Algebraic Fractions, addition #1 - interactive learning from GCSE Maths Tutor

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Algebraic Fractions - Addition #1

Worked Solution #1 of 3, increasing in difficulty.

Expand the following:

\begin{align} \quad\quad\quad\quad\quad\quad\quad\quad\Large { \frac{\color{#0000FF}{3x}}{\color{#CC0000}{4y}} + \frac{\color{#0000FF}{2y}}{\color{#CC0000}{5x}} }\\ \\ &\cssId{Step1}{\Large = \frac{( \quad \ )( \quad \ ) + ( \quad \ )( \quad \ ) }{( \ \color{#CC0000}{4y} \ )( \ \color{#CC0000}{5x} \ ) } }\\ \\ &\cssId{Step2}{\Large = \frac{( \quad \ )( \quad \ ) + ( \quad \ )( \quad \ ) }{\color{#CC0000}{20xy} } }\\ \\ &\cssId{Step3}{\Large = \frac{ ( \ \color{#0000FF}{3x} \ )( \ \color{#CC0000}{5x} \ ) + ( \quad \ )( \quad \ ) }{\color{#CC0000}{20xy} } }\\ \\ &\cssId{Step4}{\Large = \frac{ ( \ \color{#0000FF}{3x} \ )( \ \color{#CC0000}{5x} \ ) + ( \ \color{#0000FF}{2y} \ )( \ \color{#CC0000}{4y} \ ) }{\color{#CC0000}{20xy} } }\\ \\ &\cssId{Step5}{\Large = \frac{ 15x^2 + 8y^2 }{20xy } }\\ \\ \end{align}

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numerators $ \quad \color{#0000FF}{n_1} \ , \color{#0000FF}{n_2} \ $

denominators $ \quad \color{#CC0000}{d_1} \ , \ \color{#CC0000}{d_2} \ $

$$ \quad \quad \quad \quad \ \ \ \ \frac{\color{#0000FF}{n_1}}{\color{#CC0000}{d_1}} + \frac{\color{#0000FF}{n_2}}{\color{#CC0000}{d_2}} $$

$$ \ = \frac{( \ \color{#0000FF}{n_1} \ )( \ \color{#CC0000}{d_2} \ ) + ( \ \color{#0000FF}{n_2} \ )( \ \color{#CC0000}{d_1} \ )}{( \ \color{#CC0000}{d_1} \ )( \ \color{#CC0000}{d_2} \ )} $$

1. Draw a horizontal line under the algebraic fraction.

2. Write the common denominator (d1)(d2) under the line.

3. Divide the denominator d1 (from the left-hand fraction) into the common denominator (d1)(d2) to get the answer d2 .

4. Multiply the numerator n1 (from the left-hand fraction) by d2, putting the answer above the line.

5. Divide the denominator d2 (from the right-hand fraction) into the common denominator (d1)(d2) to get the answer d1 .

6. Multiply the numerator n2 (from the right-hand fraction) by d1, putting the answer above the line and added to the left-hand fraction result.

7. Add the terms above the line.

8. Cancel terms above and below the line

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2. Write the common denominator (d₁)(d₂) under the line.

3. Divide the denominator d₁ (from the left-hand fraction) into the common denominator (d₁)(d₂) to get the answer d₂ .

4. Multiply the numerator n₁ (from the left-hand fraction) by d₂, putting the answer above the line.

5. Divide the denominator d₂ (from the right-hand fraction) into the common denominator (d₁)(d₂) to get the answer d₁ .

6. Multiply the numerator n₂ (from the right-hand fraction) by d₁, putting the answer above the line and added to the left-hand fraction result.