中1数学 1学期の計算 第1回 全19問
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① $(+1)+(+2)$
答え $+3$
② $(-3)+(-4)$
答え $-7$
③ $(-4)+(+6)$
答え $+2$
④ $(+0.3)+(-1)$
答え $-0.7$
⑤ $\left(-\cfrac{2}{3}\right)+\left(-\cfrac{1}{2}\right)$
答え $-\cfrac{7}{6}$
\begin{eqnarray*} &&\left(-\cfrac{2}{3}\right)+\left(-\cfrac{1}{2}\right)\\ &=&\left(-\cfrac{4}{6}\right)+\left(-\cfrac{3}{6}\right)\\ &=&-\cfrac{7}{6} \end{eqnarray*}⑥ $(-2)+(+5)+(-7)+(+1)$
答え $-3$
\begin{eqnarray*} &&(-2)+(+5)+(-7)+(+1)\\ &=&(+5)+(+1)+(-2)+(-7)\\ &=&(+6)+(-9)\\ &=&-3 \end{eqnarray*}⑦ $(-0.5)+(+1.8)+(-2)+(+3.3)+(-2.8)$
答え $-0.2$
\begin{eqnarray*} \require{cancel} &&(-0.5)+(+1.8)+(-2)+(+3.3)+(-2.8)\\ &=&(+1.8)+(+3.3)+(-0.5)+(-2)+(-2.8)\\ &=&(+5.1)+(-5.3)\\ &=&-0.2 \end{eqnarray*}⑧ $\left(-\cfrac{3}{4}\right)+\left(-\cfrac{1}{2}\right)+\left(-\cfrac{1}{8}\right)$
答え $-\cfrac{11}{8}$
\begin{eqnarray*} &&\left(-\cfrac{3}{4}\right)+\left(-\cfrac{1}{2}\right)+\left(-\cfrac{1}{8}\right)\\ &=&\left(-\cfrac{6}{8}\right)+\left(-\cfrac{4}{8}\right)+\left(-\cfrac{1}{8}\right)\\ &=&-\cfrac{11}{8} \end{eqnarray*}⑨ $\left(-\cfrac{2}{3}\right)+\left(-\cfrac{3}{4}\right)+\left(+\cfrac{5}{6}\right)$
答え $-\cfrac{7}{12}$
\begin{eqnarray*} &&\left(-\cfrac{2}{3}\right)+\left(-\cfrac{3}{4}\right)+\left(+\cfrac{5}{6}\right)\\ &=&\left(+\cfrac{5}{6}\right)+\left(-\cfrac{2}{3}\right)+\left(-\cfrac{3}{4}\right)\\ &=&\left(+\cfrac{10}{12}\right)+\left(-\cfrac{8}{12}\right)+\left(-\cfrac{9}{12}\right)\\ &=&\left(+\cfrac{10}{12}\right)+\left(-\cfrac{17}{12}\right)\\ &=&-\cfrac{7}{12} \end{eqnarray*}⑩ $(-1)+\left(+\cfrac{3}{5}\right)+\left(-\cfrac{1}{2}\right)$
答え $-\cfrac{9}{10}$
\begin{eqnarray*} &&(-1)+\left(+\cfrac{3}{5}\right)+\left(-\cfrac{1}{2}\right)\\ &=&\left(+\cfrac{3}{5}\right)+(-1)+\left(-\cfrac{1}{2}\right)\\ &=&\left(+\cfrac{6}{10}\right)+\left(-\cfrac{10}{10}\right)+\left(-\cfrac{5}{10}\right)\\ &=&\left(+\cfrac{6}{10}\right)+\left(-\cfrac{15}{10}\right)\\ &=&-\cfrac{9}{10} \end{eqnarray*}⑪ $\left(+\cfrac{2}{3}\right)+\left(-\cfrac{3}{8}\right)+\left(-\cfrac{5}{6}\right)+\left(+\cfrac{11}{12}\right)$
答え $+\cfrac{3}{8}$
\begin{eqnarray*} &&\left(+\cfrac{2}{3}\right)+\left(-\cfrac{3}{8}\right)+\left(-\cfrac{5}{6}\right)+\left(+\cfrac{11}{12}\right)\\ &=&\left(+\cfrac{2}{3}\right)+\left(+\cfrac{11}{12}\right)+\left(-\cfrac{3}{8}\right)+\left(-\cfrac{5}{6}\right)\\ &=&\left(+\cfrac{16}{24}\right)+\left(+\cfrac{22}{24}\right)+\left(-\cfrac{9}{24}\right)+\left(-\cfrac{20}{24}\right)\\ &=&\left(+\cfrac{38}{24}\right)+\left(-\cfrac{29}{24}\right)\\ &=&+\cfrac{\bcancel{9}}{\bcancel{24}}=+\cfrac{3}{8} \end{eqnarray*}① $(-8)-(+8)$
答え $-16$
\begin{eqnarray*} &&(-8)-(+8)\\ &=&(-8)+(-8)\\ &=&-16 \end{eqnarray*}② $0-(+3)$
答え $-3$
\begin{eqnarray*} &&0-(+3)\\ &=&0+(-3)\\ &=&-3 \end{eqnarray*}③ $(-13)-(-12)$
答え $-1$
\begin{eqnarray*} &&(-13)-(-12)\\ &=&(-13)+(+12)\\ &=&-1 \end{eqnarray*}④ $0-\left(-\cfrac{4}{5}\right)$
答え $+\cfrac{4}{5}$
\begin{eqnarray*} &&0-\left(-\cfrac{4}{5}\right)\\ &=&0+\left(+\cfrac{4}{5}\right)\\ &=&+\cfrac{4}{5} \end{eqnarray*}① $(-7)+(-5)-(-10)$
答え $-2$
\begin{eqnarray*} &&(-7)+(-5)-(-10)\\ &=&(-7)+(-5)+(+10)\\ &=&(+10)+(-7)+(-5)\\ &=&(+10)+(-12)\\ &=&-2 \end{eqnarray*}② $(+2)-\left(+\cfrac{2}{3}\right)+\left(-\cfrac{8}{9}\right)$
答え $+\cfrac{4}{9}$
\begin{eqnarray*} &&(+2)-\left(+\cfrac{2}{3}\right)+\left(-\cfrac{8}{9}\right)\\ &=&(+2)+\left(-\cfrac{2}{3}\right)+\left(-\cfrac{8}{9}\right)\\ &=&\left(+\cfrac{18}{9}\right)+\left(-\cfrac{4}{9}\right)+\left(-\cfrac{8}{9}\right)\\ &=&\left(+\cfrac{18}{9}\right)+\left(-\cfrac{12}{9}\right)\\ &=&+\cfrac{4}{9} \end{eqnarray*}③ $(-0.2)-\left(-\cfrac{1}{3}\right)+\left(-\cfrac{7}{15}\right)-\left(-\cfrac{2}{5}\right)$
答え $+\cfrac{1}{15}$
\begin{eqnarray*} &&(-0.2)-\left(-\cfrac{1}{3}\right)+\left(-\cfrac{7}{15}\right)-\left(-\cfrac{2}{5}\right)\\ &=&(-0.2)+\left(+\cfrac{1}{3}\right)+\left(-\cfrac{7}{15}\right)+\left(+\cfrac{2}{5}\right)\\ &=&\left(+\cfrac{1}{3}\right)+\left(+\cfrac{1}{5}\right)+(-0.2)+\left(-\cfrac{7}{15}\right)\\ &=&\left(+\cfrac{1}{3}\right)+\left(+\cfrac{2}{5}\right)+\left(-\cfrac{{}^1\bcancel{2}}{{}^5\bcancel{10}}\right)+\left(-\cfrac{7}{15}\right)\\ &=&\left(+\cfrac{5}{15}\right)+\left(+\cfrac{6}{15}\right)+\left(-\cfrac{3}{15}\right)+\left(-\cfrac{7}{15}\right)\\ &=&\left(+\cfrac{11}{15}\right)+\left(-\cfrac{10}{15}\right)\\ &=&+\cfrac{1}{15} \end{eqnarray*}④ $\left(-\cfrac{7}{3}\right)+\left(+\cfrac{3}{4}\right)-\left(+1\right)-\left(-\cfrac{1}{2}\right)$
答え $-\cfrac{25}{12}$
\begin{eqnarray*} &&\left(-\cfrac{7}{3}\right)+\left(+\cfrac{3}{4}\right)-\left(+1\right)-\left(-\cfrac{1}{2}\right)\\ &=&\left(-\cfrac{7}{3}\right)+\left(+\cfrac{3}{4}\right)+\left(-1\right)+\left(+\cfrac{1}{2}\right)\\ &=&\left(+\cfrac{3}{4}\right)+\left(+\cfrac{1}{2}\right)+\left(-\cfrac{7}{3}\right)+\left(-1\right)\\ &=&\left(+\cfrac{9}{12}\right)+\left(+\cfrac{6}{12}\right)+\left(-\cfrac{28}{12}\right)+\left(-\cfrac{12}{12}\right)\\ &=&\left(+\cfrac{15}{12}\right)+\left(-\cfrac{40}{12}\right)\\ &=&-\cfrac{25}{12} \end{eqnarray*}答え
$\boxed{\large{\ 1\ }}①+3②-7③+2④-0.7⑤-\cfrac{7}{6}⑥-3\\ ⑦-0.2⑧-\cfrac{11}{8}⑨-\cfrac{7}{12}⑩-\cfrac{9}{10}⑪+\cfrac{3}{8}\\ \boxed{\large{\ 2\ }}①-16②-3 ③-1④+\cfrac{4}{5}\\ \boxed{\large{\ 3\ }}①-2②+\cfrac{4}{9} ③+\cfrac{1}{15}④-\cfrac{25}{12} $