小6算数 3学期の計算 第17回 全20問
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① $18\times(9+9)$
答え $324$
\begin{eqnarray*} &&18\times(9+9)\\ &=&18\times18\\ &=&324 \end{eqnarray*}② $8+7\times3$
答え $29$
\begin{eqnarray*} &&8+7\times3\\ &=&8+21\\ &=&29 \end{eqnarray*}③ $81-72\div9$
答え $73$
\begin{eqnarray*} &&81-72\div9\\ &=&81-8\\ &=&73 \end{eqnarray*}④ $15\times15-289\div17$
答え $208$
\begin{eqnarray*} &&15\times15-289\div17\\ &=&225-17\\ &=&208 \end{eqnarray*}⑤ $(100-51)\div99\times198$
答え $98$
\begin{eqnarray*} \require{cancel} &&(100-51)\div99\times198\\ &=&49\div99\times198\\ &=&\cfrac{49\times{}^2\bcancel{198}}{{}^1\bcancel{99}}\\ &=&98 \end{eqnarray*}⑥ $4761\div69$
答え $69$
⑦ $87.22\div8.9$
答え $9.8$
⑧ $10.1-9.99$
答え $0.11$
⑨ $10-0.101$
答え $9.899$
⑩ $0.101\times1.01$
答え $0.10201$
⑪ $59.9\times6.99$
答え $418.701$
⑫ $111.111\div3.3$
答え $33.67$
⑬ $\cfrac{3}{5}-\cfrac{5}{12}$
答え $\cfrac{11}{60}$
\begin{eqnarray*} &&\cfrac{3}{5}-\cfrac{5}{12}\\ &=&\cfrac{36}{60}-\cfrac{25}{60}\\ &=&\cfrac{11}{60} \end{eqnarray*}⑭ $3-\cfrac{9}{4}$
答え $\cfrac{3}{4}$
\begin{eqnarray*} &&3-\cfrac{9}{4}\\ &=&\cfrac{3}{1}-\cfrac{9}{4}\\ &=&\cfrac{12}{4}-\cfrac{9}{4}\\ &=&\cfrac{3}{4} \end{eqnarray*}⑮ $\cfrac{45}{46}\times\cfrac{23}{24}$
答え $\cfrac{15}{16}$
\begin{eqnarray*} \require{cancel} &&\cfrac{45}{46}\times\cfrac{23}{24}\\ &=&\cfrac{{}^{15}\bcancel{45}}{{}^2\bcancel{46}}\times\cfrac{{}^1\bcancel{23}}{{}^{8}\bcancel{24}}\\ &=&\cfrac{15}{16} \end{eqnarray*}⑯ $\cfrac{100}{27}\div\cfrac{200}{81}$
答え $\cfrac{3}{2} \left(1\cfrac{1}{2}\right)$
\begin{eqnarray*} &&\cfrac{100}{27}\div\cfrac{200}{81}\\ &&\cfrac{100}{27}\times\cfrac{81}{200}\\ &=&\cfrac{{}^1\bcancel{100}}{{}^1\bcancel{27}}\times\cfrac{{}^3\bcancel{81}}{{}^2\bcancel{200}}\\ &=&\cfrac{3}{2} \end{eqnarray*}⑰ $\cfrac{20}{21}\div\cfrac{10}{9}\div\cfrac{8}{7}$
答え $\cfrac{3}{4}$
\begin{eqnarray*} &&\cfrac{20}{21}\div\cfrac{10}{9}\div\cfrac{8}{7}\\ &=&\cfrac{20}{21}\times\cfrac{9}{10}\times\cfrac{7}{8}\\ &=&\cfrac{{}^1\bcancel{{}^2}\bcancel{20}}{{}^1\bcancel{{}^7}\bcancel{21}}\times\cfrac{{}^3\bcancel{9}}{{}^1\bcancel{10}}\times\cfrac{{}^1\bcancel{7}}{{}^4\bcancel{8}}\\ &=&\cfrac{3}{4} \end{eqnarray*}⑱ $\cfrac{5}{6}\times\cfrac{9}{10}+\cfrac{15}{16}\div\cfrac{25}{24}$
答え $\cfrac{33}{20} \left(1\cfrac{13}{20}\right)$
\begin{eqnarray*} &&\cfrac{5}{6}\times\cfrac{9}{10}+\cfrac{15}{16}\div\cfrac{25}{24}\\ &=&\cfrac{5}{6}\times\cfrac{9}{10}+\cfrac{15}{16}\times\cfrac{24}{25}\\ &=&\cfrac{{}^1\bcancel{5}}{{}^2\bcancel{6}}\times\cfrac{{}^3\bcancel{9}}{{}^2\bcancel{10}}+\cfrac{{}^3\bcancel{15}}{{}^2\bcancel{16}}\times\cfrac{{}^3\bcancel{24}}{{}^5\bcancel{25}}\\ &=&\cfrac{3}{4}+\cfrac{9}{10}\\ &=&\cfrac{15}{20}+\cfrac{18}{20}\\ &=&\cfrac{33}{20} \end{eqnarray*}⑲ $3.25-\cfrac{19}{6}$
答え $\cfrac{1}{12}$
\begin{eqnarray*} &&3.25-\cfrac{19}{6}\\ &=&\cfrac{{}^{13}\bcancel{325}}{{}^4\bcancel{100}}-\cfrac{19}{6}\\ &=&\cfrac{13}{4}-\cfrac{19}{6}\\ &=&\cfrac{39}{12}-\cfrac{38}{12}\\ &=&\cfrac{1}{12} \end{eqnarray*}⑳ $\cfrac{21}{8}\div1.75\div1.5$
答え $1$
\begin{eqnarray*} &&\cfrac{21}{8}\div1.75\div1.5\\ &=&\cfrac{21}{8}\div\cfrac{175}{100}\div\cfrac{15}{10}\\ &=&\cfrac{21}{8}\times\cfrac{{}^4\bcancel{100}}{{}^7\bcancel{175}}\times\cfrac{{}^2\bcancel{10}}{{}^3\bcancel{15}}\\ &=&\cfrac{{}^1\bcancel{{}^3}\bcancel{21}}{{}^1\bcancel{{}^2}\bcancel{8}}\times\cfrac{{}^1\bcancel{4}}{{}^1\bcancel{7}}\times\cfrac{{}^1\bcancel{2}}{{}^1\bcancel{3}}\\ &=&1 \end{eqnarray*}答え
$\boxed{\large{\ 1\ }}①324②29③73④208⑤98⑥69\\ ⑦9.8⑧0.11⑨9.899⑩0.10201⑪418.701⑫33.67\\ \boxed{\large{\ 2\ }}⑬\cfrac{11}{60}⑭\cfrac{3}{4}\\ ⑮\cfrac{15}{16}⑯\cfrac{3}{2} \left(1\cfrac{1}{2}\right)⑰\cfrac{3}{4}⑱\cfrac{33}{20} \left(1\cfrac{13}{20}\right)\\ ⑲\cfrac{1}{12}⑳1 $