Step-by-step explanation:
what is the question ?
what problem needs to be solved ?
is it to find the ratio between fruit and nuts ?
then remember, a ratio is a fraction.
so, the ratio fruit : nuts is
1/5 / 1/3 = 1×3 / 5×1 = 3/5 or 3 : 5
or is it about any fraction problems and we need to bring them to the same denominator to add our compare them ?
to compare the 1/5 cup of fruit with the 1/3 cup of nuts, the smallest common multiple of 5 and 3 is 15. so we need to bring all to .../15.
how to make 15 out of 5 ? by multiplying 5 by 3. and we need to do this on the top of the fraction as well to keep the original value of the fraction.
1/5 = 1/5 × 3/3 = 3/15.
and with the same line of thinking :
1/3 = 1/3 × 5/5 = 5/15.
so, when mixing 1/5 cup of fruit with 1/3 cup of nuts, we get 3/15 + 5/15 = 8/15 cup of trail mix.
here you can clearly see the ratio again : 3/15 : 5/15 = 3:5
the first solution to get only full cups of trail mix is
3 cups of fruit and 5 cups of nuts = 8 cups of trail mix.
anything less will always end up with parts of cups (since 3/5 can't be simplified anymore).
