Question

in a given training week a swimmer completes 1/4 mile on day one 2/5 mile on day two    and 3/7 mile on day three,,                                                          how many total miles does the athlete swim in the given week  

Answer 1

We'll have to add up all the fractions. 
First, find the LCM of the denominators.
To do this, we'll use the listing method. 

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, all the way to 140.
5: 5, 10, 15, 20, 25, 30, 35, all the way to 140.
7: 7, 14, 21, 28, 35, 42, 49, all the way to 140.

So, 140 is the Least Common Multiple. 

Multiply the numerator of 1 as many times you multiplied 4 to get to 140, which is 35.
1 x 35 = 35.

Multiply the numerator of 2 as many times you multiplied 5 to get to 140, which is 28.
2 x 28 = 56

Multiply the numerator of 3 as many times you multiplied 7 to get to 140, which is 20.
3 x 20 = 60.

So: 35/140 + 56/140 + 60/140 
=35/140 + 116/140 
=151/140
=1 11/140

So, the swimmer swam 1 and 11/140th of a mile.

Answer 2

Step-by-step explanation:

We’ll have to add up all the fractions.  

First, find the LCM of the denominators.

To do this, we’ll use the listing method.  

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, all the way to 140.

5: 5, 10, 15, 20, 25, 30, 35, all the way to 140.

7: 7, 14, 21, 28, 35, 42, 49, all the way to 140.

So, 140 is the Least Common Multiple.  

Multiply the numerator of 1 as many times you multiplied 4 to get to 140, which is 35.

1 x 35 = 35.

Multiply the numerator of 2 as many times you multiplied 5 to get to 140, which is 28.

2 x 28 = 56

Multiply the numerator of 3 as many times you multiplied 7 to get to 140, which is 20.

3 x 20 = 60.

So: 35/140 + 56/140 + 60/140  

=35/140 + 116/140  

=151/140

=1 11/140

So, the swimmer swam 1 and 11/140th of a mile.