02Ffractions-times

= Algebraic Fractions - Multiplying = toc

Note : When dealing with algebraic fractions, the line in the fraction that separates numerator from denominator must absolutely __always__ be horizontal. Never, ever write anything that looks like : //**3x/4**//

Literacy
In any fraction
 * the ** numerator ** is the value on the top of the fraction
 * the ** denominator ** is the value on the bottom of the fraction

Note : The fraction line (that is always horizontal) is called the ** vinculum ** {but you don't need to remember that}

Multiplying Fractions
Fractions with pronumerals in them should be dealt with in the same way as normal fractions.
 * SImplify first, {anything from the top row (numerators) can cancel with anything from the bottom row(denominators)
 * then multiply across the numerators
 * and multiply across the denominators

** Example 1 **
math \textbf{(a)} \quad \text{Simplify : } \dfrac{5y}{3x} \times \dfrac{6z}{7y} math



math \textbf{(b)} \quad \text{Simplify : } \dfrac{4x}{ \big(x-5\big)\big( 2x+3 \big)} \times \dfrac{x-5}{3x} math



math \textbf{(c)} \quad \text{Simplify : } \dfrac{\big( x-3 \big)^2}{\big(x+4\big)\big(3x-1\big)} \times \dfrac{5\big(3x-1\big)}{x-3} math

Hint: Remember that: math . \qquad \big( x-3 \big)^2 = \big(x-3\big)\big(x-3\big) math

Dividing
Remember, to divide fractions
 * write the **__reciprocal__** of the second fraction {flip the second fraction upside down}
 * then simplify
 * then multiply

** Example 2 **
math \textbf{(a)} \quad \text{Simplify : } \dfrac{y+5}{3x} \div \dfrac{2 \big( y+6 \big)}{5} math

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