Explanation:
1.
a mother is a she, not a he ...
anyway, we need to make 2/3 and 3/4 comparable.
for this we need to bring both fractions to a common denominator, which is usually the smallest common multiple of the denominators.
yes, 12 is the smallest number that can be divided by 3 and by 4 without remainder.
to transform a fraction too another denominator, we need to multiply it by a fraction a/a, which has the value 1, of course (so we don't change the value of the original fraction), but changes the denominator to the desired number.
what do I multiply with 4 to get 12 ? 3.
so, I multiply 3/4 by 3/3 = 9/12.
what do I multiply with 3 to get 12 ? 4.
so, I multiply 2/3 by 4/4 = 8/12.
now we can compare and calculate :
out of the total of 9/12kg 8/12kg were used.
that means
1/12kg of carrots are left.
2.
this is a strange question, as watermelons, bananas and melons are very differently sized. so, for example 1/2 watermelon and 1/2 banana are very different quantities.
so, what does e.g. 1 fruit mean ?
or if we understand the fractions as shares of the overall smoothie, then we have too much. 4/6 (watermelon) + 2/6 (melon) = 6/6 = 1 (whole smoothie).
so, what to do with the banana ?
this question does not make any sense at all.
but if it is just to add fractions, we can do that :
4/6 + 1/2 + 2/6
as mentioned above, 4/6 + 2/6 = 6/6 = 1
1 + 1/2 = 2/2 + 1/2 = 3/2 = 1.5 or 1 1/2
so there is 1 1/2 fruit in the smoothie (whatever that means).
3.
1 1/2 + 2 1/2 = 2/2 + 1/2 + 4/2 + 1/2 = 8/2 = 4
in total, there are 4 cups of sugar needed.