算数【入試】小数・分数を含む四則計算（問題文に）

問１

解き方: ( \(2\displaystyle\frac{11}{40}\) + \(\displaystyle\frac{3}{16}\) ) ÷ 1.25 – \(\displaystyle\frac{7}{12}\)

= ( \(\displaystyle\frac{91}{40}\) + \(\displaystyle\frac{3}{16}\) ) ÷ \(\dfrac{5}{4}\) – \(\displaystyle\frac{7}{12}\)

= ( \(\displaystyle\frac{91}{5}\) + \(\displaystyle\frac{3}{2}\) ) × \(\dfrac{1}{8}\) × \(\dfrac{4}{5}\) – \(\displaystyle\frac{7}{12}\)

= ( \(\displaystyle\frac{182}{10}\) + \(\displaystyle\frac{15}{10}\) ) × \(\dfrac{1}{\cancelto{2}{8}}\) × \(\dfrac{\cancel{4}}{5}\) – \(\displaystyle\frac{7}{12}\)

= \(\displaystyle\frac{197}{10}\) × \(\dfrac{1}{10}\) – \(\displaystyle\frac{7}{12}\)

= \(\displaystyle\frac{197}{100}\) – \(\displaystyle\frac{7}{12}\)

= \(\dfrac{1}{4}\) × ( \(\displaystyle\frac{197}{25}\) – \(\displaystyle\frac{7}{3}\) )

= \(\dfrac{1}{4}\) × ( \(\displaystyle\frac{591}{75}\) – \(\displaystyle\frac{175}{75}\) )

= \(\dfrac{1}{\cancel{4}}\) × \(\displaystyle\frac{\cancelto{104}{416}}{75}\) = \(1\dfrac{29}{75}\)

解き方: \(1\dfrac{1}{5}\) × ( \(2\dfrac{1}{3}\) – 1.75 ) ÷ \(2\dfrac{1}{3}\) + \(\dfrac{1}{4}\)

= \(\dfrac{6}{5}\) × ( \(\dfrac{7}{3}\) – \(\dfrac{7}{4}\) ) ÷ \(\dfrac{7}{3}\) + \(\dfrac{1}{4}\)

= \(\dfrac{6}{5}\) × ( \(\dfrac{7}{3}\) – \(\dfrac{7}{4}\) ) × \(\dfrac{3}{7}\) + \(\dfrac{1}{4}\)

= \(\dfrac{6}{5}\) × ( \(\dfrac{1}{3}\) – \(\dfrac{1}{4}\) ) × 3 + \(\dfrac{1}{4}\)

= \(\dfrac{\cancel{6}}{5}\) × \(\dfrac{1}{\cancelto{2}{12}}\) × 3 + \(\dfrac{1}{4}\)

= \(\dfrac{3}{10}\) + \(\dfrac{1}{4}\)

= \(\dfrac{6}{20}\) + \(\dfrac{5}{20}\) = \(\dfrac{11}{20}\)

解き方: 4.2 × ( \(\dfrac{5}{6}\) – \(\dfrac{5}{7}\) ) + \(\dfrac{5}{8}\) ÷ 0.5

= \(\dfrac{21}{5}\) × ( \(\dfrac{5}{6}\) – \(\dfrac{5}{7}\) ) + \(\dfrac{5}{8}\) ÷ \(\dfrac{1}{2}\)

= 21 × ( \(\dfrac{1}{6}\) – \(\dfrac{1}{7}\) ) + \(\dfrac{5}{8}\) × 2

= \(\cancel{21}\) × \(\dfrac{1}{\cancelto{2}{42}}\) + \(\dfrac{5}{\cancelto{4}{8}}\) × \(\cancel{2}\)

= \(\dfrac{2}{4}\) + \(\dfrac{5}{4}\) = \(\dfrac{7}{4}\) = \(1\dfrac{3}{4}\)

解き方: \(3\dfrac{3}{7}\) × \(2\dfrac{5}{8}\) ÷ 7.2 + \(\dfrac{1}{8}\) ÷ 0.7 – \(\dfrac{3}{56}\)

= \(\dfrac{\cancelto{3}{24}}{\cancel{7}}\) × \(\dfrac{\cancelto{3}{21}}{\cancel{8}}\) ÷ \(\dfrac{36}{5}\) + \(\dfrac{1}{8}\) ÷ \(\dfrac{7}{10}\) – \(\dfrac{3}{56}\)

= \(\cancel{9}\) × \(\dfrac{5}{\cancelto{4}{36}}\) + \(\dfrac{1}{\cancelto{4}{8}}\) × \(\dfrac{\cancelto{5}{10}}{7}\) – \(\dfrac{3}{56}\)

= \(\dfrac{5}{4}\) + \(\dfrac{5}{28}\) – \(\dfrac{3}{56}\)

= \(\dfrac{70}{56}\) + \(\dfrac{10}{56}\) – \(\dfrac{3}{56}\) = \(\dfrac{77}{56}\) = \(\dfrac{11}{8}\) = \(1\dfrac{3}{8}\)

解き方: 4.2 × \(\dfrac{7}{64}\) ÷ ( 4.5 – \(3\dfrac{5}{8}\) ) × \(2\dfrac{2}{3}\)

= \(\dfrac{21}{5}\) × \(\dfrac{7}{64}\) ÷ ( \(\dfrac{9}{2}\) – \(\dfrac{29}{8}\) ) × \(\dfrac{8}{3}\)

= \(\dfrac{21}{5}\) × \(\dfrac{7}{64}\) ÷ ( \(\dfrac{36}{8}\) – \(\dfrac{29}{8}\) ) × \(\dfrac{8}{3}\)

= \(\dfrac{21}{5}\) × \(\dfrac{7}{64}\) ÷ \(\dfrac{7}{8}\) × \(\dfrac{8}{3}\)

= \(\dfrac{\cancel{21}}{5}\) × \(\dfrac{7}{\cancel{64}}\) × \(\dfrac{\cancel{8}}{\cancel{7}}\) × \(\dfrac{\cancel{8}}{\cancel{3}}\) = \(\dfrac{7}{5}\) = \(1\dfrac{2}{5}\)

解き方: \(\dfrac{15}{16}\) – ( 4.2 × 0.375 + 1.8 ÷ \(2\dfrac{2}{3}\) ) ÷ 8

= \(\dfrac{15}{16}\) – ( \(\dfrac{21}{5}\) × \(\dfrac{3}{8}\) + \(\dfrac{9}{5}\) ÷ \(\dfrac{8}{3}\) ) × \(\dfrac{1}{8}\)

= \(\dfrac{15}{16}\) – ( \(\dfrac{63}{40}\) + \(\dfrac{9}{5}\) × \(\dfrac{3}{8}\) ) × \(\dfrac{1}{8}\)

= \(\dfrac{15}{16}\) – ( \(\dfrac{63}{40}\) + \(\dfrac{27}{40}\) ) × \(\dfrac{1}{8}\)

= \(\dfrac{15}{16}\) – \(\dfrac{\cancelto{9}{90}}{\cancelto{4}{40}}\) × \(\dfrac{1}{8}\)

= \(\dfrac{30}{32}\) – \(\dfrac{9}{32}\) = \(\dfrac{21}{32}\)