Question

Add or subtract the following mixed numbers. First change each mixed number to an equivalent improper fraction. Then find a common denominator, and proceed as before. Leave your answer as an improper fraction. Be sure your answers are reduced to lowest terms. 1/5 + 2 1/3 =
a 7/8
b 38/15
c 7/15
d 38/30

Answer 1

1/5 + 2 1/3    To change it to improper fraction multiply 2 by 3 and add 1 so it will be 7/3 
1/5 + 7/3   Find a common denominator 
1/5 x 3 = 3/15 
7/3 x 5= 35/ 15 
3/15 + 35/15 = 38/15
So the answer is b) 38/15 

Answer 2

Answer: b) $\dfrac{38}{15}$

Step-by-step explanation:

The given expression  : $\dfrac{1}{5}+2\dfrac{1}{3}$

First we convert the mixed fraction into the improper fraction :

$2\dfrac{1}{3}=\dfrac{3\times2+1}{3}=\dfrac{7}{3}$

Now, the expression becomes :

$\dfrac{1}{5}+\dfrac{7}{3}$

Now, we find a common denominator by finding the LCM of both denominators.

LCM (5,3)=$5\times3=15$

Now, expression becomes :

$\dfrac{1}{5}\times\dfrac{3}{3}+\dfrac{7}{3}\times\dfrac{5}{5}\\\\\dfrac{3}{15}+\dfrac{35}{15}=\dfrac{3+35}{15}=\dfrac{38}{15}$