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
[tex]\frac{1}{3}\div3[/tex]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:
[tex]\frac{3}{1}[/tex]Then swap the places of the numerator and denominator to determine the reciprocal fraction
[tex]\frac{3}{1}\to\frac{1}{3}[/tex]Next, multiply the dividend of the division by the reciprocal fraction:
[tex]\frac{1}{3}\cdot\frac{1}{3}=\frac{1\cdot1}{3\cdot3}=\frac{1}{9}[/tex]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:
[tex]\frac{6}{\frac{1}{9}}=\frac{x}{1}[/tex]"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:
[tex]\frac{1}{9}\to\frac{9}{1}=9[/tex]Now multiply 6 by 9
[tex]\begin{gathered} 6\cdot9=x \\ x=54\text{pounds} \end{gathered}[/tex]And we get that there are 54 pounds of M&Ms in the container
