Math help with proportions and fractions.

[gardenia]

I need help with the steps to solve this type of problem. Three friends have a pie. One friend eats 1/2 of the pie, One friend eats 1/3 of what is left over of the pie. The third friend eats half of what remains of the pie. How much pie is leftover?

I understand the pie is cut in half with the first friend and then thirds with the second friend. I'm confused as to the steps to solve for the remaining part after the third friend eats 1/2 of the 2/3 remaining pie and how that relates to the whole pie.

Thank you.

 

[gardenia]

I am finding that there is 1/3 of the whole pie left. If I'm not solving or missing something - feel free to correct me.

 

[mmm4444bot]

I am finding that there is 1/3 of the whole pie left.

That is what's left after friends 1 and 2 eat their shares.

Friend #3 gets half of that remaining third.

Did you try drawing some pictures, to help you understand? :cool:

 

[gardenia]

half of 1/3 = 1/6 of pie left. Sorry for some reason this question confused me.

 

[mmm4444bot]

Good job.

By the way, confusion is why I draw lots of pictures.

 

[soroban]

Hello, gardenia!

When all else fails, draw some pictures!

Three friends have a pie.
One friend eats 1/2 of the pie.
One friend eats 1/3 of what is left over of the pie.
The third friend eats 1/2 of what remains of the pie.
How much pie is left over?

Divide the pie into six equal pieces.

              * * *
          *     *     *
        *       *       *
       *        *        *
          *     *     *
      *      *  *  *      *
      *         *         *
      *      *  *  *      *
          *     *     *
       *        *        *
        *       *       *
          *     *     *
              * * *

The first friend eats half of the pie (3 pieces)
.

              * * *
          *:::::*     *
        *:::::::*       *
       *::::::::*        *
       :::*:::::*     *
      *::::::*::*  *      *
      *:::::::::*         *
      *::::::*::*  *      *
       :::*:::::*     *
       *::::::::*        *
        *:::::::*       *
          *:::::*     *
              * * *

Half of the pie remains.

                * *
                *     *
                *       *
                *        *
                *     *
                *  *      *
                *         *
                *  *      *
                *     *
                *        *
                *       *
                *     *
                * *

The second friend eats one-third of this (1 piece).

                * *
                *:::::*
                *:::::::*
                *::::::::*
                *:::::*
                *::*      *
                *         *
                *  *      *
                *     *
                *        *
                *       *
                *     *
                * *

This much remains.

                         *
                      *
                   *      *
                *         *
                *  *      *
                *     *
                *        *
                *       *
                *     *
                * *

The third friend eats one-half of this (1 piece).

                         *
                      *::::
                   *::::::*
                *:::::::::*
                *  *::::::*
                *     *:::
                *        *
                *       *
                *     *
                * *

This much remains.

                *
                *  *
                *     *
                *        *
                *       *
                *     *
                * *

What fraction of the pie is this?

 

[gardenia]

Thanks for the references and drawings to refer to in the future. I wasn't dividing the pie into six pieces to begin with, just in half.

 

[mmm4444bot]

I wasn't dividing the pie into six pieces to begin with, just in half.

:idea: It's not necessary to start by dividing the pie into sixths.

I began by dividing the pie in half, too. I didn't know there were 6ths, until after the half-pie was cut into three pieces.

1/2 = 3/6

 

[HallsofIvy]

The first friend ate 1/2 of the pie. That left 1- 1/2= 2/2- 1/2= 1/2 of the pie. The second friend ate 1/3 of that. The second friend ate (1/3)(1/2)= 1/6 of the pie. That leaves 1/2- 1/6= 3/6- 1/6= 2/6= 1/3 of the pie.