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JSS2: MATHEMATICS - 2ND TERM

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  1. Transactions in the Homes and Offices | Week 1
    5 Topics
    |
    1 Quiz
  2. Expansion and Factorization of Algebraic Expressions | Week 2
    4 Topics
    |
    1 Quiz
  3. Algebraic Expansion and Factorization of Algebraic Expression | Week 3
    4 Topics
    |
    1 Quiz
  4. Algebraic Fractions I | Week 4
    4 Topics
    |
    1 Quiz
  5. Addition and Subtraction of Algebraic Fractions | Week 5
    2 Topics
    |
    1 Quiz
  6. Solving Simple Equations | Week 6
    4 Topics
    |
    1 Quiz
  7. Linear Inequalities I | Week 7
    4 Topics
    |
    1 Quiz
  8. Linear Inequalities II | Week 8
    2 Topics
    |
    1 Quiz
  9. Quadrilaterals | Week 9
    2 Topics
    |
    1 Quiz
  10. Angles in a Polygon | Week 10
    4 Topics
    |
    1 Quiz
  11. The Cartesian Plane Co-ordinate System I | Week 11
    3 Topics
    |
    1 Quiz
  12. The Cartesian Plane Co-ordinate System II | Week 12
    1 Topic
    |
    1 Quiz



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What are Algebraic Fractions?

Algebraic fractions are factions that contain both letters and numbers e.g. 

\( \frac{x}{5}, \frac{2y}{3}, \frac{3x^2}{5y}, \frac{a \: + \: b}{x \: – \: 2y}, \scriptsize \: etc \)

Equivalent Algebraic Fractions

Equivalent algebraic fractions can be obtained by multiplying or dividing both the numerator and denominator by the same quantity. 

Example 1 

 Copy and complete these equivalent fractions. 

(a) \( \frac{3x}{7} = \frac{?}{21} \)

(b) \( \frac{1}{x} = \frac{3}{?} \)

(c) \( \frac{a}{b} = \frac{?}{11bx} \)

Solution

(a) \( \frac{3x}{7} = \frac{?}{21} \)

7 multiplied by what number will give you 21

7 x ? = 21

7 x 3 = 21

Remember: Equivalent algebraic fractions can be obtained by multiplying or dividing both the numerator and denominator by the same quantity. 

\( \frac{3x}{7} = \frac{3x \: \times \: 3}{7 \: \times \: 3} = \frac{9x}{21} \)

\( \normalsize \frac{3x}{7} \scriptsize \: is \: equivalent \: to \: \normalsize \frac{9x}{21} \)

(b) \( \frac{1}{x} = \frac{3}{?} \)

1 multiplied by what number will give you 3

1 x ? = 3

1 x 3 = 3

\( \frac{1}{x} = \frac{1 \: \times \: 3}{x \: \times \: 3} = \frac{3}{3x} \)

\( \normalsize \frac{1}{x} \scriptsize \: is \: equivalent \: to \: \normalsize \frac{3}{3x} \)

(c) \( \frac{a}{b} = \frac{?}{11bx} \)

b multiplied by what will give 11bx

b x ? = 11bx

b x 11x = 11bx

\( \frac{a}{b} = \frac{a \: \times \: 11x}{b \: \times \: 11x} = \frac{11ax}{11bx} \)

\( \normalsize \frac{a}{b} \scriptsize \: is \: equivalent \: to \: \normalsize \frac{11ax}{11bx} \)

Example 2

Write any three equivalent fractions of these fractions 

(a) \( \frac{2}{x}\)

(b) \( \frac{3a}{5}\)

Solution

Let’s multiply the numerator and denominator by 2, 3 and 4

(a)

i. \( \frac{2}{x} = \frac{2 \: \times \: 2}{x \: \times \: 2} = \frac{4}{2x} \)

ii. \( \frac{2}{x} = \frac{2 \: \times \: 3}{x \: \times \: 3} = \frac{6}{3x} \)

ii. \( \frac{2}{x} = \frac{2 \: \times \: 4}{x \: \times \: 4} = \frac{8}{4x} \)

(b)

i. \( \frac{3a}{5} = \frac{3a \: \times \: 2}{5 \: \times \: 2} = \frac{6a}{10} \)

ii. \( \frac{3a}{5} = \frac{3a \: \times \: 3}{5 \: \times \: 3} = \frac{9a}{15} \)

iii. \( \frac{3a}{5} = \frac{3a \: \times \: 4}{5 \: \times \: 4} = \frac{12}{20} \)

Evaluation

1. Write down 3 equivalent fractions of these fraction 

(a) \( \frac{5a}{3y}\)

(b) \( \frac{6x}{5}\)

(c) \( \frac{2a}{6y}\)

2. Find the missing number 

(a) \( \frac{3b}{2} = \frac{?}{8a} \)

(b) \( \frac{10a}{1} = \frac{?}{4} \)

(c) \( \frac{?}{3a} = \frac{6x}{9ax} \)

c) \( \frac{4x}{?} = \frac{32x}{8ax} \)

Answers 

1a. \( \frac{10a}{6y}, \frac{15a}{9y}, \frac{20a}{12y} \)

(b) \( \frac{12x}{10}, \frac{18x}{15}, \frac{24x}{20} \)

(c) \( \frac{4a}{2y}, \frac{6a}{3y}, \frac{8a}{4y} \)

2(a) 12ab 

(b) 40a 

(c) 2 

(d) ax

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