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.
[tex]\bf 12\frac{1}{18}\implies \cfrac{12\cdot 18+1}{18}\implies \cfrac{217}{18}
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1\frac{13}{16}\implies \cfrac{1\cdot 16+13}{16}\implies \cfrac{29}{16}\\\\
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\textit{how many times does }\frac{29}{16}\textit{go into }\frac{217}{18}\quad ?\quad \cfrac{\frac{217}{18}}{\frac{29}{16}}\implies \cfrac{217}{18}\cdot \cfrac{16}{29}
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\cfrac{3456}{522}\implies \cfrac{192}{29}\implies \boxed{6\frac{18}{29}}
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\cfrac{6\cdot 29+18}{29}\implies \cfrac{192}{29}[/tex]
so, he can cut 6 whole pieces only with that measurement, and a little bit more, but whole pieces, is only 6.
