# Lesson Notes By Weeks and Term - Junior Secondary School 1

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 1st TERM

WEEK SEVEN

TOPIC: ADDITION AND SUBTRACTION OF FRACTIONS

CONTENT

1. Introduction

iii. Subtraction of Fractions

1. Further Examples.

1. 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 ?

Summary

If fractions have different denominators:

1. Find a common denominator by expressing each fractions as an equivalent fraction
2. Add or subtract their numerators.

Example:  Simplify the following fractions

(a) ¼  + ½     (b) 2/3  + 5/6  (c) 2/5  + ½ + ¼

Solution

1. 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   =  9   = 1 3/6

3        6        3 x 2       6       6      6         6            6

= 1 ½ mixed fraction

(c )  + 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. 1 ¾  + 2 2/3 + ½
2. 3 ¾ + 5/8  1 7/12
3. 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

1. 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

1. 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

= 123136

EVALUATION

Simplify the following:

1. 3 7/8 + 2 3/4
2. 1 ½ + 2 1/3  + 3 ¼
3. 5 + 1 ¾  + 2 2/3

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:

1. 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.

1. ¾ - 5/8

3 x 2   5

4 x 2       8

6   - 5

8      8

6 – 5

8

1

8

1. 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 :

1. 5 1/6 -  3 2/3 + 6 7/12
2. 2 ½  + 3 + 7/102/5 - 2
3. 2 ½ + ¾  - 11/6 + 4 – 1 2/3

Solution

1. 51/6 – 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

1. 2 ½  + 3  + 7/102/5 – 2

= 5/2 3/1 +7/102/5 2/1

5 x 5  -  3 x 10  +  7  -  2 x 22 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

1. 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      1x12      3 x 4

30  + - 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 45

1114

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

1. = 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?

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.

1. Simplify 4 2/5 – 3 ¼

(a) 1 3/20   (b) 3 2/5   (c) 1 7/20   (d) 1 5/8

1. The common denominator of the fractions 316-212+223is

(a) 8        (b) 12    (c ) 6    (d) 15

1. Simplify 223-379+213

(a) 1 43/45   (b) 43/45    (c) 2 37/45    1 41/45

1. 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) 37/8 + 2 ¾  (b)      2 56 + 5 7/8

(c)   245+712-8310

1. 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?