Question

Emily needs enough Fabric for 3 1/2 hats. Since she has half a hat done. If each bag requires 1 2/7 ft of Fabric, how much fabric will she need to make the 3 1/2 hats?

Answer 1

first off let's convert the mixed fractions to improper fractions.

$\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} ~\hfill \stackrel{mixed}{1\frac{2}{7}}\implies \cfrac{1\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{9}{7}}$

she already did half a hat, so we can say   $\cfrac{7}{2}-\cfrac{1}{2}\implies \cfrac{7-1}{2}\implies 3$

so she only needs enough fabric to make 3 more full hats, we know each one uses 9/7 ft, so

$3\cdot \cfrac{9}{7}\implies \cfrac{27}{7}\implies 3\frac{6}{7}$