Given a water bucket that holds
[tex]5\frac{1}{4}gallons[/tex]A container with the measurement below was used to fill the water bucket
[tex]\frac{3}{4}\text{gallon}[/tex](a) The division problem that shows how many containers are needed to fill the water bucket is
[tex]\frac{5\frac{1}{4}}{\frac{3}{4}}[/tex]The quotient is as solved below:
[tex]5\frac{1}{4}=\frac{5\times4+1}{4}=\frac{21}{4}[/tex][tex]\begin{gathered} \frac{5\frac{1}{4}}{\frac{3}{4}}=\frac{\frac{21}{4}}{\frac{3}{4}} \\ \frac{21}{4}\frac{\square}{\square}\frac{3}{4} \\ =\frac{21}{4}\times\frac{4}{3} \end{gathered}[/tex][tex]\frac{7\times1}{1\times1}=7[/tex]Hence, the quotient is 7 Containers
(b) Checking the answer using a product as shown below
[tex]\begin{gathered} 7\times\frac{3}{4}=5\frac{1}{4} \\ \frac{7\times3}{4}=\frac{21}{4} \end{gathered}[/tex][tex]\frac{21}{4}=5\frac{1}{4}[/tex]Hence, the product of 7 and 3/4 gallons container will fill 5 1/4 water bucket
