Question

Find the LCD to each the fractions and then add them together 1/4 + 2/5 + 1/3

Answer 1

Answer:

LCD is 60 and the sum is $\left(\frac{59}{60}\right)$

Solution:

First let’s list the multiple of the denominators,

Multiples of 4 is 4,8,12,16,20,24,28,32,36,40,44,48,52,56, 60,64

Multiples of 5 is 5,10,15,20,25,30,35,40,45,50,55,60,65

Multiples of 3 is 3,6,9,12,15,18,21,24,27,30,33,36,39,42,25,48,51,54,57,60,63

We can see that the least common number of the set of denominators in the list is 60 .

So, the LCD of the fractions are 60.

To add or subtract fractions with different denominators, multiply each numerator and denominator by same factor used to multiply the corresponding denominator when reaching the LCD.

Now adding them we get,

$\frac{1}{4}+\frac{2}{5}+\frac{1}{3} = \frac{1\times15}{4\times15}+\frac{2\times12}{5\times12}+\frac{1\times20}{3\times20}$ (as the LCD is 60)

On solving we get,

$\Rightarrow\left(\frac{15+24+20}{60}\right)$

$\Rightarrow\left(\frac{59}{60}\right)$

The sum is $\left(\frac{59}{60}\right)$

Answer 2

The LCD of these fractions is 60!

The sum of these fractions is $\frac{59}{60}$!

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