Multiplying & Dividing Algebraic Fractions Flashcards

All 6 cards in this deck

What is the rule for multiplying two algebraic fractions?

e.g. $\frac{2}{x}\times\frac{x+1}{3}$

Multiply the numerators and multiply the denominators.

e.g. $\frac{2(x+1)}{3x}$

What is the rule for dividing by an algebraic fraction?

e.g. $\frac{x}{2}\div\frac{x+1}{3}$

Multiply by the reciprocal of the divisor (invert the second fraction and multiply).

e.g. $\frac{x}{2}\times\frac{3}{x+1}=\frac{3x}{2(x+1)}$

True or false? To divide one algebraic fraction by another, you invert the first fraction and multiply.

False. You invert the second fraction (the divisor) and multiply.

True or false? You need a common denominator before multiplying two algebraic fractions.

False. A common denominator is only needed for adding or subtracting.

What are the steps to multiply algebraic fractions and simplify?

e.g. $\frac{x^2-4}{x^2}\times\frac{3x}{x+2}$

1. Factorise: $\frac{(x-2)(x+2)}{x^2}\times\frac{3x}{x+2}$
2. Multiply numerators and denominators: $\frac{3x(x-2)(x+2)}{x^2(x+2)}$
3. Cancel common factors: $\frac{3(x-2)}{x}$

How do you divide an expression that is not a fraction by an algebraic fraction?

e.g. $(x+5)\div\frac{x^2+3x-10}{x-1}$

Write it over $1$, then multiply by the reciprocal.

e.g. $(x+5)\times\frac{x-1}{(x+5)(x-2)}=\frac{x-1}{x-2}$