whats 3 divided by 2 5/8

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$$\\3\div 2\frac{ 5}{8}\\\\ =3\div \frac{2*8+ 5}{8}\\\\ =3\div \frac{21}{8}\\\\ =3\times \frac{8}{21}\\\\ =1\times \frac{8}{7}\\\\ =\frac{8}{7}\\\\ =1\frac{1}{7}\\\\$$

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3 / 2 5/8

first, lets put these fractions improper3*8/8=24/8

2*8=16+5=21/8

now its: $${\frac{{\frac{{\frac{{\mathtt{24}}}{{\mathtt{8}}}}}{{\mathtt{21}}}}}{{\mathtt{8}}}}$$

now, lets do the recipicult to the numerator and denomenator of the second fraction, in this case, 21/8

now we converted this division situation to a multiplication situation

$${\frac{{\frac{{\mathtt{24}}}{{\mathtt{8}}}}{\mathtt{\,\times\,}}{\mathtt{8}}}{{\mathtt{21}}}}$$

cross cancel both 8s on both fractions cuz they cross

which leads to this after cross canceling:

$${\frac{{\frac{{\mathtt{24}}}{{\mathtt{1}}}}{\mathtt{\,\times\,}}{\mathtt{1}}}{{\mathtt{21}}}}$$

now multiply, which should equal:

$${\frac{{\mathtt{24}}}{{\mathtt{21}}}}$$ =1 3/21=1 1/7

overall, 3 divided by 2 5/8=1 1/7