Question

The empirical formula of cuprite consist of 88.8% Cu and 11.2% O by mass

Answer 1

We have to find the empirical formula of cuprite
empirical formula is the simplest ratio of whole numbers of components in a compound 
calculating for 100 g of the compound 
      
                                      Cu                                       O
mass                        88.8 g                                       11.2 g
number of moles     88.8 g / 63.5 g/mol                  11.2 g / 16 g/mol 
                                 = 1.40                                     = 0.7
              divided by the least number of moles 
                                  1.40 / 0.7 = 2                          0.7 / 0.7 = 1
number of atoms 
Cu - 2
O  - 1 

empirical formula Cu₂O

Answer 2

Answer is: the empirical formula of cuprite is Cu₂O.
If we use 100 grams of cuprite:
m(Cu) = ω(Cu) · m(cuprite).
ω(Cu) = 88.8% ÷ 100% = 0.888.
m(Cu) = 0.888 · 100 g.
m(Cu) = 88.8 g.
n(Cu) = m(Cu) ÷ M(Cu).
n(Cu) = 88.8 g ÷ 63.55 g/mol.
n(Cu) = 1.4 mol.
m(O) = 0.112 · 100 g.
m(O) = 11.2 g.
n(O) = 11.2 g ÷ 16 g/mol.
n(O) = 0.7 mol.
n(Cu) : n(O) = 1.4 mol : 0.7 mol /0.7.
n(Cu) : n(O) = 2 : 1.