The total amount of time he has spent doing homework:
[tex]3\frac{1}{2}[/tex]And the time it takes to complete each assignment:
[tex]\frac{1}{4}[/tex]To find the number of assignments he has completed in that time, we divide the total time 3 1/2 by the time for each assignment 1/4:
[tex]3\frac{1}{2}\div\frac{1}{4}[/tex]To make this division we need to convert 3 1/2 to a fraction as follows:
[tex]3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{6+1}{2}=\frac{7}{2}[/tex]We multiply the whole number by the denominator 3x2 and we add to that the numerator 1, and divide that by the original denominator 2.
Now instead of 3 1/2 we use 7/2 for our division:
[tex]\frac{7}{2}\div\frac{1}{4}[/tex]And we use the formula to divide two fractions, which is:
[tex]\frac{a}{b}\div\frac{c}{d}=\frac{a\times d}{b\times c}[/tex]Applying this to our division:
[tex]\frac{7}{2}\div\frac{1}{4}=\frac{7\times4}{2\times1}[/tex]Solving the operations:
[tex]\frac{7}{2}\div\frac{1}{4}=\frac{28}{2}=14[/tex]Answer: 14 assignments
