算数【応用】逆算

□に当てはまる数を答えなさい。

問１

100 – ( 31 ÷ □ + 6 ) = 1

答え
\(\dfrac{1}{3}\)
解き方
100 – ( 31 ÷ □ + 6 ) = 1
31 ÷ □ + 6 = 100 – 1 = 99
31 ÷ □ = 99 – 6 = 93
93 × □ = 31
□ = \(\dfrac{31}{93}\) = \(\dfrac{1}{3}\)

問２

( □ – 8 × 7 ) ÷ ( 16 × 4 – 17 × 2 ) + 1 = 100

答え
3026
解き方
( □ – 8 × 7 ) ÷ ( 16 × 4 – 17 × 2 ) + 1 = 100
( □ – 56 ) ÷ ( 64 – 34 ) = 100 – 1
( □ – 56 ) ÷ 30 = 99
□ – 56 = 99 × 30 = 2970
□ = 2970 + 56 = 3026

問３

2 ÷ ( \(\dfrac{4}{5}\) – \(\dfrac{3}{4}\) ) ÷ □ = \(\dfrac{5}{9}\)

答え
72
解き方
2 ÷ ( \(\dfrac{4}{5}\) – \(\dfrac{3}{4}\) ) ÷ □ = \(\dfrac{5}{9}\)
\(\dfrac{5}{9}\) × □ = 2 ÷ ( \(\dfrac{16}{20}\) – \(\dfrac{15}{20}\) )
□ = 2 ÷ \(\dfrac{1}{20}\) × \(\dfrac{9}{5}\)
□ = 2 × 20 × \(\dfrac{9}{5}\) = 72

問４

\(\dfrac{1}{2}\) + 0.6 × 4 – ( □ – 4 ) × \(\dfrac{5}{6}\) = 2

答え
\(5\dfrac{2}{25}\)
解き方
\(\dfrac{1}{2}\) + 0.6 × 4 – ( □ – 4 ) × \(\dfrac{5}{6}\) = 2
0.5 + 2.4 – ( □ – 4 ) × \(\dfrac{5}{6}\) = 2
( □ – 4 ) × \(\dfrac{5}{6}\) = 0.5 + 2.4 – 2 = 0.9
□ – 4 = \(\dfrac{9}{10}\) × \(\dfrac{6}{5}\) = \(\dfrac{27}{25}\) = \(1\dfrac{2}{25}\)
□ = \(1\dfrac{2}{25}\) + 4 = \(5\dfrac{2}{25}\)

問５

4.368 ÷ □ – 1.26 ÷ 14 = 1.002

答え
4
解き方
4.368 ÷ □ – 1.26 ÷ 14 = 1.002
4.368 ÷ □ – 0.09 = 1.002
4.368 ÷ □ = 1.002 + 0.09 = 1.092
1.092 × □ = 4.368
□ = 4.368 ÷ 1.092 = 4

問６

\(2\dfrac{6}{7}\) – \(\dfrac{1}{7}\) × ( □ – 4.5 ) = \(2\dfrac{1}{2}\)

答え
7
解き方
\(2\dfrac{6}{7}\) – \(\dfrac{1}{7}\) × ( □ – 4.5 ) = \(2\dfrac{1}{2}\)
\(\dfrac{1}{7}\) × ( □ – 4.5 ) = \(2\dfrac{6}{7}\) – \(2\dfrac{1}{2}\)
□ – 4.5 = ( \(\dfrac{20}{7}\) – \(\dfrac{5}{2}\) ) × 7
□ = 20 – 17.5 + 4.5 = 7

問７

( 1.8 – \(\dfrac{4}{3}\) ÷ 0.8 ) × ( \(1\dfrac{1}{3}\) – □ ) = \(\dfrac{1}{45}\)

答え
\(1\dfrac{1}{6}\)
解き方
( 1.8 – \(\dfrac{4}{3}\) ÷ 0.8 ) × ( \(1\dfrac{1}{3}\) – □ ) = \(\dfrac{1}{45}\)
( \(\dfrac{9}{5}\) – \(\dfrac{4}{3}\) ÷ \(\dfrac{4}{5}\) ) × ( \(\dfrac{4}{3}\) – □ ) = \(\dfrac{1}{45}\)
( \(\dfrac{9}{5}\) – \(\dfrac{4}{3}\) × \(\dfrac{5}{4}\) ) × ( \(\dfrac{4}{3}\) – □ ) = \(\dfrac{1}{45}\)
( \(\dfrac{9}{5}\) – \(\dfrac{5}{3}\) ) × ( \(\dfrac{4}{3}\) – □ ) = \(\dfrac{1}{45}\)
\(\dfrac{2}{15}\) × ( \(\dfrac{4}{3}\) – □ ) = \(\dfrac{1}{45}\)
\(\dfrac{4}{3}\) – □ = \(\dfrac{1}{45}\) × \(\dfrac{15}{2}\) = \(\dfrac{1}{6}\)
□ = \(\dfrac{4}{3}\) – \(\dfrac{1}{6}\) = \(\dfrac{7}{6}\) = \(1\dfrac{1}{6}\)

問８

1.75 + { ( 6 – \(1\dfrac{2}{7}\) × □ ) × 8.4 } ÷ 1.2 = \(7\dfrac{3}{4}\)

答え
4
解き方
1.75 + { ( 6 – \(1\dfrac{2}{7}\) × □ ) × 8.4 } ÷ 1.2 = \(7\dfrac{3}{4}\)
\(\dfrac{7}{4}\) + { ( 6 – \(\dfrac{9}{7}\) × □ ) × \(\dfrac{21}{2}\) } ÷ \(\dfrac{6}{5}\) = \(\dfrac{31}{4}\)
{ ( 6 – \(\dfrac{9}{7}\) × □ ) × \(\dfrac{42}{5}\) } × \(\dfrac{5}{6}\) = \(\dfrac{31}{4}\) – \(\dfrac{7}{4}\) = 6
( 6 – \(\dfrac{9}{7}\) × □ ) × 7 = 6
6 – \(\dfrac{9}{7}\) × □ = \(\dfrac{6}{7}\)
\(\dfrac{9}{7}\) × □ = 6 – \(\dfrac{6}{7}\) = \(\dfrac{36}{7}\)
□ = \(\dfrac{36}{7}\) × \(\dfrac{7}{9}\) = 4

問９

3 – ( 7.5 × \(\dfrac{2}{21}\) – 0.8 ÷ □ ) = \(2\dfrac{6}{7}\)

答え
\(1\dfrac{2}{5}\)
解き方
3 – ( 7.5 × \(\dfrac{2}{21}\) – 0.8 ÷ □ ) = \(2\dfrac{6}{7}\)
3 – ( \(\dfrac{15}{2}\) × \(\dfrac{2}{21}\) – \(\dfrac{4}{5}\) ÷ □ ) = \(\dfrac{20}{7}\)
3 – ( \(\dfrac{5}{7}\) – \(\dfrac{4}{5}\) ÷ □ ) = \(\dfrac{20}{7}\)
\(\dfrac{5}{7}\) – \(\dfrac{4}{5}\) ÷ □ = 3 – \(\dfrac{20}{7}\) = \(\dfrac{1}{7}\)
\(\dfrac{4}{5}\) ÷ □ = \(\dfrac{5}{7}\) – \(\dfrac{1}{7}\) = \(\dfrac{4}{7}\)
\(\dfrac{4}{7}\) × □ = \(\dfrac{4}{5}\)
□ = \(\dfrac{4}{5}\) × \(\dfrac{7}{4}\) = \(\dfrac{7}{5}\) = \(1\dfrac{2}{5}\)

問１０

( □ – \(\dfrac{5}{12}\) ) × \(1\dfrac{1}{8}\) = \(1\dfrac{11}{16}\)

答え
\(1\dfrac{11}{12}\)
解き方
( □ – \(\dfrac{5}{12}\) ) × \(1\dfrac{1}{8}\) = \(1\dfrac{11}{16}\)
( □ – \(\dfrac{5}{12}\) ) × \(\dfrac{9}{8}\) = \(\dfrac{27}{16}\)
□ – \(\dfrac{5}{12}\) = \(\dfrac{27}{16}\) × \(\dfrac{8}{9}\) = \(\dfrac{3}{2}\)
□ = \(\dfrac{3}{2}\) + \(\dfrac{5}{12}\) = \(\dfrac{23}{12}\) = \(1\dfrac{11}{12}\)

問１１

7 × 13 + □ × 6 + \(4\dfrac{1}{2}\) = 100

答え
\(\dfrac{3}{4}\) ( または 0.75 )
解き方
7 × 13 + □ × 6 + \(4\dfrac{1}{2}\) = 100
91 + □ × 6 + 4.5 = 100
□ × 6 = 100 – 91 – 4.5 = 4.5
□ = \(\dfrac{4.5}{6}\) = \(\dfrac{45}{60}\) = \(\dfrac{3}{4}\)

問１２

7 – ( □ – 1.4 ÷ \(2\dfrac{4}{5}\) ) × 5 = 1

答え
\(1\dfrac{7}{10}\) ( または 1.7 )
解き方
7 – ( □ – 1.4 ÷ \(2\dfrac{4}{5}\) ) × 5 = 1
7 – ( □ – \(\dfrac{7}{5}\) ÷ \(\dfrac{14}{5}\) ) × 5 = 1
( □ – \(\dfrac{7}{5}\) × \(\dfrac{5}{14}\) ) × 5 = 7 – 1 = 6
□ – \(\dfrac{1}{2}\) = \(\dfrac{6}{5}\)
□ = \(\dfrac{6}{5}\) + \(\dfrac{1}{2}\) = \(\dfrac{17}{10}\) = \(1\dfrac{7}{10}\)

問１３

16 × ( □ ÷ 7 – 35 ) – 8 = 88

答え
287
解き方
16 × ( □ ÷ 7 – 35 ) – 8 = 88
16 × ( □ ÷ 7 – 35 ) = 88 + 8 = 96
□ ÷ 7 – 35 = 96 ÷ 16 = 6
□ ÷ 7 = 6 + 35 = 41
□ = 41 × 7 = 287

問１４

( \(1\dfrac{6}{7}\) × \(1\dfrac{1}{6}\) – \(\dfrac{2}{7}\) ) ÷ \(\dfrac{1}{3}\) = □ × \(\dfrac{1}{2}\) + 4 ÷ 3.5

答え
9
解き方
( \(1\dfrac{6}{7}\) × \(1\dfrac{1}{6}\) – \(\dfrac{2}{7}\) ) ÷ \(\dfrac{1}{3}\) = □ × \(\dfrac{1}{2}\) + 4 ÷ 3.5
( \(\dfrac{13}{7}\) × \(\dfrac{7}{6}\) – \(\dfrac{2}{7}\) ) × 3 = □ × \(\dfrac{1}{2}\) + 4 ÷ \(\dfrac{7}{2}\)
( \(\dfrac{13}{6}\) – \(\dfrac{2}{7}\) ) × 3 = □ × \(\dfrac{1}{2}\) + 4 × \(\dfrac{2}{7}\)
\(\dfrac{13}{2}\) – \(\dfrac{6}{7}\) = □ × \(\dfrac{1}{2}\) + \(\dfrac{8}{7}\)
□ × \(\dfrac{1}{2}\) = \(\dfrac{13}{2}\) – \(\dfrac{6}{7}\) – \(\dfrac{8}{7}\) = \(\dfrac{63}{14}\) = \(\dfrac{9}{2}\)
□ = \(\dfrac{9}{2}\) × \(\dfrac{2}{1}\) = 9

問１５

{ ( \(3\dfrac{1}{6}\) + □ ) ÷ 1.25 – \(\dfrac{5}{6}\) } × \(5\dfrac{5}{18}\) = \(9\dfrac{1}{2}\)

答え
\(\dfrac{1}{8}\) ( または 0.125 )
解き方
{ ( \(3\dfrac{1}{6}\) + □ ) ÷ 1.25 – \(\dfrac{5}{6}\) } × \(5\dfrac{5}{18}\) = \(9\dfrac{1}{2}\)
{ ( \(\dfrac{19}{6}\) + □ ) ÷ \(\dfrac{5}{4}\) – \(\dfrac{5}{6}\) } × \(\dfrac{95}{18}\) = \(\dfrac{19}{2}\)
( \(\dfrac{19}{6}\) + □ ) × \(\dfrac{4}{5}\) – \(\dfrac{5}{6}\) = \(\dfrac{19}{2}\) × \(\dfrac{18}{95}\) = \(\dfrac{9}{5}\)
( \(\dfrac{19}{6}\) + □ ) × \(\dfrac{4}{5}\) = \(\dfrac{9}{5}\) + \(\dfrac{5}{6}\) = \(\dfrac{79}{30}\)
\(\dfrac{19}{6}\) + □ = \(\dfrac{79}{30}\) × \(\dfrac{5}{4}\) = \(\dfrac{79}{24}\)
□ = \(\dfrac{79}{24}\) – \(\dfrac{19}{6}\) = \(\dfrac{3}{24}\) = \(\dfrac{1}{8}\)

問１６

{ \(2\dfrac{3}{5}\) ÷ ( □ – 1.3 ) + \(\dfrac{1}{2}\) } × 0.6 = \(2\dfrac{1}{4}\)

答え
2.1 ( または \(2\dfrac{1}{10}\) )
解き方
{ \(2\dfrac{3}{5}\) ÷ ( □ – 1.3 ) + \(\dfrac{1}{2}\) } × 0.6 = \(2\dfrac{1}{4}\)
{ \(\dfrac{13}{5}\) ÷ ( □ – 1.3 ) + \(\dfrac{1}{2}\) } × \(\dfrac{3}{5}\) = \(\dfrac{9}{4}\)
\(\dfrac{13}{5}\) ÷ ( □ – 1.3 ) + \(\dfrac{1}{2}\) = \(\dfrac{9}{4}\) × \(\dfrac{5}{3}\) = \(\dfrac{15}{4}\)
\(\dfrac{13}{5}\) ÷ ( □ – 1.3 ) = \(\dfrac{15}{4}\) – \(\dfrac{1}{2}\) = \(\dfrac{13}{4}\)
\(\dfrac{13}{4}\) × ( □ – 1.3 ) = \(\dfrac{13}{5}\)
□ – 1.3 = \(\dfrac{13}{5}\) × \(\dfrac{4}{13}\) = \(\dfrac{4}{5}\) = 0.8
□ = 0.8 + 1.3 = 2.1

問１７

2 ÷ ( □ ÷ \(1\dfrac{1}{4}\) – 3.52 ÷ 0.8 × \(\dfrac{1}{4}\) ) = \(\dfrac{1}{2}\)

答え
\(6\dfrac{3}{8}\) ( または 6.375 )
解き方
2 ÷ ( □ ÷ \(1\dfrac{1}{4}\) – 3.52 ÷ 0.8 × \(\dfrac{1}{4}\) ) = \(\dfrac{1}{2}\)
2 ÷ ( □ ÷ \(\dfrac{5}{4}\) – 1.1 ) = \(\dfrac{1}{2}\)
\(\dfrac{1}{2}\) × ( □ ÷ \(\dfrac{5}{4}\) – 1.1 ) = 2
□ ÷ \(\dfrac{5}{4}\) – 1.1 = 2 × 2 = 4
□ ÷ \(\dfrac{5}{4}\) = 4 + 1.1 = 5.1
□ = \(\dfrac{51}{10}\) × \(\dfrac{5}{4}\) = \(\dfrac{51}{8}\) = \(6\dfrac{3}{8}\)

問１８

( □ – 11 ) × 0.25 – 3 = 5.25 ÷ 0.125 × \(3\dfrac{2}{3}\) ÷ 7

答え
111
解き方
( □ – 11 ) × 0.25 – 3 = 5.25 ÷ 0.125 × \(3\dfrac{2}{3}\) ÷ 7
( □ – 11 ) × \(\dfrac{1}{4}\) – 3 = \(\dfrac{21}{4}\) × 8 × \(\dfrac{11}{3}\) × \(\dfrac{1}{7}\) = 22
( □ – 11 ) × \(\dfrac{1}{4}\) = 22 + 3 = 25
□ – 11 = 25 × 4 = 100
□ = 100 + 11 = 111

問１９

( 1.25 – \(\dfrac{1}{8}\) ) × ( □ – \(\dfrac{4}{25}\) ÷ 0.075 ) = \(\dfrac{3}{8}\)

答え
\(2\dfrac{7}{15}\)
解き方
( 1.25 – \(\dfrac{1}{8}\) ) × ( □ – \(\dfrac{4}{25}\) ÷ 0.075 ) = \(\dfrac{3}{8}\)
( \(\dfrac{5}{4}\) – \(\dfrac{1}{8}\) ) × ( □ – \(\dfrac{4}{25}\) × \(\dfrac{40}{3}\) ) = \(\dfrac{3}{8}\)
\(\dfrac{9}{8}\) × ( □ – \(\dfrac{32}{15}\) ) = \(\dfrac{3}{8}\)
□ – \(\dfrac{32}{15}\) = \(\dfrac{3}{8}\) × \(\dfrac{8}{9}\) = \(\dfrac{1}{3}\)
□ = \(\dfrac{1}{3}\) + \(\dfrac{32}{15}\) = \(\dfrac{37}{15}\) = \(2\dfrac{7}{15}\)