Activated magnetite ($Fe_3O_{4-{delta}}$) has the capability of decomposing $CO_2$ proportional to the ${delta}$-value at comparatively low temperature of $300^{circ}C$. To enhance the $CO_2$ decomposition capability of $Fe_3O_{4-{delta}}$, $(Fe_{1-x}Co_x)_3O_{4-{delta}}$ and $(Fe_{1-x}Mn_x)_3O_{4-{delta}}$ were synthesized and then reacted with $CO_2$. $Fe_{1-x}Co_xC_2O_4{cdot}2H_2O$ powders having Fe to Co mixing ratios of 9:1, 8:2, 7:3, 6:4, and 5:5 were synthesized by co-precipitation of $FeSO_4{cdot}7H_2O$ and $CoSO_4{cdot}7H_2O$ solutions with a $(NH_4)_2C_2O_4{cdot}H_2O$ solution. The same method was used to synthesize $Fe_{1-x}Mn_xC_2O_4{cdot}2H_2O$ powders having Fe to Mn mixing ratios of 9:1, 8:2, 7:3, 6:4, 5:5 with a $MnSO_4{cdot}4H_2O$ solution. The thermal decomposition of synthesized $Fe_{1-x}Co_xC_2O_4{cdot}2H_2O$ and $Fe_{1-x}Mn_xC_2O_4{cdot}2H_2O$ was analyzed in an Ar atmosphere with TG/DTA. The synthesized powders were heat-treated for 3 hours in an Ar atmosphere at $450^{circ}C$ to produce activated powders of $(Fe_{1-x}Co_x)_3O_{4-{delta}}$ and $(Fe_{1-x}Mn_x)_3O_{4-{delta}}$. The activated powders were reacted with a mixed gas (Ar : 85 %, $CO_2$ : 15 %) at $300^{circ}C$ for 12 hours. The exhaust gas was analyzed for $CO_2$ with a $CO_2$ gas analyzer. The decomposition of $CO_2$ was estimated by measuring $CO_2$ content in the exhaust gas after the reaction with $CO_2$. For $(Fe_{1-x}Mn_x)_3O_{4-{delta}}$, the amount of $Mn^{2+}$ oxidized to $Mn^{3+}$ increased as x increased. The ${delta}$ value and $CO_2$ decomposition efficiency decreased as x increased. When the ${delta}$ value was below 0.641, $CO_2$ was not decomposed. For $(Fe_{1-x}Co_x)_3O_{4-{delta}}$, the ${delta}$ value and $CO_2$ decomposition efficiency increased as x increased. At a ${delta}$ value of 0.857, an active state was maintained even after 12 hours of reaction and the amount of decomposed $CO_2$ was $52.844cm^3$ per 1 g of $(Fe_{0.5}Co_{0.5})_3O_{4-{delta}}$.