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

FRACTIONS

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 1st TERM

WEEK FIVE

TOPIC: FRACTIONS

CONTENT

1. Equivalent fractions
2. Concept of equivalent fractions in sharing commodities.

III. Problem solving in quantitative aptitude (QR).

Equivalent Fraction:  Two or more fractions are said to be equivalent if they have the same values. Equivalent fractions can be obtained by multiplying or dividing the numerator and the denominator by the same number.

When the operation performed on the original fraction to get the new fraction is division, it is referred to as simplification .Here their common factor is used in dividing the numerator and the denominator.

i.Multiplication

35= 610= 1220

:. The fraction 3/5, 6/10 and 12/20 are said to be equivalent fractions.

1. Division

=  150  =   75    =  15

200         100       20

:. The fractions 150/200, 75/100 and 15/ 20 are said to be equivalent fractions.

iii. Simplification: by dividing both numerator and denominator by a common factor.

44  = 22

70        35

Example 1.

Find the missing numbers

(a) 1/3= 3/9 = 6/A = B/24  = 50/C = D/900 = 100/E

(b) 1/5  = 10/50 = 100= 4 =24

solution

(a) = 1/3  =3/9 = 6/A =B/24 = 50/C= D/900 = 100/E

= 1/3  =6/A, 1/3 = 1 x 6  = 6/18  A = 18.

= 1/3 =B/241/3 = 1 x 8  = 8/24 B = 8

3 x 8

= 1/3 = 50/C, 1/3 = 1 x 50 = 50/150 , C = 150

= 1/3  =D/900 , 1/3 = 1 x 300 = 300/900 , D = 300

3 x 50

= 1/3 = 100/E, 1/3 =   1 x 100   = 100/300 , E = 300

3 x 100.

Thus, the missing numbers calculated will make the fractions equivalent.

= 1/3 =3/9 = 6/18 = 8/24 = 50/150 = 300/900 = 100/300.

(b) 15= 1050= 20100= 420= 24120

= 1/5    =     10    , 1/5 x 2/2, missing number = 2

= 1/51/5 x 4/4 = 4/20 , missing number = 20

= 1/51/5 x 20/20 = 20/100, missing number  = 20

= 1/5= 24, 1/5 x 24/24  = 24/120,missing number = 120

Example

Find the missing numbers.

(a) 23 = 8

(b) 56  = 20

( c ) 35 = 15

(d)  7    =  14

9

Solution

(a)  2   = …….      think of what will multiply 3 to give 18..

3           18

= 2/3 x 6/6  =2 x 6   = 12/18

3 x 6

:. The missing number is 12.

(b)  5     = 20  think of what will multiply 5 to give 20

6

=  5 x  =  20

6     4       24

the missing number is 24

(c ) = ……

5          15 .think of what will multiply 5 to give 15.

=  3 3   =  3 x 3  =  9

5        3        5 x 3     15

:.the missing number is 9.

(d)  7   x  2   =  7 x 2  = 14

9       2      9 x 2      18     think of what will multiply 9 to give 18

:. The missing number is 18

EVALUATION

1.Find the missing numbers

¾  =6/8  = 15/A  = 24/B  = C/28  = D/100 = E/24

1. Find the missing numbers
2. 3    =

8             48

ii 5    =

9           36

iii.  5  =  20

6

1. Essential Mathematics for JSS1 by AJS Oluwasanmipg 38

2.New General Mathematics for JSS1 by M.F Macrae eta l pg 30-31.

II.Equivalent Fractions in Sharing Commodities

Problems involving sharing of commodities can be resolved with the knowledge of fractions.  Some examples below will help us to understand this aspect of fraction.

Example1

Some notebooks where shared into 18 equally. If 5 exercise books were given to Ojo, what fraction is left?

Solution

Number of notebooks =18

Ojo’s share = 6

Number left  =  18 – 6 = 12

Fraction left  =12/18   = 12/18 ÷ 6/6

= 2/

Example 2

Amarket woman had  90 yams. She  sold2/3 of it. How many yam did she sell?

Solution

No of yams    = 90

No sold    = 2/3 of 90

= 2/3 x 90 = 2 x 30

= 60 yams

:. 60 yams where sold.

Examples

Some oranges were shared out. Olu got 3/8of them. He gave 5 to his brother and 4 to her sister and had 6 left. How many oranges were there altogether?

Solution

Fraction received by Olu = 3/8

No of oranges he gave out = 5 + 4 = 9

No of oranges left with him = 6  = 9 + 6 = 15.

As equivalent fraction, 3/8  =15/?   = 3 x 5 =15/40.

8 x 5

:.40oranges were there altogether.

Example 4

In a shop, the price of a radio is reduced by one third .If the original price of the radio is N24, 000 what is the reduced price?

Solution

Original price = N2400

1/3 of this price = 1/3 x 2400 =N800

reduced price =2400- 800  = N1600.

Alternatively,

Consider the original price as unit

:. Reduced price = 1 - 1/3 = 2/3

2/3 of the unit price  =2/3 x 2400 = N1600

EVALUATION

1. In a class of 40 students, ¼ are doing science subjects, 1/5are doing arts and the remaining are doing commercial subjects.  How many students are :(a) doing science    (b) commercial?
2. In a service. ¼ of the people are men , 1/3 are women and the rest are children.  If there are 50 children, how many (a) people are there altogether       (b) more women than men are there ?

1. Essential Mathematics for JSS1 by AJS Oluwasanmipg 49-51
2. New General Mathematics for JSS1 by MF Macraeetalpg 33 -36.

III. Problem Solving in Quantitative Aptitude

Some of the examples under quantitative aptitude(reasoning ) have been seriously dealt with at the early part of this topic.  Let us take some more examples .

Example 1

Find the missing numbers

( a)   16    =                 (B )  10    =

48         3                    168

( c )   3     =

749

Solution

(a)   16    =                think of a number that will divide 48  to give 3

48        3

=   16 ÷ 16     =   1

48 ÷ 16          3

:. The missing number is 1.

(b)  10   =

16           8     ‘ think of a number which will divide 16 to give 8’

= 10  ÷ 2    =   5

16 ÷ 2         8.

The missing number is 5.

( c)   3     =                   think of a number  that will multiply 7 to give 49

7        49

=   3    x   7  =  3 x 7    =  21

7       7        7 x 7         49

:. The missing number is 21.

Example 2

Reduce the following fractions to their lowest terms/

(a)  5      (b)   24  ( c )  14

100          54                   21

Solution

The concept of equivalent fraction using division as the operation can be very helpful.

(a)  5     =   5 ÷ 5    =   1

100         100 ÷5      20

(b)   24   =   24 ÷2   =  12 = 12 ÷ 13   = 4

54         54 ÷2       27     27 ÷ 3       9

(c)   14   =  14 ÷7   =  12

21           21 ÷ 7        3

Example 3

What fraction of

1. 6 weeks is 6 days?
2. 650m is 1km?
3. 4mm  is 10cm?
4. 500g is 2kg?

Solution

Before reducing fractions, the quantities must be in the same units.

(a) 6 weeks  ………..6 days.

=  6 days

6 weeks

= 6 days=  6

6 x 7 days    6 x 7

=  1    the fraction = 1

7                          7

(b) 650m -------- 1km

=  650 m  =   650m   = 65 ÷ 5  =   13

1km         1000m    1000 ÷ 5      20

(c)  4mm ……….10cm

=   4mm      =    4mm    =    4

10cm            10 x10     100

= 4 ÷ 4      =   1

100 ÷ 4        25

The fraction = 1/25.

(d)  500g   ……….2kg

=  500g = 500g  =   500    =  5

2kg           2000g      2000     20

=  5÷ 5     =  1

20 ÷ 5    4

the fraction is ¼

EVALUATION

1. Find the missing numbers

(a)   55       =   11

305          ?

(b)   9  =  ?

11        99

1. Express 13 weeks as a fraction of 1 year.

1. Essential Mathematics   for JSS 1 by AJS Oluwasanmi ,pg
2. New General Mathematics for JSS1 by Mf Macraeetalpg 37.

WEEKEND ASSIGNMENT

1. Which of the following is not equivalent to ½ ?
2. 9/18    b. 11/22    c. 15/30    d. 16/32    e. 24/42
3. To express the fraction 30/48 in its lowest term, divide the numerator and demominator by
4. 2     B. 3        C.5        D. 6    E.  8

3.45 minutes , expressed as a fraction of  one hour is

1. 1/60 b. 1/45        c. ¾        d. 4/5        e. 4/3
2. The missing number in the fraction   3    = ?

4       20   is

1. 6     b. 9        c. 12      d. 5    e. 15.
2. A woman bought  2 crates of eggs. ¼ of them are bad.  How many of the eggs are good?
a. 3/6        b. 24        c. 48        d.12         e. 32.

THEORY

1.Find the missing numbers

? =   ?     =  ?    =    5

4         8          12       16         ?

(b) 2   ??   8 =  10

5        10      15       ?         ?

1.   A drum holds 2 ½ litres of water when itsis  ¾ full. How many litres of water can it hold when  it is

(a) full,    b, two-third   (c)empty.