算数【応用】小数・分数を含む四則計算（問題文に）

問１

{ 5.5 × ( 2.2 – \(\dfrac{11}{15}\) ) – 1.4 } ÷ \(1\dfrac{2}{3}\) =

答え

4

解き方

{ 5.5 × ( 2.2 – \(\dfrac{11}{15}\) ) – 1.4 } ÷ \(1\dfrac{2}{3}\)
= { \(\dfrac{11}{2}\) × ( \(\dfrac{11}{5}\) – \(\dfrac{11}{15}\) ) – \(\dfrac{7}{5}\) } ÷ \(\dfrac{5}{3}\)
= { \(\dfrac{11}{2}\) × ( \(\dfrac{33}{15}\) – \(\dfrac{11}{15}\) ) – \(\dfrac{7}{5}\) } × \(\dfrac{3}{5}\)
= ( \(\dfrac{11}{\cancel{2}}\) × \(\dfrac{\cancelto{11}{22}}{15}\) – \(\dfrac{7}{5}\) ) × \(\dfrac{3}{5}\)
= ( \(\dfrac{121}{15}\) – \(\dfrac{21}{15}\) ) × \(\dfrac{3}{5}\)
= \(\dfrac{\cancelto{20}{100}}{\cancelto{5}{15}}\) × \(\dfrac{\cancel{3}}{\cancel{5}}\) = 4

問２

7.2 – { \(2\dfrac{1}{12}\) – ( 3.25 – \(2\dfrac{5}{6}\) ) } × \(2\dfrac{2}{5}\) =

答え

3.2 ( または、\(3\dfrac{1}{5}\))

解き方

7.2 – { \(2\dfrac{1}{12}\) – ( 3.25 – \(2\dfrac{5}{6}\) ) } × \(2\dfrac{2}{5}\)
= 7.2 – { \(\dfrac{25}{12}\) – ( \(\dfrac{\cancelto{13}{325}}{\cancelto{4}{100}}\) – \(\dfrac{17}{6}\) ) } × \(\dfrac{12}{5}\)
= 7.2 – { \(\dfrac{25}{12}\) – ( \(\dfrac{39}{12}\) – \(\dfrac{34}{12}\) ) } × \(\dfrac{12}{5}\)
= 7.2 – ( \(\dfrac{25}{12}\) – \(\dfrac{5}{12}\) ) × \(\dfrac{12}{5}\)
= 7.2 – \(\dfrac{20}{12}\) × \(\dfrac{12}{5}\)
= 7.2 – 4 = 3.2

問３

{ ( \(1\dfrac{6}{7}\) + \(\dfrac{4}{5}\) ) × 1.25 – \(\dfrac{9}{28}\) } ÷ 2.5 + \(2\dfrac{4}{5}\) =

答え

4

解き方

{ ( \(1\dfrac{6}{7}\) + \(\dfrac{4}{5}\) ) × 1.25 – \(\dfrac{9}{28}\) } ÷ 2.5 + \(2\dfrac{4}{5}\)
= { ( \(\dfrac{13}{7}\) + \(\dfrac{4}{5}\) ) × \(\dfrac{5}{4}\) – \(\dfrac{9}{28}\) } ÷ \(\dfrac{5}{2}\) + \(\dfrac{14}{5}\)
= ( \(\dfrac{65\ +\ 28}{\cancelto{7}{35}}\) × \(\dfrac{\cancel{5}}{4}\) – \(\dfrac{9}{28}\) ) × \(\dfrac{2}{5}\) + \(\dfrac{14}{5}\)
= ( \(\dfrac{93}{28}\) – \(\dfrac{9}{28}\) ) × \(\dfrac{2}{5}\) + \(\dfrac{14}{5}\)
= \(\dfrac{\cancelto{3}{84}}{\cancel{28}}\) × \(\dfrac{2}{5}\) + \(\dfrac{14}{5}\)
= \(\dfrac{6}{5}\) + \(\dfrac{14}{5}\) = \(\dfrac{20}{5}\) = 4

問４

( 1.6 + 1.3 ÷ 0.2 ) × \(1\dfrac{1}{9}\) ÷ 8 – ( \(\dfrac{3}{4}\) ÷ 0.75 × \(\dfrac{3}{8}\) – \(\dfrac{1}{4}\) ) =

答え

1

解き方

( 1.6 + 1.3 ÷ 0.2 ) × \(1\dfrac{1}{9}\) ÷ 8 – ( \(\dfrac{3}{4}\) ÷ 0.75 × \(\dfrac{3}{8}\) – \(\dfrac{1}{4}\) )
= ( 1.6 + 6.5 ) × \(\dfrac{\cancelto{5}{10}}{9}\) × \(\dfrac{1}{\cancelto{4}{8}}\) – ( \(\dfrac{3}{4}\) ÷ \(\dfrac{3}{4}\) × \(\dfrac{3}{8}\) – \(\dfrac{1}{4}\) )
= 8.1 × \(\dfrac{5}{36}\) – ( \(\dfrac{3}{4}\) × \(\dfrac{4}{3}\) × \(\dfrac{3}{8}\) – \(\dfrac{1}{4}\) )
= \(\dfrac{\cancelto{9}{81}}{\cancelto{2}{10}}\) × \(\dfrac{\cancel{5}}{\cancelto{4}{36}}\) – ( \(\dfrac{3}{8}\) – \(\dfrac{2}{8}\) )
= \(\dfrac{9}{8}\) – \(\dfrac{1}{8}\) = \(\dfrac{8}{8}\) = 1

問５

( 0.875 – \(\dfrac{3}{4}\) ) ÷ 2 + 2 ÷ \(\dfrac{4}{3}\) – \(\dfrac{3}{4}\) =

答え

\(\dfrac{13}{16}\)

解き方

( 0.875 – \(\dfrac{3}{4}\) ) ÷ 2 + 2 ÷ \(\dfrac{4}{3}\) – \(\dfrac{3}{4}\)
= ( \(\dfrac{\cancelto{\cancelto{7}{35}}{875}}{\cancelto{\cancelto{8}{40}}{1000}}\) – \(\dfrac{3}{4}\) ) × \(\dfrac{1}{2}\) + 2 × \(\dfrac{3}{4}\) – \(\dfrac{3}{4}\)
= \(\dfrac{7\ -\ 6}{8}\) × \(\dfrac{1}{2}\) + \(\dfrac{3}{4}\)
= \(\dfrac{1}{16}\) + \(\dfrac{12}{16}\) = \(\dfrac{13}{16}\)

問６

0.9 × ( \(7\dfrac{7}{8}\) – \(3\dfrac{3}{4}\) ) ÷ \(4\dfrac{1}{2}\) =

答え

\(\dfrac{33}{40}\)

解き方

0.9 × ( \(7\dfrac{7}{8}\) – \(3\dfrac{3}{4}\) ) ÷ \(4\dfrac{1}{2}\)
= \(\dfrac{9}{10}\) × ( \(7\dfrac{7}{8}\) – \(3\dfrac{6}{8}\) ) ÷ \(\dfrac{9}{2}\)
= \(\dfrac{\cancel{9}}{\cancelto{5}{10}}\) × \(4\dfrac{1}{8}\) × \(\dfrac{\cancel{2}}{\cancel{9}}\)
= \(\dfrac{1}{5}\) × \(\dfrac{33}{8}\) = \(\dfrac{33}{40}\)

問７

( 3 – 1.04 ) ÷ \(1\dfrac{2}{5}\) =

答え

1.4 ( または、\(1\dfrac{2}{5}\) )

解き方

( 3 – 1.04 ) ÷ \(1\dfrac{2}{5}\)
= 1.96 ÷ \(\dfrac{7}{5}\)
= 1.96 ÷ 1.4 = 1.4

問８

( \(2\dfrac{2}{7}\) × 0.625 – 0.5 ) ÷ ( 0.75 + 7 ÷ 8 ) =

答え

\(\dfrac{4}{7}\)

解き方

( \(2\dfrac{2}{7}\) × 0.625 – 0.5 ) ÷ ( 0.75 + 7 ÷ 8 )
= ( \(\dfrac{\cancelto{2}{16}}{7}\) × \(\dfrac{5}{\cancel{8}}\) – \(\dfrac{1}{2}\) ) ÷ ( \(\dfrac{3}{4}\) + \(\dfrac{7}{8}\) )
= ( \(\dfrac{10}{7}\) – \(\dfrac{1}{2}\) ) ÷ ( \(\dfrac{6}{8}\) + \(\dfrac{7}{8}\) )
= ( \(\dfrac{20}{14}\) – \(\dfrac{7}{14}\) ) ÷ \(\dfrac{13}{8}\)
= \(\dfrac{\cancel{13}}{\cancelto{7}{14}}\) × \(\dfrac{\cancelto{4}{8}}{\cancel{13}}\) = \(\dfrac{4}{7}\)

問９

( \(1\dfrac{3}{5}\) – \(\dfrac{3}{4}\) ) ÷ { ( 2 – 0.75 ) × \(\dfrac{17}{25}\) } =

答え

1

解き方

( \(1\dfrac{3}{5}\) – \(\dfrac{3}{4}\) ) ÷ { ( 2 – 0.75 ) × \(\dfrac{17}{25}\) }
= ( \(\dfrac{8}{5}\) – \(\dfrac{3}{4}\) ) ÷ ( 1.25 × \(\dfrac{17}{25}\) )
= \(\dfrac{32\ -\ 15}{20}\) ÷ ( \(\dfrac{\cancel{5}}{4}\) × \(\dfrac{17}{\cancelto{5}{25}}\) )
= \(\dfrac{17}{20}\) ÷ \(\dfrac{17}{20}\) = 1

問１０

( 2.19 + \(\dfrac{3}{20}\) × 7 – \(\dfrac{17}{50}\) + 1.6 ) × \(\dfrac{2}{9}\) =

答え

1

解き方

( 2.19 + \(\dfrac{3}{20}\) × 7 – \(\dfrac{17}{50}\) + 1.6 ) × \(\dfrac{2}{9}\)
= ( \(\dfrac{219}{100}\) + \(\dfrac{21}{20}\) – \(\dfrac{17}{50}\) + \(\dfrac{8}{5}\) ) × \(\dfrac{2}{9}\)
= \(\dfrac{219\ +\ 105\ -\ 34\ +\ 160}{100}\) × \(\dfrac{2}{9}\)
= \(\dfrac{\cancelto{9}{450}}{\cancelto{2}{100}}\) × \(\dfrac{2}{9}\) = 1

問１１

4 × \(1\dfrac{1}{7}\) ÷ \(2\dfrac{6}{7}\) – \(4\dfrac{1}{2}\) ÷ \(\dfrac{15}{16}\) × 0.225 =

答え

\(\dfrac{13}{25}\)

解き方

4 × \(1\dfrac{1}{7}\) ÷ \(2\dfrac{6}{7}\) – \(4\dfrac{1}{2}\) ÷ \(\dfrac{15}{16}\) × 0.225
= 4 × \(\dfrac{8}{7}\) ÷ \(\dfrac{20}{7}\) – \(\dfrac{9}{2}\) × \(\dfrac{16}{15}\) × \(\dfrac{9}{40}\)
= \(\cancel{4}\) × \(\dfrac{8}{\cancel{7}}\) × \(\dfrac{\cancel{7}}{\cancelto{5}{20}}\) – \(\dfrac{\cancelto{3}{9}}{\cancel{2}}\) × \(\dfrac{\cancelto{\cancel{2}}{16}}{\cancelto{5}{15}}\) × \(\dfrac{9}{\cancelto{5}{40}}\)
= \(\dfrac{8}{5}\) – \(\dfrac{27}{25}\) = \(\dfrac{40\ -\ 27}{25}\) = \(\dfrac{13}{25}\)

問１２

2.5 – ( \(\dfrac{1}{6}\) × 4.5 ÷ 0.375 – \(\dfrac{1}{3}\) ) =

答え

\(\dfrac{5}{6}\)

解き方

2.5 – ( \(\dfrac{1}{6}\) × 4.5 ÷ 0.375 – \(\dfrac{1}{3}\) )
= 2.5 – ( \(\dfrac{1}{6}\) × \(\dfrac{9}{2}\) ÷ \(\dfrac{3}{8}\) – \(\dfrac{1}{3}\) )
= 2.5 – ( \(\dfrac{1}{\cancelto{\cancel{2}}{6}}\) × \(\dfrac{\cancelto{\cancel{3}}{9}}{\cancel{2}}\) × \(\dfrac{\cancelto{\cancelto{2}{4}}{8}}{\cancel{3}}\) – \(\dfrac{1}{3}\) )
= 2.5 – ( 2 – \(\dfrac{1}{3}\) )
= \(\dfrac{5}{2}\) – \(\dfrac{5}{3}\)
= \(\dfrac{15}{6}\) – \(\dfrac{10}{6}\) = \(\dfrac{5}{6}\)

問１３

1.4 × \(2\dfrac{6}{7}\) – \(4\dfrac{2}{3}\) ÷ 3.5 + \(\dfrac{7}{12}\) =

答え

\(3\dfrac{1}{4}\)

解き方

1.4 × \(2\dfrac{6}{7}\) – \(4\dfrac{2}{3}\) ÷ 3.5 + \(\dfrac{7}{12}\)
= \(\dfrac{\cancel{7}}{\cancel{5}}\) × \(\dfrac{\cancelto{4}{20}}{\cancel{7}}\) – \(\dfrac{14}{3}\) ÷ \(\dfrac{7}{2}\) + \(\dfrac{7}{12}\)
= 4 – \(\dfrac{\cancelto{2}{14}}{3}\) × \(\dfrac{2}{\cancel{7}}\) + \(\dfrac{7}{12}\)
= 4 – \(\dfrac{4}{3}\) + \(\dfrac{7}{12}\)
= \(\dfrac{48\ -\ 16\ +\ 7}{12}\) = \(\dfrac{\cancelto{13}{39}}{\cancelto{4}{12}}\) = \(3\dfrac{1}{4}\)

問１４

0.5 × \(\dfrac{16}{3}\) + \(\dfrac{8}{25}\) × ( 2.125 – \(\dfrac{1}{4}\) ) =

答え

\(3\dfrac{4}{15}\)

解き方

0.5 × \(\dfrac{16}{3}\) + \(\dfrac{8}{25}\) × ( 2.125 – \(\dfrac{1}{4}\) )
= \(\dfrac{1}{\cancel{2}}\) × \(\dfrac{\cancelto{8}{16}}{3}\) + \(\dfrac{8}{25}\) × ( \(\dfrac{\cancelto{\cancelto{17}{85}}{2125}}{\cancelto{\cancelto{8}{40}}{1000}}\) – \(\dfrac{1}{4}\) )
= \(\dfrac{8}{3}\) + \(\dfrac{8}{25}\) × ( \(\dfrac{17}{8}\) – \(\dfrac{2}{8}\) )
= \(\dfrac{8}{3}\) + \(\dfrac{\cancel{8}}{\cancelto{5}{25}}\) × \(\dfrac{\cancelto{3}{15}}{\cancel{8}}\)
= \(\dfrac{40\ +\ 9}{15}\) = \(\dfrac{49}{15}\) = \(3\dfrac{4}{15}\)