When carbon reacts with iron(III)oxide it displaces the iron as follows:
`3 C + 4 Fe_2O_3 -> 4Fe + 3CO_2`
This is an example of a single replacement reaction. Carbon is more reactive than iron so it reduces iron from Fe3+ to Fe. The carbon is oxidized to carbon dioxide.
There are other oxides of iron that don't react with carbon. Fe2+ in FeO has a lower tendency to be reduced but it reacts with carbon monoxide in a blast furnace to produce steel. The high temperature causes the carbon to burn in oxygen and produce CO (carbon monoxide). The CO then reacts with FeO as follows:
`FeO + CO -> Fe + CO_2`
This reduces FeO to Fe and oxidizes CO to CO2.