Question

Tony has 7/8 of a candy bar. He wants to split the bar into 3/10 of the bar. How many servings can he make? plz show work!

Answer 1

2 servings

Explanation:

I'm reading this question to ask the following:

There is a candy bar and some way, some how, Tony has `7/8` of it. He wants to break the bar he has into servings that are `3/10` of the bar each. How many servings can he make?

Before I do this, let's use some different numbers. For instance, if I had a whole bar and wanted to break it into servings that were `1/4` each, I'd have 4 servings. I could find that number mathematically by dividing 1 (the bar) by the size of the serving `(1/4)` and seeing that the result is 4 (the number of servings):

`1/(1/4)=(1/1)/(1/4)=(1/1)xx(4/1)=4`

We can do the same here with the bar `(7/8)` with each serving being `(3/10)`:

`(7/8)/(3/10)=(7/8)xx(10/3)=70/24~=2.92`

which means that we can make 2 whole servings and while the third serving would be close to being the right size, it wouldn't be big enough to count.

We can make 2 servings.

Answer 2

There are 2 servings with a bit left over

Explanation:

`color(blue)("Method:")`

Step 1
change both fractions so that they both have the same bottom number (denominator).

Step 2
Determine how many of the equivalent fraction for `3/10` you can fit into the equivalent fraction for `7/8` by division.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question:")`

Multiply by 1 and you do not change the value. However, 1 comes in many forms

Combining both step 1 and 2 we start with:

`color(green)(color(white)("d") [7/8color(red)(xx1)]color(white)("d") -:[3/10color(red)(xx1)])`

`color(green)( [7/8color(red)(xx10/10)] -:[3/10color(red)(xx8/8)])`

`color(green)(color(white)("dd")[70/80]color(white)("dd")-:color(white)("dd")[24/80]`

Note that `70/80 -:24/80` gives the same answer as `70-:24`

`1xx24 = 24larr" will fit"`
`2xx24=48larr" will fit"`
`3xx24=72color(red)(larr"wil NOT fit"`

So we can fit 2 with a bit left over.

There are 2 servings with a bit left over