7}/_{12}
b. 2 ½ + 3 + ^{7}/_{10} – ^{2}/_{5} – 2
c. 2 ½ + ¾ – ^{11}/_{6} + 4 – 1^{ 2}/_{3}
Solution
a. 5^{1}/_{6} – 3 ^{2}/_{3} + ^{6 7}/_{12}
= ^{31}/_{6} –^{11}/_{3} + ^{79}/_{12}
= 31 x 2 – 11 x 14 + 79
6 x 2 3 x 4 12
^{62}/_{12} –^{44}/_{12} +^{ 79}/_{12}
= 62 – 44 + 79
12
97
12 = 8 ^{1}/_{12}
b. 2 ½ + 3 + ^{7}/_{10} – ^{2}/_{5} – 2
= ^{5}/_{2 }– ^{3}/_{1} +^{7}/_{10} – ^{2}/_{5} –^{ 2}/_{1}
5 x 5 – 3 x 10 + 7 – 2 x 2 – 2 x 10
2 x 5 1 x10 10 5 x 2 1x 10
25 30+ 7 – 4 – 20
10 10 10 10 10
= 25 – 30 + 7 – 4 – 20
10
= 25 + 7 – 30 – 4 20
10
= 32 – 30 – 4 – 20
10
= 22
10
2 ^{2}/_{10} = – 2 ^{1}/_{5}
c. 2 ½ + ¾ – 1 ^{1}/_{6} + 4 – 1 ^{2}/_{3}
^{5}/_{2 }+ ¾ –^{7}/_{6} +^{4}/1 – ^{5}/_{3}
5 x 6 +3x 3 – 7 x 2 + 4 x 12 – 5 x 4
2 x 6 4 x 3 6 x 2 1×12 3 x 4
30 + 9 – 14 + 48 – 20
12 12 12 12 12
30+99 – 14 + 48 – 20
12
30 + 9 14 + 48 – 20
12
30 +9 + 48 – 14 – 20
12
87 – 34
12
^{53}/12
4 ^{5}/_{12}
EVALUATION
Simplify the following :
1. 2 ½ – 1 ^{4}/_{5} + 2 ^{3}/2 – 1
2.7 ½ + 3 ^{1}/_{6} – 3 ¼
3.14 ^{4}/_{15} – 4 ^{2}/_{3} + 7 ^{1}/_{5}
III. Further examples
Example 1
What is the sum of 2 ¾ and 2^{ 4}/_{5}?
Solution
Sum = addition 9 + 0
Hence, sum of 2 ¾ and 2 ^{4}/_{5} is
= 2 ¾ + 2 ^{4}_{5}
11+ 14
4 5
11 x 5 + 14 x 4
4 x 5 5 x 4
= 55 + 56
20 20
55 + 56
20
111
20 = 5 11/20
Example 2
A 2 ¼ kg piece of meat is cut from a meat that weighs 3 2/5kg. What is the weight of the meat left?
Solution
Original weights of meat = 2 2/5kg
Weight of meat cut = 2 ¼ kg
Final weight of meat = 3 2/5 – 2 ¼
= 17/5 – 9/4
= 17 x 4 – 9 x 5
5 x 4 4 x 5
68 – 45
20 20.
68 – 45
20
23

 = 2 3/20
The weight of the meat left = 2 3/20 kg.
Example 3
A fruit grower uses 1/3 of his land for bananas, 3/8 for pineapples, 1/6 for mangoes and the remainder for oranges. What fraction of his land is used for oranges.
Solution.
The entire land is a unit = 1
Every other fractions add up to give 1
;.oranges + bananas + pineapple + mango = 1
:. Orange = 1 – ( 1/3 + 3/8 + 1/6)
= 1 – ( 1 x 8 + 3 x 3 + 1 x 4 )
3 x 8 8 x 3 6 x 4
= 1 – ( 8/4 + 9/24 + 4/24 )
= 1 – 8 (8 + 9 + 4 )
24
1/1 – 21/24
= 24 – 21
24
= 3/24 = 1/8.
:. The fruit grower used 1/8 for oranges.
EVALUATION
1. By how much is the sum of 2 4/5 and 4 ½ less than 8 1/10?
2. A boy plays football for 13/4 hours, listens to radio for ¾ hours and then spends 1 ¼ hours doing his homework. How much time does he spend altogether doing these things?
READING ASSIGNMENT
1. Essential Mathematics for JSS 1 by AJS Oluwasanmipg 45
2. New General Mathematics for JSS1 by M.F. Macraepg 33
WEEKEND ASSIGNMENT
1. Simplify 2 ½ + ¼
(a) 3 ¾ (b).2 1/8 (c) 1 ¾ (d) 2 ¾.
2. Simplify 4 2/5 – 3 ¼
(a) 1 3/20 (b) 3 2/5 (c) 1 7/20 (d) 1 5/8
3. The common denominator of the fractions is
(a) 8 (b) 12 (c ) 6 (d) 15
4. Simplify
(a) 1 43/45 (b) 43/45 (c) 2 37/45 1 41/45
5. What is the sum of 1 ¾, 2 3/5 and 5 ¾
(a0 3 1/30 (b) 5 1/60 (c) 7 1/60 (d) 8 1/50.
THEORY
1. Simplify the following;
( a) 3^{7}/8 + 2 ¾ (b) 2 ^{5}6 + 5 ^{7}/8
(c)
2. Mr. Hope spends 1/3 of his earnings on food and ¼ on clothes. He then saves the rest. What fraction does he
(a) spend altogether
(b) save?
Presentation
The topic is presented step by step
Step 1:
The class teacher revises the previous topics
Step 2.
He introduces the new topic
Step 3:
The class teacher allows the pupils to give their own examples and he corrects them when the needs arise
Conclusion
The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.
The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.
He or she does the necessary corrections when and where the needs arise.