Question

David has a piece of wood measuring 12 1/8 feet that he wants to use for a project. He needs to cut the wood into pieces that measure 1 13/16 feet. How many pieces of wood can he cut measuring exactly 1 13/16 feet?

Answer 1

namely, how many times does 1 13/16 go into 12 1/8... well, first off, let's make them "improper fractions" with only one numerator and denominator, and not mixed, and then, we'll just divide them.


`\bf 12(1)/(18)\implies \cfrac{12\cdot 18+1}{18}\implies \cfrac{217}{18} \\\\\\ 1(13)/(16)\implies \cfrac{1\cdot 16+13}{16}\implies \cfrac{29}{16}\\\\ -------------------------------\\\\ \textit{how many times does }(29)/(16)\textit{go into }(217)/(18)\quad ?\quad \cfrac{(217)/(18)}{(29)/(16)}\implies \cfrac{217}{18}\cdot \cfrac{16}{29} \\\\\\ \cfrac{3456}{522}\implies \cfrac{192}{29}\implies \boxed{6(18)/(29)} \\\\\\ \cfrac{6\cdot 29+18}{29}\implies \cfrac{192}{29}`

so, he can cut 6 whole pieces only with that measurement, and a little bit more, but whole pieces, is only 6.