Đáp án:
$\begin{array}{l}
a)2600\\
b)1285\\
c)22500\\
d)0\\
e)0\\
g)4\\
h)100\\
k)1\\
i)1
\end{array}$
Giải thích các bước giải:
$\begin{array}{l}
a)13.64 + 52.34\\
= 13.4.16 + 52.34\\
= 52.16 + 52.34\\
= 52\left( {16 + 34} \right)\\
= 52.50\\
= 2600\\
b)15.12 + 85.13\\
= 15.12 + 85\left( {12 + 1} \right)\\
= 15.12 + 85.12 + 85\\
= 12\left( {15 + 85} \right) + 85\\
= 12.100 + 85\\
= 1285\\
c)225.92 + 4.450\\
= 25.9.4.23 + 4.25.18\\
= 100.9.23 + 100.18\\
= 100\left( {9.23 + 18} \right)\\
= 100.9.\left( {23 + 2} \right)\\
= 100.9.25\\
= 22500\\
d)\left( {2 + 4 + 6 + ... + 100} \right).\left( {16.333 - 48.111} \right)\\
= \left( {2 + 4 + 6 + ... + 100} \right).\left( {16.3.111 - 48.111} \right)\\
= \left( {2 + 4 + 6 + ... + 100} \right).\left( {48.111 - 48.111} \right)\\
= 0\\
e)20142014.2013 - 20132013.2014\\
= \left( {2014.10000 + 2014} \right).2013 - \left( {2013.10000 + 2013} \right).2014\\
= 2014.10001.2013 - 2013.10001.2014\\
= 0\\
g)2990.2990 - 2992.2988\\
= 2990.2990 - \left( {2990 + 2} \right)\left( {2990 - 2} \right)\\
= 2990.2990 - \left( {2990.2990 - 2.2990 + 2.2990 - 4} \right)\\
= 2990.2990 - \left( {2990.2990 - 4} \right)\\
= 2990.2990 - 2990.2990 + 4\\
= 4\\
h)\left( {1276.62 + 638.76} \right):\left( {24.12 + 76.13} \right)\\
= \left( {1276.62 + 638.2.38} \right):\left( {24.12 + 76\left( {12 + 1} \right)} \right)\\
= \left( {1276.62 + 1276.38} \right):\left( {24.12 + 76.12 + 76} \right)\\
= \left( {1276.\left( {62 + 38} \right)} \right):\left( {12.\left( {24 + 76} \right) + 76} \right)\\
= \left( {1276.100} \right):\left( {12.100 + 76} \right)\\
= 1276.100:1276\\
= 100\\
k)\left( {226.337 + 150} \right):\left( {1272 + 335.224} \right)\\
= \left( {226.337 + 150} \right):\left( {1272 + \left( {337 - 2} \right).\left( {226 - 2} \right)} \right)\\
= \left( {226.337 + 150} \right):\left( {1272 + 337.226 - 2\left( {337 + 226} \right) + 4} \right)\\
= \left( {226.337 + 150} \right):\left( {1272 + 337.226 - 2.563 + 4} \right)\\
= \left( {226.337 + 150} \right):\left( {337.226 + 150} \right)\\
= 1\\
i)\dfrac{{423134.846267 - 423133}}{{846267.423133 + 423134}}\\
= \dfrac{{846267.\left( {423133 + 1} \right) - 423133}}{{846267.423133 + 423134}}\\
= \dfrac{{846267.423133 + 846267 - 423133}}{{846267.423133 + 423134}}\\
= \dfrac{{846267.423133 + 423134}}{{846267.423133 + 423134}}\\
= 1
\end{array}$
