Lesson Notes By Weeks and Term - Junior Secondary School 1

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 1st TERM

 
WEEK SIX

TOPIC: FRACTIONS

CONTENT

Ordering of Fractions

Percentages – Conversion

Conversion of Fractions to Decimals and Vice–versa.

Ordering of Fractions

It is much easier to compare the size of fractions, when they have the same denominator.

Example 1

Which is the larger fraction: 5/7 or 6/8?

Solution

= 5/7  or6/8

to have a common denominator 

 = 5/7 x 8/8  or6/8 x 7/7

=  40/56  or 42/56

hence 6/8 is larger than 5/7,

Examples

Which has the greater mass:  3054g or 3.56kg

Solution

= 3054g  or 3.56kg

=  3054kg or  3.56kg

     1000

=  3.054kg or 3.56kg

therefore, 3.56kg is greater than 3054kg

Examples

Which is the larger fraction in this pairs?

1. 3 21/50 or 3 31/60       b.  37/45  or19/24

Solution

1. 3 21/50 or 3 31/60

The whole number  “3” can be ignored in the working . Consider the fractional part of the mixed fraction.

=  21/50 or  31/60

 = 21/50 x 6/6 or 31/60 x 5/5

 = 126/ 300 or 155/300.

Considering the values of the numerator 155 > 126

Therefore, 3 31/60 is larger than 3 21/50.

(b)  37/45  or19/24

   = 37/45  x8/8  or 19/24  x 15/15

   = 296/360  or285/360

Considering the values of their numerators,

296 > 285.

:. The fraction 37/45 is larger than 19/24.

Example

Arrange the following fractions in ascending order

1. 1/3 , 1/9, 5/18
2. 2/3, 5/6, 7/12, ¾

Solution

1. 1/3, 1/9, 5/18

  = 1/3 x 6/6  =6/ 18

  = 1/9  x2/2  = 2/ 18

  = 15/18 x 1/1  =5/ 18.

Comparing their numerator, 2,5,6,

:. The fractions are

1/9, 5/18, 1/3.

(b) 2/3,  5/6, 7/12, 3/4/

 = 2/3  =2/3 x 4/4 =8/ 12

 = 5/6  =5/6 x2/2  = 10/12

  = 7/12  =7/12 x 1/1  =7/ 12

¾  =3/4x 3/3  =9/12.

Comparing their numerators, 7,8,9 10. 

The fractions  are

7/12, 2/3, 3/6, 5/6.

READING ASSIGNMENT

Essential Mathematics for JSS 1 by AJS Oluwasanmipg 51

New General Mathematics for JSS 1 by MF.Macraepg 31-32.

EVALUATION

1. Which of the following fractions is larger?
2. 2/5 or 5/7     b. 5/6 or4/9
3. Arrange the following fractions in ascending order

3/5, 8/15, 17/30     (b) 3/5, 5/8, 7/10, 13/20.

PERCENTAGES

“Per cent’ means per hundred or ‘out of ‘hundred’ or ‘in every hundred’. For example, when we say a student obtained 63 percent in  a test, what we mean is that he or she had 63 marks out of 100 marks this is usually written as 63%. Where the symbol % means per cent.

1. Converting From percentage to fraction.

   Here, the given value in percentage is divided by 100.

  A% = A100 in fraction or A ÷ 100,  A x 1/100.

Express the following as  a fraction in its simplest form

1. 30%   ii. 75%   iii.7 ½ %   iv. 13 ¾ %

Solution.

1. 30%  = 30  =  3

               100       10

1. 75% = 75100= ¾ 

iii.  7 ½ %  =  15    =  3

                      100 x 2 40

1. 13 ¾ %  = 55 x 1      =   11

                        4 x 100          80

1. Converting a percentage into  a decimal 

To convert a percentage to a fraction divide the percentage by 100.

Examples

Change these to decimals

I 45%   ii. 34 ¾ %  iii. 5.8%

Solution

i.45%  = 45/100  = 0.45

ii.34 ¾ %= 34.75/100 = 0.3475

iii.5.8% = 5.8/100 = 0.0058.

1. Converting a fraction into percentage

To convert a fraction into a percentage, multiply it by 100.

Examples

Express these fractions as percentages

1. ¼   ii.25/400  iii. 5/8

Solution

¼ = ¼ x 100%  = 25%

1. 125/400 = 125 x 100

                         400 = 125/4  = 31.25%

iii. 5/8  = 5/8  x 100 %  =500/6  = 62.5%.

1. Converting a decimal into a percentage.

To change a decimal to a percentage  multiply it by 100

Example.

Express the following as a percentage 

a.0.75 b.0.045

Solution

a.0.75  =0.75 x 100 = 75

1. 0.048 =0.048 x 100 = 4.8%.

e.Finding the percentage of a quantity 

To find the percentage of a quantity, express the percentage as a fraction, then multiply by the quantity.

Examples

4. 4.5%  of N 248   ii.  205 of N250

Solution 

4. 4.5% of N 248

=  4.5 x 248

        100

=N1116/100  =N11.16.

1. 20% of N250

= 20/100  x 250

=N50.

f.Expressing one quantity as a percentage of another .

To express one quantity as percentage of another write, the first quantity as fraction of the second and then multiply by 100.

Examples

i.8 students did not do their assignments in a class of 40.

1. What is this as a percentage?
2. What percentage of the class did their assignment?

Solution 

40. Writing the first quantity as a fraction of the second gives 8/40.

Multiply the fraction by 100

Therefore, 8/40 x 100= 2 x 10  = 20%

20% of the student did not do their assignment .

c.Those who did their assignment were:

    40 -8 = 32 students 32/40 x 100  = 32/ 4 x10 =80

80% did their assignments.

2.What percentage of N5 is 150 kobo?

Solution 

Convert N5 to  kobo first.

N5 = 5 x 100 = 500kobo

Expressing as a fraction , we have 150/500

Therefore,  150 x 100

                      501

the percentage is 30%

3.What percentage of 15km is 20,000cm?

Solution

Convert both quanities to same unit first

1 km = 100,000cm

15km = 100000 x 15 =1500 000cm

Expressing as a fraction 20000/1500 000

Then multiply by 100

20 000/1500 000 x 100 = 20/15 = 1.33%

EVALUATION

1. Calculate the following :

(a) 5% of N500     (b) 18% of 144km.

2. Convert the following fraction into decimal:

 (a) 4/5    (b) 1 2/5

READING ASSIGNMENT

1. Essential Mathematics for JSS1 by AJS Oluwasanmipg 53-56
2. New General Mathematics for JSS I by MF. Macraepg 36-38.

III.Converting Fractions to Decimal

To convert a fraction into decimal first re-write the number as a decimal then divide it by the denominator

Terminating decimal

When the denominator divides exactly into numerator a terminating decimal is obtained.

Example

Change ¾ into a terminating decimal number

Solution 

 0.75

4   30

25

       20

20

 ¾ = 0.75.

Recurring or Repeating Decimals

Sometimes when changing fractions to decimal gives the same figure or group figures repeating themselves on and on.  These types  of fraction are called non-terminating decimals or recurring decimals.

Examples

Change the following into decimals :

(a) 4/9        (b) 6/11

Solution

1. 4/9  =  0.444

9   40

    36

                   40

36

                     4

Therefore 4/9 = 0.444

= 0.4.

1. 6/11 0.545454

                  11     60

55

                             50

44

                             60

55

                                  50

44

   60

55

  50

44

       6  

Therefore,  6/11 = 0.545454…..= 0.54.

Converting the following into fractions

1. 0.4 ii.0.067

Solution

1. 0.4  = 4/10  = 2/5
2. 0.067  = 67/1000

(d) Addition and subtraction in decimal

Simplify the following :

1. 0.6 + 1. 7     ii. 0.59 – 0.55  iii. 7.5 + 1.8   iv.9.3 – 6.2

Solution

i.0.6 + 1.7

  0.6

+1.7

 2.3

1. 0.59

  - 0.55

0.44

iii. 7.5

  + 1.8

9.3

iv.9.3

 - 6.2

 3.1

1. Multiplication and Division of Decimals

examples

Simplify the following :

1. 0.08 x 0.7   ii. 0.5 x 7   iii. 0.18 ÷ 1.2

Solution

1. 0.08

  x0.7

0.056

1. 0. 5          

x     7

  3.5 

iii. 0.18 ÷ 6 = 0.03

1. 1.56  ÷ 1.2

    1.3

12  15.6

12

               36

therefore, 1.56 ÷ 1.2 = 1.3

EVALUATION

Simplify the following :

14. 14.5 – 2.5 x 3.14
15. 0.6 x 0.08

        0.8

READING ASSIGNMENT

1. Essential Mathematics for JSS1 by AJS Oluwasanmi.
2. New General Mathematics for JSS1 by M.F Macrae et al.