A fraction is part of a whole number which contains a
numerator and denominator. A numerator is the figure placed on top while the
denominator is the figure placed below. There are three types of fractions
which are;
1.
Proper Fraction; This is a fraction which has its numerator
lower than the denominator E.g. ½, 2/5, 7/9,
etc.
2.
Improper Fraction; This has its numerator higher (bigger) than
the denominator. E.g. 3/2,
4/3, 9/5, etc.
3.
Mixed Fractions; This consists of a whole number and a proper
fraction written together. E.g. 11/2, 23/4,
56/7, etc.
Solving any question related to fractions shouldn’t be
difficult if students can master the term BODMAS. BODMAS stands for the order
which arithmetic are carried out, which are as follows;
B; Bracket
O; Of
D;
Division
M;
Multiplication
A;
Addition
S;
Subtraction
Example
1;
Simplify 52/3 ÷ (232/5 of 31/4
– 22)
Note;
Before applying the BODMAS rule to this question, you
will have to convert all the mixed fractions to proper fractions. You can do
these by multiplying the whole number with first the denominator and second add
the result with the numerator and finally dividing your total result with the
denominator. (This is the format of conversion; Whole Number × Denominator +
Numerator ÷ Denominator).
= 17/3 ÷ (117/5
of 13/4 – 22)
Applying the rule means you’ll first deal with the ones
in bracket where “of” stands for multiplication.
= 17/3 ÷ (117/5
× 13/4 – 22)
= 17/3 ÷ (1521/20
– 22)
Find the L.C.M of the fractions in bracket;
= 17/3 ÷ (1521/20
– 440/20)
= 17/3 ÷ (1081/20)
Remove the bracket;
= 17/3 ÷ 1081/20
Note;
It is impossible to divide two fractions, so you’ll have
to change the mathematical sign to multiplication (It’s a rule in mathematics)
which makes the fraction to the right take an inverse form.
= 17/3 × 20/1081
= 340/3243 (Answer).
Example
2;
Evaluate
Convert all mixed fractions to proper fractions;
Find the L.C.M of both fractions above and below;
= 11/4 ÷ 11/8
(Change division sign to multiplication sign just like example 1 above)
= 11/4 × 8/11
(11 cancels 11 while 4 in 8 gives 2)
= 2 (Answer).
Practice
these questions below;
Simplify the following;
1. (a)
23/4 + 32/5 – 11/2
(b) 21/6
+ (33/5 ÷ 11/8)
(c) (25/6
– 31/2) ÷ 11/2 of 52/3
2. Simplify this fraction;
3. (a)
5/9 ÷ (13/8 – 1/3)
(b) 51/3 ÷ (45/6
– 31/5)
(c) 21/2
÷ (21/4 ÷ 41/3)
4. Simplify this fraction below;
