Adding Using the LCD

Adding Using the LCD

 

Let’s  finish adding \frac{5}{12} and \frac{7}{30}:

 

\frac{5}{12}+\frac{7}{30}=\frac{5}{2.2.3}+\frac{7}{2.3.5}.

 

The least common denominator, LCD, is 2 . 2 . 3 . 5. To get the LCD in the first denominator, we need a 5. To get the LCD in the second denominator, we need another 2. We get these numbers by multiplying by form of 1:

 

\frac{5}{12}+\frac{7}{30}=\frac{5}{2.2.3}.\frac{5}{5}+\frac{7}{2.3.5}.\frac{2}{2}   Multiplying by 1

= \frac{25}{2 . 2 .3.5}+\frac{14}{2.3.5.2} Each denominator is now the LCD.

=   \frac{39}{2.2.3.5}  Adding the numerators and keeping the LCD

= \frac{3.13}{2.2.3.5}  Factoring the numerator and removing a factor of 1: \frac{3}{3} = 1

= \frac{13}{20}.  Simplifying

 

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