Needs to cut a piece of rope so that one piece is one-third the length of the other piece. if she begins with a 2 and 2/3 ft rope, what will the 2 lengths be?

Question

Not sure how to set up equation, Ive been trying a while, Help!

Answer 1

Let x = the length of "the other piece"

  that means

    (1/3)x = the length of the "one piece"   ["one piece is one-third the length of the other piece"]

 

The total length is:

    length of "one piece"     +    length of "other piece"    =     total length

              (1/3)x                +                    x                  =      2 2/3

 

    (1/3)x + x = 2 2/3

    (1/3)x + x = 10/3       [convert to improper fraction]

        x    +  3x   = 10      [multiply by 3 to get rid of fracrtions]

          4x = 10

            x = 2 1/2 feet      {or 5/2]

 

The "other piece" is (1/3)x = (1/3)(5/2) = 5/6 foot

 

Check:

   Is   5/6 + 5/2 = 10/3   ?

         5/6 + 15/6 = 10/3   ?

             20/6  = 10/3   ?

             10/3 = 10/3   ?yes

 

 

 

Needs to cut a piece of rope so that one piece is one-third the length of the other piece. if she begins with a 2 and 2/3 ft rope, what will the 2 lengths be?

 

 

 

Answer 2

You need 1/3 of rope. Multiply 2 2/3 by 1/3 but you need to change 2 2/3 to an improper fraction by multiplying the denominator to the whole part and then add the numerator.

 

3 *2 + 2 = 8     2 2/3 = 8/3

 

8/3 * 1/3 = 8/9     This is the one third of 2 2/3.

 

Now subtract 8/9 from 2 2/3

 

   2 2/3     Change 2/3 to ninths     2/3 = 6/9

-    8/9

 

   2 6/9

-    8/9

 

Can't subtract so we must borrow 1. Subtract 1 from 2 and add to 6/9

 

   1 15/9     Adding 9/9 is the same as adding 1 to the fraction

-     8/9

 

The other piece is 1 7/9