MATHEMATICS FORM 1 – FRACTIONS

FRACTIONS

A fraction is a number that can be written in the form of
Where a and b are intergers and b 0

The number which is written on top of fraction is called Numerator and the bottom is called denominator e.g

Type of fraction

(i) Proper fractions

– A proper fraction is the one in which the numerator is less than denominator

e.g. etc

(ii) Improper fractions

– These are the ones which the numerators are greater than the denominator

etc

(iii) Mixed fractions or mixed numbers

– These are the ones formed after improper fractions are divided complete
e.g. = 2, 6, 9

(iv) Equivalent fractions

These are two or more fractions that can be simplified to equal lowest fraction.

Example: Change the following into mixed numbers

1. = 7

2. = 3

3. = 6

 

Fractions can be represented on number lines

e.g. represent on a number line.

Exercise 1

1. (i)Which of the following are: –

(a) Proper fractions

(b) Mixed fractions

(c) Improper fractions

(ii) List four equivalent fractions

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

(xiii)

(xiv)

(xv)

(xvi) 3

Solution

(a) Proper fraction

, , , , , , , , ,

(b) Improper fraction

, , , ,

(c) Mixed fraction

1, 3

Four equivalent fractions are:-

1. ,

2. ,

3. ,

4. ,

 

2. Write the following fractions in words

(a)

three quarters

(b)

A half

(c)

A third

(d)

Five over six

(e)

Nine over Ten

(f)

A quarter

2. Write the name of the fraction of the shaded part in figures ABCD and EFGH

= one over three (A third)

Which is a proper fraction

 

EH

 

 

 

 

 

F G

= one over four (A quarter)

Which is a proper fraction

 

Comparison of fraction

Fraction can be compared by using two methods

(i) Number line

(ii)L.C.M of the denominators

(I) Number line

Example 1. show and on a number line and then find which is greater than the other

 

Example 2. Which is greater between and ?

Solution:

(II) L.C.M of the denominators

Determine which fraction is greater between and

Solution

1^st find the L.C.M of 5 and 7

L. C. M of 5 and 7 = 35

2^nd multiply by that L. C. M each fraction

35 = 14

35 = 20

Conclusion, check the one which has given us bigger number after multiplication with L.C.M

Example: which is greater or ?

Solution:

L.C.M = 44

44

=99

44

=12

:-

Operations on Fractions

Addition and Subtraction of Fraction

NOTE:
1 .Add the numerator together if each fraction has the same denominator.

2. If the fraction has different denominator, you must find the smallest number that each denominator divides into exactly. (LCM)

3. When adding fractions, do not add the denominator.

Example:

Evaluate the following fractions

Multiplication

NOTE: 1. Before multiplying a number convert mixed number into improper fractions
2. Multiply the numerators and multiply the denominator.
Examples:

Dividing Fractions

1. When dividing fractions invert the second fraction then multiply the first fraction by the inverted fraction.

2. Before dividing number convert mixed numbers into improper fraction.