FRACTIONS

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;