This means the examiners have lost their minds.
No one balances equations this way.
Which isn't to say that you can't...
You just shouldn't.
A question might read like the following:
"A student burns 1.6g of Methane in 6.4g of Oxygen and finds that 4.4g of Carbon Dioxide are made as well as 3.6g of water.
Use these figures to balance the equation below:"
___CH4 + ___O2 --> ____CO2 + ___H2O
Answer:
i) Since Chemistry works in moles we'll first find their Mrs.
Mr (CH4) = 16 g/mol, Mr (O2) = 32 g/mol,
Mr (CO2) = 44 g/mol, Mr (H2O) = 18 g/mol
ii) Then we'll find the moles of each and make a ratio
Moles (CH4) = 1.6/16 = 0.1 mol, Moles (O2) = 6.4/32 = 0.2 mol,
Moles (CO2) = 4.4/44 = 0.1 mol, Moles (H2O) = 3.6/18 = 0.2 mol
CH4: O2: CO2: H2O
0.1: 0.2: 0.1: 0.2
iii) To convert to a simpler ratio we just divide all the numbers in the ratio by the smallest
CH4: O2: CO2: H2O
0.1/0.1 : 0.2/0.1 :0.1/0.1 :0.2/0.1
1: 2: 1: 2
iv) and then put them in the equation
_1_CH4 + _2_O2 --> _1_CO2 + _2_H2O
Or
"A student heats 32.4g of Aluminium in 28.8.g of Oxygen and finds that 61.2g of Aluminium Oxide are made.
Use these figures to balance the equation below:"
___Al + ___O2 --> ____Al2O3
Answer:
i) Since Chemistry works in moles we'll first find their Mrs.
Ar (Al) = 27 g/mol, Mr (O2) = 32 g/mol,
Mr (Al2O3) = 102 g/mol
ii) Then we'll find the moles of each and make a ratio
Moles (Al) = 32.4/27 = 1.2 mol, Moles (O2) = 28.8/32 = 0.9 mol,
Moles (Al2O3) = 61.2/102 = 0.6 mol
Al: O2: Al2O3
1.2: 0.9: 0.6
iii) To convert to a simpler ratio we just divide all the numbers in the ratio by the smallest
Al: O2: Al2O3
1.2/0.6: 0.9/0.6: 0.6/0.6
2: 1.5: 1
iv) Because there's a half we double all of them
Al: O2: Al2O3
4: 3 : 2
v) and put the numbers in the equation
_4_Al + _3_O2 --> __2_Al2O3