Question

which is greater the sum of 5 3/6 and 4 1/4 or the sum of 6 1/2 and 2 4/5 and by how much?​

Answer 1

Answer:

The greater one is the first sum and their difference is $\frac{9}{20}$

Step-by-step explanation:

As we have been given here that we need to compare the sum of the two fractions in two different cases. Therefore first we will calculate the answer one by one and then compare them.

Firstly we have;

The sum of  $5 \frac{3}{6}$ and $4 \frac{1}{4}$

= $5 + \frac{3}{6} + 4 + \frac{1}{4}$

= $5 + 4 + \frac{3}{6} + \frac{1}{4}$

= $9 + \frac{3}{6} + \frac{1}{4}$

Now the respective lcm of 6 and 4 is 12,

= $9 + \frac{6}{12} + \frac{3}{12}$

= $9 + \frac{6 + 3}{12}$

= $9 + \frac{9}{12}$

= $9 + \frac{3}{4}$

= $9 \frac{3}{4}$

Hence we have the answer to be $9 \frac{3}{4}$

Another one we have,

$6 \frac{1}{2} + 2 \frac{4}{5}$

= $6 + \frac{1}{2} + 2 + \frac{4}{5}$

= $6 + 2 + \frac{1}{2} + \frac{4}{5}$

= The LCM of 5 and 2 is 10 we have,

= $8 + \frac{5}{10} + \frac{8}{10}$

= $8 + \frac{5 + 8}{10}$

= $8 + \frac{13}{10}$

= $8 + 1 + \frac{3}{10}$

= $9 + \frac{3}{10}$

= $9 \frac{3}{10}$

Therefore among $9 \frac{3}{10}$ and $9 \frac{3}{4}$

The $9 \frac{3}{4}$ is greater as the wholes here are the same and they both have the same numerator as well, therefore comparing the denominator we have the lesser denominator to be the greater fraction.

Subtracting them we get,

$9 \frac{3}{4} - 9 \frac{3}{10}$

= $\frac{39}{4} - \frac{93}{10}$

LCM of 4 and 10 is 20,

= $\frac{195}{20} - \frac{186}{20}$

= $\frac{195 - 186 }{20}$

= $\frac{9}{20}$

Hence the answer is $\frac{9}{20}$

Answer 2

Answer:

Step-by-step explanation: