与えられた分数計算の問題を解く必要があります。合計14問あります。

1. 問題の内容

与えられた分数計算の問題を解く必要があります。合計14問あります。

2. 解き方の手順

分数の掛け算は分子同士、分母同士を掛けます。分数の割り算は、割る数の逆数を掛けることで計算します。約分できる場合は、計算の途中や計算結果で行います。

(1) $\frac{1}{2} \times \frac{1}{3} \div \frac{4}{3} = \frac{1}{2} \times \frac{1}{3} \times \frac{3}{4} = \frac{1 \times 1 \times 3}{2 \times 3 \times 4} = \frac{3}{24} = \frac{1}{8}$

(2) $\frac{12}{5} \times \frac{3}{8} \div \frac{3}{5} = \frac{12}{5} \times \frac{3}{8} \times \frac{5}{3} = \frac{12 \times 3 \times 5}{5 \times 8 \times 3} = \frac{180}{120} = \frac{3}{2}$

(3) $\frac{3}{10} \div \frac{1}{4} \times \frac{7}{12} = \frac{3}{10} \times \frac{4}{1} \times \frac{7}{12} = \frac{3 \times 4 \times 7}{10 \times 1 \times 12} = \frac{84}{120} = \frac{7}{10}$

(4) $\frac{5}{2} \div \frac{8}{5} \times \frac{4}{3} = \frac{5}{2} \times \frac{5}{8} \times \frac{4}{3} = \frac{5 \times 5 \times 4}{2 \times 8 \times 3} = \frac{100}{48} = \frac{25}{12}$

(5) $\frac{1}{9} \div \frac{6}{7} \div \frac{3}{8} = \frac{1}{9} \times \frac{7}{6} \times \frac{8}{3} = \frac{1 \times 7 \times 8}{9 \times 6 \times 3} = \frac{56}{162} = \frac{28}{81}$

(6) $\frac{1}{7} \div \frac{11}{6} \div \frac{2}{7} = \frac{1}{7} \times \frac{6}{11} \times \frac{7}{2} = \frac{1 \times 6 \times 7}{7 \times 11 \times 2} = \frac{42}{154} = \frac{3}{11}$

(7) $\frac{7}{12} \div \frac{1}{6} \div \frac{4}{9} = \frac{7}{12} \times \frac{6}{1} \times \frac{9}{4} = \frac{7 \times 6 \times 9}{12 \times 1 \times 4} = \frac{378}{48} = \frac{63}{8}$

(8) $\frac{3}{10} \div \frac{12}{5} \div \frac{1}{8} = \frac{3}{10} \times \frac{5}{12} \times \frac{8}{1} = \frac{3 \times 5 \times 8}{10 \times 12 \times 1} = \frac{120}{120} = 1$

(9) $\frac{4}{5} \times \frac{1}{2} \div \frac{2}{5} \times \frac{8}{11} = \frac{4}{5} \times \frac{1}{2} \times \frac{5}{2} \times \frac{8}{11} = \frac{4 \times 1 \times 5 \times 8}{5 \times 2 \times 2 \times 11} = \frac{160}{220} = \frac{8}{11}$

(10) $\frac{7}{4} \times \frac{3}{4} \div \frac{3}{5} \times \frac{8}{9} = \frac{7}{4} \times \frac{3}{4} \times \frac{5}{3} \times \frac{8}{9} = \frac{7 \times 3 \times 5 \times 8}{4 \times 4 \times 3 \times 9} = \frac{840}{432} = \frac{35}{18}$

(11) $\frac{3}{2} \div \frac{1}{6} \times \frac{4}{5} \times \frac{3}{8} = \frac{3}{2} \times \frac{6}{1} \times \frac{4}{5} \times \frac{3}{8} = \frac{3 \times 6 \times 4 \times 3}{2 \times 1 \times 5 \times 8} = \frac{216}{80} = \frac{27}{10}$

(12) $\frac{7}{4} \times \frac{3}{10} \times \frac{5}{6} \div \frac{1}{8} = \frac{7}{4} \times \frac{3}{10} \times \frac{5}{6} \times \frac{8}{1} = \frac{7 \times 3 \times 5 \times 8}{4 \times 10 \times 6 \times 1} = \frac{840}{240} = \frac{7}{2}$

(13) $\frac{3}{8} \div \frac{10}{7} \times \frac{6}{7} \div \frac{7}{10} = \frac{3}{8} \times \frac{7}{10} \times \frac{6}{7} \times \frac{10}{7} = \frac{3 \times 7 \times 6 \times 10}{8 \times 10 \times 7 \times 7} = \frac{1260}{3920} = \frac{9}{28}$

(14) $\frac{1}{6} \div \frac{8}{3} \times \frac{3}{2} \div \frac{1}{12} = \frac{1}{6} \times \frac{3}{8} \times \frac{3}{2} \times \frac{12}{1} = \frac{1 \times 3 \times 3 \times 12}{6 \times 8 \times 2 \times 1} = \frac{108}{96} = \frac{9}{8}$

3. 最終的な答え

(1) $\frac{1}{8}$

(2) $\frac{3}{2}$

(3) $\frac{7}{10}$

(4) $\frac{25}{12}$

(5) $\frac{28}{81}$

(6) $\frac{3}{11}$

(7) $\frac{63}{8}$

(8) $1$

(9) $\frac{8}{11}$

(10) $\frac{35}{18}$

(11) $\frac{27}{10}$

(12) $\frac{7}{2}$

(13) $\frac{9}{28}$

(14) $\frac{9}{8}$