ALGEBRA FRACTIONS

The term Algebra is derived from these two words; Alphabet and Numbers. It is a combination of both Alphabet (letters) and Numbers.

Therefore, we can say that Alphabet + Numbers = Algebra and Hence Alphabet + Numbers + Fractions = Algebra Fractions.

Types of Algebra Fraction

There are two types of Algebra fractions;

1. Monomial Fractions; These are fractions with only one value as denominator. Examples are; 

, etc…

2. Binomial Fractions; These are fractions with two values as denominator. Examples are;

 

, etc…

Rules for Solving Algebra Fractions

1. If the values are three digits, you factorise both numerator and denominator.

2. If the values are two digits, you look for their common factors.

3. If the values are single digit, just go ahead and simplify as there’s no need to factorise or look for common factors!

Types of Algebra Fractions

1. Simplification of Algebra Fractions

2. Multiplication & Division of Algebra Fractions

3. Substitution in Algebra Fractions

4. Equations in Algebra Fractions

1. Simplification of Algebra Fractions

Examples; Simplify the following Algebra;

Solution

Step 1

Note;

The example above contains three digit values, am I right? So we will factorise both the numerator and denominator before simplification;

NUMERATOR

a² - 5a + 6                +6a² (×)    (-3a & -2a)

                                   -5a (+)

a² – 3a – 2a + 6

a(a – 3) -2(a – 3)

(a – 3) (a – 2)

Step 2

DENOMINATOR

2 – 3a + a² (Rearrange)

a² – 3a + 2               +2a² (x)     (-2a & -1a)

                                   -3a (+)

a² – 2a – 1a + 2

a (a – 2) -1(a – 2)

(a – 2)(a – 1)

Step 3

Bring the Numerator and Denominator together;

Step 4

Cancellation Process; (a – 2) cancels (a – 2);

Step 1

The example 2 above contains two digit values, so we will look for common factors for both the Numerator and Denominator as well.

NUMERATOR;

6m²u² - 4mu³ ---The common factor is 2mu².

2mu²(3m – 2u)

Step 2

DENOMINATOR;

9m³u – 4mu³ ---The common factor is mu.

mu (9m² – 4u²) ….this can also be written thus as 3² gives 9 and 2² gives 4;

mu (3²m² – 2²u²)

mu (3m – 2u)² ….the “raise to power 2” has been brought out as the common factor;

mu (3m – 2u)(3m + 2u)

Step 3

Combining the Numerator and Denominator;

Step 4

Cancellation Process; mu goes in 2mu² to give 2u while (3m – 2u) cancels each other;

Step 1

This is a three digit value, remember you factorise when dealing with three digit values;

NUMERATOR;

a² + ax – 6x²         -6a²x² (×)    (+3ax & - 2ax)

                                       +ax (+)

a² + 3ax – 2ax – 6x²

a(a + 3x) – 2x(a + 3x)

(a + 3x)(a – 2x)

Step 2

DENOMINATOR;

2x² + ax – a²  (Rearrange)

- a² + ax + 2x²       -2a²x² (×)    (+2ax & - 1ax)

                                       +ax (+)

- a² + 2ax – 1ax + 2x²

-a(a – 2x) – x(a – 2x)

(a – 2x)(-a – x)

Step 3

Combining the Numerator and Denominator;

Step 4

Cancellation Process; (a - 2x) cancels each other;

Note; The minus sign was brought out as a common factor;

Note; The minus sign went up! This is a rule as minus sign must always remain with the numerator;

Step 1

NUMERATOR;

ab + ac  ----the common factor will be a;

a(b + c)

Step 2

DENOMINATOR;

ad + ae   -----the common factor here will also be a;

a(d + e)

Step 3

Combining the Numerator and Denominator;

Step 4

Cancellation Process; a cancels each other;

Step 1

Note; The values above are single digit, so there’s no need for factorization or common factors. Just go ahead and simplify!

 Step 2

Cancellation Process; 2 goes in 8 gives 4 and 2 goes in 10 gives 5 while x goes in x² gives x and z cancels z;