Question

A container filled with M&Ms. 1/3 of the M&Ms are then poured equally into three bowls.what fraction of the total M&Ms is in each bowl? Draw a model to support your answer if each bowl has 6 pounds of M&Ms in it, how many pounds of M&Ms were in the full container to start with?

Answer 1

The container is filled with M&Ms, 1/3 of the M&Ms of the container were distributed equally into three bowls.

To determine the fraction of M&Ns that was poured into each bowl, you have to divide 1/3 by 3

`(1)/(3)/3`

To divide a fraction, you have to invert the divisor, to determine its reciprocal fraction, and then multiply the dividend by the reciprocal fraction.

To invert 3, first, you have to express it as a fraction, to do so you have to divide it by 1 since it is a whole number:

`(3)/(1)`

Then swap the places of the numerator and denominator to determine the reciprocal fraction

`(3)/(1)\to(1)/(3)`

Next, multiply the dividend of the division by the reciprocal fraction:

`(1)/(3)\cdot(1)/(3)=(1\cdot1)/(3\cdot3)=(1)/(9)`

So if 1/3 M&Ms was divided equally into 3 bowls, each bowl received 1/9 M&Ms

If each bowl has 6 pounds of M&Ms, and we know that this represents 1/9 of the total amount of M&Ms on the container, to determine how many M&Ms there are in the container you can use cross multiplication.

If in each bowl there is 1/9 of the amount of the container, then the total amount of the container can be considered as "1 whole"

1/9 represents 6 pounds in one bowl.

1 whole represents x pounds in the container.

Both relationships have to be at the same ratio so that:

`(6)/((1)/(9))=(x)/(1)`

"1/9" is the divisor of the first rate, so you have to invert the fraction to determine its reciprocal fraction and multiply the dividend "6" by the reciprocal fraction:

`(1)/(9)\to(9)/(1)=9`

Now multiply 6 by 9

`\begin{gathered} 6\cdot9=x \\ x=54\text{pounds} \end{gathered}`

And we get that there are 54 pounds of M&Ms in the container