Question

A jewelry store has 9/10 of an ounce of gold. They need to split it into 1/6 ounce groups. How many groups can they make?

Answer 1

the amount of gold present is - 9/10 of an ounce of gold

from this gold they have to split into groups of 1/6 ounce each

so we have to divide 9/10 ounce in to groups of 1/6

for this we have to divide 9/10 by 1/6

$\frac{9}{10} / \frac{1}{6}$

when dividing fractions we mutiply the first fraction by the reciprocal of the second fraction

reciprocal of 1/6 is - 6/1

$\frac{9}{10}*\frac{6}{1} = \frac{54}{10} = 5.4$

so the number of groups that can be made is 5 whole groups with 0.4 ounce of gold remaining

the whole number of groups that can be made - 5

Answer 2

Set up an equation like this where x is the number of groups:

$\frac{1}{6}$x = $\frac{1}{6}$

Now just solve the equation by dividing by $\frac{1}{6}$ (or multiplying by the reciprocal: 6).

x = 27/5 = 5 and 2/5ths

Since you can't have 5 and 2/5ths groups, the answer is just the biggest number of groups that could be made without resorting to a fraction.

So just 5 groups.