Step-by-step explanation:
a
2/3 of 14 kg.
that means multiplying 2/3 × 14 = 28/3.
now we only need to do the division with remainder.
how often does 3 fit into 28 ? 9 times (9×3 = 27).
and then there is 1 left. and that means 1/3, since we are dividing by 3.
so, 2/3 of 14 kg = 9 1/3 kg
b
3/5 × 18
simply multiplication
54/5
and again division with remainder.
how often does 5 fit into 54 ? 10 times (10×5 = 50).
and there are 4 left. for a divisible by 5 that means 4/5.
so, 3/5 × 18 = 10 4/5
c
7/8 × 22
simply multiplication
154/8
again division with remainder.
how often does 8 fit into 154 ? 19 times (19×8 = 152).
and there are 2 left. so, 2/8 or 1/4.
so, 7/8 × 22 = 19 1/4
d
14 + 4/5
how many 1/5 are in 1 ? 5 !!! that defines the size of 1/5, because it is 1/5 of the whole, and the whole is 5/5 or 5×1/5.
so, if 1 has 5 times 1/5, how many 1/5 are in 14 ? well, 14×5 = 70
so, 14 = 70/5
and therefore,
14 + 4/5 = 70/5 + 4/5 = 74/5 = 14 4/5
surprise, surprise !
when we write something like 14 4/5, it has exactly the meaning 14 + 4/5.
but if the symbol was "÷" instead of "+" (it is really not to see in that picture) :
14 ÷ 4/5
remember, a division by a fraction is the same as the multiplication with the upside-down fraction :
14 × 5/4 = 70/4
how often does 4 fit into 70 ? 17 times (17×4 = 68).
and there are 2 left. that means 2/4 or 1/2.
14 ÷ 4/5 = 17 1/2
e
as for d.
if the operation is "+" then the result is for the same reasons 24 12/19.
if the operation is "÷" then we have
24 ÷ 12/19 = 24 × 19/12 = 2 × 19 = 38
