To add numbers with different denominators, a student is consistently using the product of the denominators as a common denominator. Is this correct? Why or why not? Give an example to support your answer

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- Oct 23rd 2006, 11:35 AM #1

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- Oct 2006
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- Oct 23rd 2006, 11:57 AM #2
Hi,

let the two fractions be:$\displaystyle \frac{a}{b}\ \text{and}\ \frac{c}{d}$

$\displaystyle b\neq 0\ and\ d\neq 0$

The sum becomes then:

$\displaystyle \frac{a}{b}+ \frac{c}{d}=\frac{a\cdot d}{b\cdot d}+ \frac{c\cdot b}{d\cdot b}=\frac{ad+bc}{bd}$

The numerator and denominator of this result might be large numbers but the result itself is always correct.

EB