Sarabeth ran 1 2/5miles on a path around the park. This was 5/8 of the distance around the park. What is the distance around the park?

Question

I have no idea how to solve this...Multiply 1 2/5 by 5/8?  or by 3/8 which is the distance left?

Answer 1

Start with what you know or what you have been given.  That 1 2/5 mile is equal to 5/8 of the total.

Write this using numbers and convert the mixed number to an improper fraction.

7/5 = 5/8 X

Multiply both sides of the equation by 8/5

7/5 * 8/5 = 5/8 * 8/5 * X

56/25 = X

2 6/25 = X

Answer 2

Hi Karen--

 

I would first divide her distance by 5, which would tell you what 1/8 of the total is, then multiply it by 8 to get the total.

 

1 2/5  ÷ 5 is a pain, so think of the mixed number as an improper fraction instead: 7/5, then do the keep-change-flip trick and instead of dividing, multiply by the reciprocal:

 

7/5 x 1/5 = 7/25. So 7/25 is equivalent to one-eighth of the total distance.

 

Now multiply that 7/25 x 8 to get the total distance around the park: 56/25, or 2 6/25 miles.

 

So the total distance is 2 6/25 miles.

 

Hope that's reasonably clear. :-)

 

Matt in New York

 

 

Answer 3

You can write this as an equation to make it simpler.

1 2/5 miles is 5/8 of the total distance around the park

1 2/5 = (5/8) * D

7/5 = (5/8) * D

 

To solve for D, either divide both sides by 5/8, or multiply both sides by its reciprocal 8/5.