Question

What number should be added to 5/6 so as to get 49/30.

Answer 1

........................

Answer 2

Answer:

Concept :

The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory.    Since the result of dividing an integer by zero is undefinable, this definition only applies if both a and b are not equal to zero. However, given that 0 is the only common multiple of a and 0, some authors define lcm(a,0) as 0 for all a. Before fractions can be added, subtracted, or compared, the "lowest common denominator" (lcd) can be employed.

Explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 6 and 30 is 30

Next, find the equivalent fraction of both fractional numbers with denominator 30

For the 1st fraction, since 6 × 5 = 30,

$\frac{5}{6}$   =  $\frac{5*5}{6*5}$ =  $\frac{25}{30}$

Likewise, for the 2nd fraction, since

30 × 1 =30,

$\frac{49}{30}$ = $\frac{49 * 1}{30 * 1}$ = $\frac{49}{30}$

Add the two like fractions:

$\frac{25}{30}$ +  $\frac{49}{30}$ = $\frac{25 + 49}{30}$  =$\frac{74}{30}$  

74/30 simplified gives

$\frac{37}{15}$

So, $\frac{5}{6}$ + $\frac{49}{30}$ = $\frac{37}{15}$

In mixed form: 2 7/15

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