小6算数 3学期の計算 第14回 全20問
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① $15\times(12-4)$
答え $120$
\begin{eqnarray*} &&15\times(12-4)\\ &=&15\times8\\ &=&120 \end{eqnarray*}② $6+3\times5$
答え $21$
\begin{eqnarray*} &&6+3\times5\\ &=&6+15\\ &=&21 \end{eqnarray*}③ $28-21\div7$
答え $25$
\begin{eqnarray*} &&28-21\div7\\ &=&28-3\\ &=&25 \end{eqnarray*}④ $12\times12-135\div15$
答え $135$
\begin{eqnarray*} &&12\times12-135\div15\\ &=&144-9\\ &=&135 \end{eqnarray*}⑤ $(66-41)\div16\times80$
答え $125$
\begin{eqnarray*} \require{cancel} &&(66-41)\div16\times80\\ &=&25\div16\times80\\ &=&\cfrac{25\times{}^5\bcancel{80}}{{}^1\bcancel{16}}\\ &=&125 \end{eqnarray*}⑥ $2795\div43$
答え $65$
⑦ $32.76\div3.9$
答え $8.4$
⑧ $6.03-2.78$
答え $3.25$
⑨ $6-0.25$
答え $5.75$
⑩ $0.05\times0.2$
答え $0.01$
⑪ $36.1\times1.69$
答え $61.009$
⑫ $316.26\div4.2$
答え $75.3$
⑬ $\cfrac{9}{14}+\cfrac{16}{21}$
答え $\cfrac{59}{42} \left(1\cfrac{17}{42}\right)$
\begin{eqnarray*} &&\cfrac{9}{14}+\cfrac{16}{21}\\ &=&\cfrac{27}{42}+\cfrac{32}{42}\\ &=&\cfrac{59}{42} \end{eqnarray*}⑭ $4-\cfrac{38}{15}$
答え $\cfrac{22}{15} \left(1\cfrac{7}{15}\right)$
\begin{eqnarray*} &&4-\cfrac{38}{15}\\ &=&\cfrac{4}{1}-\cfrac{38}{15}\\ &=&\cfrac{60}{15}-\cfrac{38}{15}\\ &=&\cfrac{22}{15} \end{eqnarray*}⑮ $\cfrac{45}{28}\times\cfrac{42}{75}$
答え $\cfrac{9}{10}$
\begin{eqnarray*} \require{cancel} &&\cfrac{45}{28}\times\cfrac{42}{75}\\ &=&\cfrac{{}^3\bcancel{45}}{{}^2\bcancel{28}}\times\cfrac{{}^3\bcancel{42}}{{}^{5}\bcancel{75}}\\ &=&\cfrac{9}{10} \end{eqnarray*}⑯ $\cfrac{38}{39}\div\cfrac{76}{65}$
答え $\cfrac{5}{6}$
\begin{eqnarray*} &&\cfrac{38}{39}\div\cfrac{76}{65}\\ &&\cfrac{38}{39}\times\cfrac{65}{76}\\ &=&\cfrac{{}^1\bcancel{38}}{{}^3\bcancel{39}}\times\cfrac{{}^5\bcancel{65}}{{}^2\bcancel{76}}\\ &=&\cfrac{5}{6} \end{eqnarray*}⑰ $\cfrac{4}{15}\div\cfrac{6}{5}\div\cfrac{8}{9}$
答え $\cfrac{1}{4}$
\begin{eqnarray*} &&\cfrac{4}{15}\div\cfrac{6}{5}\div\cfrac{8}{9}\\ &=&\cfrac{4}{15}\times\cfrac{5}{6}\times\cfrac{9}{8}\\ &=&\cfrac{{}^1\bcancel{{}^2}\bcancel{4}}{{}^1\bcancel{{}^3}\bcancel{15}}\times\cfrac{{}^1\bcancel{5}}{{}^1\bcancel{{}^3}\bcancel{6}}\times\cfrac{{}^1\bcancel{{}^3}\bcancel{9}}{{}^4\bcancel{8}}\\ &=&\cfrac{1}{4} \end{eqnarray*}⑱ $\cfrac{15}{16}\times\cfrac{4}{5}+\cfrac{7}{8}\div\cfrac{21}{32}$
答え $\cfrac{25}{12} \left(2\cfrac{1}{12}\right)$
\begin{eqnarray*} &&\cfrac{15}{16}\times\cfrac{4}{5}+\cfrac{7}{8}\div\cfrac{21}{32}\\ &=&\cfrac{15}{16}\times\cfrac{4}{5}+\cfrac{7}{8}\times\cfrac{32}{21}\\ &=&\cfrac{{}^3\bcancel{15}}{{}^4\bcancel{16}}\times\cfrac{{}^1\bcancel{4}}{{}^1\bcancel{5}}+\cfrac{{}^1\bcancel{7}}{{}^1\bcancel{8}}\times\cfrac{{}^4\bcancel{32}}{{}^3\bcancel{21}}\\ &=&\cfrac{3}{4}+\cfrac{4}{3}\\ &=&\cfrac{9}{12}+\cfrac{16}{12}\\ &=&\cfrac{25}{12} \end{eqnarray*}⑲ $1.25-\cfrac{7}{6}$
答え $\cfrac{1}{12}$
\begin{eqnarray*} &&1.25-\cfrac{7}{6}\\ &=&\cfrac{{}^5\bcancel{125}}{{}^4\bcancel{100}}-\cfrac{7}{6}\\ &=&\cfrac{5}{4}-\cfrac{7}{6}\\ &=&\cfrac{15}{12}-\cfrac{14}{12}\\ &=&\cfrac{1}{12} \end{eqnarray*}⑳ $\cfrac{4}{5}\times2.25\div\cfrac{18}{5}$
答え $\cfrac{1}{2}$
\begin{eqnarray*} &&\cfrac{4}{5}\times2.25\div\cfrac{18}{5}\\ &=&\cfrac{4}{5}\times\cfrac{225}{100}\times\cfrac{5}{18}\\ &=&\cfrac{4}{5}\times\cfrac{{}^9\bcancel{225}}{{}^4\bcancel{100}}\times\cfrac{5}{18}\\ &=&\cfrac{{}^1\bcancel{4}}{{}^1\bcancel{5}}\times\cfrac{{}^1\bcancel{9}}{{}^1\bcancel{4}}\times\cfrac{{}^1\bcancel{5}}{{}^2\bcancel{18}}\\ &=&\cfrac{1}{2} \end{eqnarray*}答え
$\boxed{\large{\ 1\ }}①120②21③25④135⑤125⑥65\\ ⑦8.4⑧3.25⑨5.75⑩0.01⑪61.009⑫75.3\\ \boxed{\large{\ 2\ }}⑬\cfrac{59}{42} \left(1\cfrac{17}{42}\right)⑭\cfrac{22}{15} \left(1\cfrac{7}{15}\right)\\ ⑮\cfrac{9}{10}⑯\cfrac{5}{6}⑰\cfrac{1}{4}⑱\cfrac{25}{12} \left(2\cfrac{1}{12}\right)\\ ⑲\cfrac{1}{12}⑳\cfrac{1}{2} $