Lesson Notes By Weeks and Term - Junior Secondary School 1

SUBJECT: MATHEMATICS

CLASS:  JSS 1

DATE:

TERM: 1st TERM

 
WEEK FOUR

TOPIC: FRACTIONS

CONTENT

A: Common Fractions

1. Types

(i) Proper Fractions

(ii) Improper Fractions

(iii) Simple Conversion

A: COMMON FRACTIONS

A fraction is a number which is represented by one integer – the numerator – divided by another integer – the denominator ( or the divisor).

Simply put, a fraction is a part of a whole number. It is not always possible to use whole numbers to describe parts of quantities. It is therefore, important to know that to describe parts of quantities, fraction is used for example.  

GENERAL FORM OF A FRACTION

From the explanation given above, we can write fraction in the form

a/b  where

    a = the numerator

    b= the denominator

Fraction is divided into

1. Common (Vulgar) Fractions

Here, the fraction is written as one number over another .

Numerator is the term given to the number on the top part of a fractions.

Denominator is the term given to the number at the bottom part of a fraction .For example

    9    Numerator

           11    Denominator

1. Decimal Fractions

     Decimal fractions are simply called decimal numbers.  It has numbers to the left and right of a decimal point. See week 5 for detail.

B.Types of Fractions (Common)

Common fractions are grouped under three headings. becausefractions are written as one integer divided by another – a ratio – they are called rational numbers.

Fractions are either proper,improper or mixed.

1.Proper Fractions : This is a common fraction having its numerator less than its denominator. Example

    (a) 4/7        (b) 3/5        (c) 2/5        etc

2 Improper Fraction: This is a common fraction having its numerator greater than its denominator .examples.

    11/5        (b) 4/3        39/11    (d)  etc

3. Mixed Numbers: This type of fraction is in the form of an integer and a fraction. That is it has two parts.

  - a whole number, and 

  -  a fraction (usually a proper fraction)

Example is shown in the figure below

From the diagram, we can describe the fraction  as  1 ½ oranges

Where,

1=whole number part and

½  = fractional part

EVALUATION

1.Give five examples each of the types of fraction

2. Using the shapes/figures below, write out the fraction stating whether it is a proper, improper or a mixed fraction.

I                    II

READING ASSIGNMENT

1. Essential Mathematics for JSS1 by AJS Oluwasanmipg 35 - 36
2. New General Mathematics for JSS1 by M.F Macraeetalpg 29 – 30.
3. Simple Conversions: Conversions can be made from improper fractions to a mixed fraction and vice versa .Lets see some examples.

Example 1

Express the following improper fractions as mixed fractions

  (a) 4/3         (b) 57/10    (c ) 93/20    (d) 113/ 3

Solution

(a) 43    = 3+13  = 33+13 = 1 + 13 = 113

Alternatively, divide the numerator by the denominator and express the remainder as the numerator of the fractional  part of the mixed fractions. The number of times the numerator can be divided before the remainder is the whole number part.

Hence,  4  = 4 ÷ 3  = 1 remainder 1

             3

    = 43  = 1 1/3

(b)  57/10  =50+710 = 50/10 + 7/10 = 5 + 7/10 = 57/10

(c )93/20            (d) 113/3

= 80 + 13                      = 111 + 2

       20                                    3

80  +13                   = 111   + 2

    20      20                        3        3

  = 4 + 13/20        = 37+ 2/3

   = 4 13/20        = 37 2/3

Example 2

Conversion from Mixed numbers to Improper Fraction 

Let Axy be the general form of a mixed number, where

    A = whole number part   

           x/y  = fractional part.

To convert to improper fraction, the following steps are followed.

1.Multiply the denominator of the fractional part by the whole number 

2. Add the numerator of the fractional part to the result in (1) above.
3. Express the result in (2) above as the numerator of the improper fraction with the original denominator of the fractional part as the same denominator.

    A xy        = A y + x

y

Example 2

Express the following mixed fractions as improper fractions

(a) 5 ½     (b) 3 2/5( c) 7 1/8    (d) 10 1/3

Solution

(a) 5 ½             (b) 3 2/5

=  5 x 2 + 1            3 x 5 + 2

          2                                          5

= 10 + 1            = 15 + 2

       2                                                5

=11/2            = 17/5

( c) 7 1/8            (d ) 10 1/3

  = 7 x 8 + 1            = 10 x 3 + 1

            8                                             3

 = 56 + 1           = 30+13

         8          

=578                          = 313

EVALUATION

1. Express the following as mixed fractions

    (a) 503/10           (b) 113/2

2. Express the following as improper fractions.

(a)    7 ½     (b) 3345

READING ASSIGNMENT .

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

WEEKEND ASSIGNMENT

1. Which of the following is not a proper fraction?(a) ¼ (b) ¾   (c )3/2 (d) 5/8
2. Express 3 1/7 as an improper fraction is (a) 11/7   (b)217( c) 7/22   (d) 22/ 7  

3.What fraction of the figure shown is shaded?(a) 2/11        (b) 3/9   ( c) 8/3        (d) 4/11.

4. Express 99/5 as a mixed fraction  (a) 19 4/5   (b) 18 4/5   ( c) 19 5/4   (d) 18 5/4

5.The figures above can best be described as 

(a) 2 ½ - mixed numbers

(b) 2 ¾  - proper fraction

(c) 2 ¾  -improper fraction

(d) 2 ¾  -decimal

THEORY

1. Distinguish clearly the various types of fraction known to you, giving 2 examples each.
2. Express   (a) 103/5 as mixed fraction   (b) 115 2/5   as improper fraction .