□ にあてはまる数を答えなさい。
問１
\(\dfrac{1}{2}\) + 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 = \(\dfrac{9}{10}\)
□ – 4 = \(\dfrac{9}{\cancelto{5}{10}}\) × \(\dfrac{\cancelto{3}{6}}{5}\) = \(\dfrac{27}{25}\) = \(1\dfrac{2}{25}\)
□ = \(1\dfrac{2}{25}\) + 4 = \(5\dfrac{2}{25}\)
問２
( 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 ) × ( \(1\dfrac{1}{3}\) – □ ) = \(\dfrac{1}{45}\)
( \(\dfrac{9}{5}\) – \(\dfrac{4}{3}\) ÷ \(\dfrac{4}{5}\) ) × ( \(\dfrac{4}{3}\) – □ ) = \(\dfrac{1}{45}\)
( \(\dfrac{9}{5}\) – \(\dfrac{\cancel{4}}{3}\) × \(\dfrac{5}{\cancel{4}}\) ) × ( \(\dfrac{4}{3}\) – □ ) = \(\dfrac{1}{45}\)
( \(\dfrac{27}{15}\) – \(\dfrac{25}{15}\) ) × ( \(\dfrac{4}{3}\) – □ ) = \(\dfrac{1}{45}\)
\(\dfrac{2}{15}\) × ( \(\dfrac{4}{3}\) – □ ) = \(\dfrac{1}{45}\)
両辺に 45 をかける
6 × ( \(\dfrac{4}{3}\) – □ ) = 1
8 – 6 × □ = 1
6 × □ = 8 – 1 = 7
□ = \(\dfrac{7}{6}\) = \(1\dfrac{1}{6}\)
※分数より整数の計算の方が間違えにくい
問３
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 – \(\dfrac{9}{7}\) × □ ) × \(\dfrac{42}{5}\) } ÷ \(\dfrac{6}{5}\) = \(\dfrac{31}{4}\)
( 6 – \(\dfrac{9}{7}\) × □ ) × \(\dfrac{\cancelto{7}{42}}{\cancel{5}}\) × \(\dfrac{\cancel{5}}{\cancel{6}}\) = \(\dfrac{31}{4}\) – \(\dfrac{7}{4}\) = \(\dfrac{24}{4}\) = 6
( 6 – \(\dfrac{9}{7}\) × □ ) × 7 = 6
6 – \(\dfrac{9}{7}\) × □ = \(\dfrac{6}{7}\)
\(\dfrac{9}{7}\) × □ = 6 – \(\dfrac{6}{7}\) = \(\dfrac{36}{7}\)
□ = \(\dfrac{\cancelto{4}{36}}{\cancel{7}}\) × \(\dfrac{\cancel{7}}{\cancel{9}}\) = 4
問４
{ ( \(3\dfrac{1}{6}\) + □ ) ÷ 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 – \(\dfrac{5}{6}\) } × \(5\dfrac{5}{18}\) = \(9\dfrac{1}{2}\)
{ ( \(\dfrac{19}{6}\) + □ ) ÷ \(\dfrac{5}{4}\) – \(\dfrac{5}{6}\) } × \(\dfrac{95}{18}\) = \(\dfrac{19}{2}\)
( \(\dfrac{19}{6}\) + □ ) × \(\dfrac{4}{5}\) – \(\dfrac{5}{6}\) = \(\dfrac{\cancelto{1}{19}}{\cancelto{1}{2}}\) × \(\dfrac{\cancelto{9}{18}}{\cancelto{5}{95}}\) = \(\dfrac{9}{5}\)
( \(\dfrac{19}{6}\) + □ ) × \(\dfrac{4}{5}\) = \(\dfrac{9}{5}\) + \(\dfrac{5}{6}\) = \(\dfrac{54\ +\ 25}{30}\) = \(\dfrac{79}{30}\)
\(\dfrac{19}{6}\) + □ = \(\dfrac{79}{\cancelto{6}{30}}\) × \(\dfrac{\cancelto{1}{5}}{4}\) = \(\dfrac{79}{24}\)
□ = \(\dfrac{79}{24}\) – \(\dfrac{19}{6}\) = \(\dfrac{79\ -\ 76}{24}\) = \(\dfrac{3}{24}\) = \(\dfrac{1}{8}\)
※覚えておこう！
1.25 = \(\dfrac{125}{100}\) = \(\dfrac{25\ ×\ 5}{25\ ×\ 4}\) = \(\dfrac{5}{4}\)
問５
{ \(2\dfrac{3}{5}\) ÷ ( □ – 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 ) + \(\dfrac{1}{2}\) = \(\dfrac{\cancelto{3}{9}}{4}\) × \(\dfrac{5}{\cancel{3}}\) = \(\dfrac{15}{4}\)
\(\dfrac{13}{5}\) ÷ ( □ – 1.3 ) = \(\dfrac{15}{4}\) – \(\dfrac{1}{2}\) = \(\dfrac{13}{4}\)
\(\dfrac{13}{4}\) × ( □ – 1.3 ) = \(\dfrac{13}{5}\)
□ – 1.3 = \(\dfrac{\cancel{13}}{5}\) × \(\dfrac{4}{\cancel{13}}\) = \(\dfrac{4}{5}\) = 0.8
□ = 0.8 + 1.3 = 2.1
問６
( \(2\displaystyle\frac{11}{40}\) + □ ) ÷ 1.25 ｰ \(\displaystyle\frac{7}{12}\) = \(1\displaystyle\frac{44}{75}\)
- 答え
- \(\displaystyle\frac{7}{16}\)
- 解き方
- ( \(2\displaystyle\frac{11}{40}\) + □ ) ÷ 1.25 ｰ \(\displaystyle\frac{7}{12}\) = \(1\displaystyle\frac{44}{75}\)
( \(\displaystyle\frac{91}{40}\) + □ ) ÷ \(\dfrac{5}{4}\) = \(\displaystyle\frac{119}{75}\) + \(\displaystyle\frac{7}{12}\)
( \(\displaystyle\frac{91}{40}\) + □ ) ÷ \(\dfrac{5}{4}\) = \(\displaystyle\frac{476\ +\ 175}{300}\) = \(\displaystyle\frac{651}{300}\) = \(\displaystyle\frac{217}{100}\)
\(\displaystyle\frac{91}{40}\) + □ = \(\displaystyle\frac{217}{\cancelto{20}{100}}\) × \(\dfrac{\cancelto{1}{5}}{4}\) = \(\displaystyle\frac{217}{80}\)
□ = \(\displaystyle\frac{217}{80}\) – \(\displaystyle\frac{91}{40}\) = \(\displaystyle\frac{217\ -\ 182}{80}\) = \(\displaystyle\frac{35}{80}\) = \(\dfrac{7}{16}\)
問７
\(\displaystyle\frac{2025\ +\ □}{29}\) = 87 + 3 ÷ 0.0625
- 答え
- 1890
- 解き方
- \(\displaystyle\frac{2025\ +\ □}{29}\) = 87 + 3 ÷ 0.0625
\(\displaystyle\frac{2025\ +\ □}{29}\) = 87 + 3 ÷ \(\dfrac{1}{16}\)
\(\displaystyle\frac{2025\ +\ □}{29}\) = 87 + 3 × 16 = 135
2025 + □ = 135 × 29 = 3915
□ = 3915 – 2025 = 1890
※覚えておこう！
0.0625 = \(\dfrac{625}{10000}\) = \(\dfrac{25\ ×\ 25}{100\ ×\ 100}\) = \(\dfrac{1\ ×\ 1}{4\ ×\ 4}\) = \(\dfrac{1}{16}\)
問８
{ 18 + ( 3 × □ – \(\dfrac{1}{4}\) ) ÷ \(\dfrac{5}{9}\) } × 0.8 = 27
- 答え
- 3
- 解き方
- { 18 + ( 3 × □ – \(\dfrac{1}{4}\) ) ÷ \(\dfrac{5}{9}\) } × 0.8 = 27
{ 18 + ( 3 × □ – \(\dfrac{1}{4}\) ) ÷ \(\dfrac{5}{9}\) } × \(\dfrac{4}{5}\) = 27
18 + ( 3 × □ – \(\dfrac{1}{4}\) ) ÷ \(\dfrac{5}{9}\) = 27 × \(\dfrac{5}{4}\) = \(\dfrac{135}{4}\)
( 3 × □ – \(\dfrac{1}{4}\) ) ÷ \(\dfrac{5}{9}\) = \(33\dfrac{3}{4}\) – 18 = \(15\dfrac{3}{4}\) = \(\dfrac{63}{4}\)
3 × □ – \(\dfrac{1}{4}\) = \(\dfrac{\cancelto{7}{63}}{4}\) × \(\dfrac{5}{\cancel{9}}\) = \(\dfrac{35}{4}\)
3 × □ = \(\dfrac{35}{4}\) + \(\dfrac{1}{4}\) = \(\dfrac{36}{4}\) = 9
□ = 9 ÷ 3 = 3
問９
4 – { 5 – ( □ – 3 ) × \(\dfrac{1}{3}\) } × \(\dfrac{3}{4}\) = \(1\dfrac{1}{4}\)
- 答え
- 7
- 解き方
- 4 – { 5 – ( □ – 3 ) × \(\dfrac{1}{3}\) } × \(\dfrac{3}{4}\) = \(1\dfrac{1}{4}\)
{ 5 – ( □ – 3 ) × \(\dfrac{1}{3}\) } × \(\dfrac{3}{4}\) = 4 – \(\dfrac{5}{4}\) = \(\dfrac{11}{4}\)
5 – ( □ – 3 ) × \(\dfrac{1}{3}\) = \(\dfrac{11}{\cancel{4}}\) × \(\dfrac{\cancel{4}}{3}\) = \(\dfrac{11}{3}\)
( □ – 3 ) × \(\dfrac{1}{3}\) = 5 – \(\dfrac{11}{3}\) = \(\dfrac{4}{3}\)
□ – 3 = \(\dfrac{4}{3}\) × 3 = 4
□ = 4 + 3 = 7
問１０
[ 9 ÷ { 3 ÷ ( \(3\dfrac{8}{9}\) + \(3\dfrac{17}{18}\) ) } × □ ] ÷ ( \(\dfrac{3}{4}\) × 0.75 ) = 47
- 答え
- \(1\dfrac{1}{8}\)
- 解き方
- [ 9 ÷ { 3 ÷ ( \(3\dfrac{8}{9}\) + \(3\dfrac{17}{18}\) ) } × □ ] ÷ ( \(\dfrac{3}{4}\) × 0.75 ) = 47
[ 9 ÷ { 3 ÷ ( \(3\dfrac{16}{18}\) + \(3\dfrac{17}{18}\) ) } × □ ] ÷ ( \(\dfrac{3}{4}\) × \(\dfrac{3}{4}\) ) = 47
{ 9 ÷ ( 3 ÷ \(6\dfrac{\cancelto{11}{33}}{\cancelto{6}{18}}\) ) × □ } ÷ \(\dfrac{9}{16}\) = 47
{ 9 ÷ ( 3 ÷ \(\dfrac{47}{6}\) ) × □ } ÷ \(\dfrac{9}{16}\) = 47
9 ÷ ( 3 × \(\dfrac{6}{47}\) ) × □ = 47 × \(\dfrac{9}{16}\)
9 ÷ \(\dfrac{18}{47}\) × □ = 47 × \(\dfrac{9}{16}\)
9 × \(\dfrac{47}{18}\) × □ = 47 × \(\dfrac{9}{16}\)
両辺を 9 × 47 で割る
\(\dfrac{1}{18}\) × □ = \(\dfrac{1}{16}\)
□ = \(\dfrac{1}{\cancelto{8}{16}}\) × \(\cancelto{9}{18}\) = \(\dfrac{9}{8}\) = \(1\dfrac{1}{8}\)
※覚えておこう！
0.75 = \(\dfrac{75}{100}\) = \(\dfrac{25\ ×\ 3}{25\ ×\ 4}\) = \(\dfrac{3}{4}\)
問１１
( 0.8 ÷ 0.26 + □ × \(\dfrac{1}{13}\) ) ÷ 0.3 = 20
- 答え
- 38
- 解き方
- ( 0.8 ÷ 0.26 + □ × \(\dfrac{1}{13}\) ) ÷ 0.3 = 20
( \(\dfrac{4}{5}\) ÷ \(\dfrac{13}{50}\) + □ × \(\dfrac{1}{13}\) ) = 20 × 0.3 = 6
( \(\dfrac{4}{\cancel{5}}\) × \(\dfrac{\cancelto{10}{50}}{13}\) + □ × \(\dfrac{1}{13}\) ) = 20 × 0.3 = 6
\(\dfrac{1}{13}\) × ( 40 + □ ) = 6
40 + □ = 6 × 13 = 78
□ = 78 – 40 = 38
問１２
{ ( \(\dfrac{1}{4}\) + \(\dfrac{1}{2}\) ) ÷ \(\dfrac{3}{8}\) – ( □ + \(1\dfrac{1}{5}\) ) } × \(1\dfrac{1}{4}\) – 1 = 0
- 答え
- 0
- 解き方
- { ( \(\dfrac{1}{4}\) + \(\dfrac{1}{2}\) ) ÷ \(\dfrac{3}{8}\) – ( □ + \(1\dfrac{1}{5}\) ) } × \(1\dfrac{1}{4}\) – 1 = 0
{ ( \(\dfrac{1}{4}\) + \(\dfrac{2}{4}\) ) × \(\dfrac{8}{3}\) – ( □ + \(\dfrac{6}{5}\) ) } × \(\dfrac{5}{4}\) – 1 = 0
{ \(\dfrac{\cancel{3}}{\cancel{4}}\) × \(\dfrac{\cancelto{2}{8}}{\cancel{3}}\) – ( □ + \(\dfrac{6}{5}\) ) } × \(\dfrac{5}{4}\) – 1 = 0
{ 2 – ( □ + \(\dfrac{6}{5}\) ) } × \(\dfrac{5}{4}\) = 1
2 – ( □ + \(\dfrac{6}{5}\) ) = 1 × \(\dfrac{4}{5}\)
□ + \(\dfrac{6}{5}\) = 2 – \(\dfrac{4}{5}\) = \(\dfrac{6}{5}\)
□ = \(\dfrac{6}{5}\) – \(\dfrac{6}{5}\) = 0
問１３
\(\dfrac{1}{6}\) + \(\dfrac{8}{3}\) ÷ ( \(\dfrac{3}{4}\) – \(\dfrac{1}{12}\) ) + □ – \(\dfrac{7}{10}\) × ( \(1\dfrac{3}{4}\) – \(\dfrac{1}{6}\) – \(\dfrac{1}{12}\) ) ÷ \(\dfrac{7}{6}\) = 4.5
- 答え
- \(1\dfrac{7}{30}\)
- 解き方
\(\dfrac{1}{6}\) + \(\dfrac{8}{3}\) ÷ ( \(\dfrac{3}{4}\) – \(\dfrac{1}{12}\) ) + □ – \(\dfrac{7}{10}\) × ( \(1\dfrac{3}{4}\) – \(\dfrac{1}{6}\) – \(\dfrac{1}{12}\) ) ÷ \(\dfrac{7}{6}\) = 4.5
( ) を先に計算する。
\(\dfrac{3}{4}\) – \(\dfrac{1}{12}\) = \(\dfrac{9}{12}\) – \(\dfrac{1}{12}\) = \(\dfrac{\cancelto{2}{8}}{\cancelto{3}{12}}\) = \(\dfrac{2}{3}\)
\(1\dfrac{3}{4}\) – \(\dfrac{1}{6}\) – \(\dfrac{1}{12}\)
= \(\dfrac{7}{4}\) – \(\dfrac{1}{6}\) – \(\dfrac{1}{12}\)
= \(\dfrac{21}{12}\) – \(\dfrac{2}{12}\) – \(\dfrac{1}{12}\) = \(\dfrac{\cancelto{3}{18}}{\cancelto{\cancel{2}}{12}}\) = \(\dfrac{3}{2}\)
\(\dfrac{1}{6}\) + \(\dfrac{8}{3}\) ÷ \(\dfrac{2}{3}\) + □ – \(\dfrac{7}{10}\) × \(\dfrac{3}{2}\) ÷ \(\dfrac{7}{6}\) = 4.5
\(\dfrac{1}{6}\) + \(\dfrac{\cancelto{4}{8}}{\cancel{3}}\) × \(\dfrac{\cancel{3}}{\cancel{2}}\) + □ – \(\dfrac{\cancel{7}}{10}\) × \(\dfrac{3}{\cancel{2}}\) × \(\dfrac{\cancelto{3}{6}}{\cancel{7}}\) = 4.5
\(\dfrac{1}{6}\) + 4 + □ – 0.9 = 4.5
\(\dfrac{1}{6}\) + □ = 4.5 + 0.9 – 4 = 1.4
□ = \(\dfrac{7}{5}\) – \(\dfrac{1}{6}\) = \(\dfrac{42\ -\ 5}{30}\) = \(\dfrac{37}{30}\) = \(1\dfrac{7}{30}\)
問１４
0.8 ÷ 0.04 × ( □ – \(\dfrac{1}{4}\) ) ÷ 5 = 7
- 答え
- 2
- 解き方
- 0.8 ÷ 0.04 × ( □ – \(\dfrac{1}{4}\) ) ÷ 5 = 7
20 × ( □ – \(\dfrac{1}{4}\) ) ÷ 5 = 7
4 × ( □ – \(\dfrac{1}{4}\) ) = 7
4 × □ – 1 = 7
4 × □ = 7 + 1 = 8
□ = 8 ÷ 4 = 2
問１５
\(1\dfrac{1}{4}\) × { 0.375 × ( □ + \(\dfrac{1}{3}\) ) – \(\dfrac{1}{2}\) } + \(\dfrac{1}{8}\) = \(\dfrac{5}{8}\)
- 答え
- \(2\dfrac{1}{15}\)
- 解き方
- \(1\dfrac{1}{4}\) × { 0.375 × ( □ + \(\dfrac{1}{3}\) ) – \(\dfrac{1}{2}\) } + \(\dfrac{1}{8}\) = \(\dfrac{5}{8}\)
\(\dfrac{5}{4}\) × { \(\dfrac{3}{8}\) × ( □ + \(\dfrac{1}{3}\) ) – \(\dfrac{1}{2}\) } = \(\dfrac{5}{8}\) – \(\dfrac{1}{8}\) = \(\dfrac{1}{2}\)
\(\dfrac{5}{4}\) × { \(\dfrac{3}{8}\) × ( □ + \(\dfrac{1}{3}\) ) – \(\dfrac{1}{2}\) } = \(\dfrac{1}{2}\)
\(\dfrac{3}{8}\) × ( □ + \(\dfrac{1}{3}\) ) – \(\dfrac{1}{2}\) = \(\dfrac{1}{\cancel{2}}\) × \(\dfrac{\cancelto{2}{4}}{5}\) = \(\dfrac{2}{5}\)
\(\dfrac{3}{8}\) × ( □ + \(\dfrac{1}{3}\) ) = \(\dfrac{2}{5}\) + \(\dfrac{1}{2}\) = \(\dfrac{4\ +\ 5}{10}\) = \(\dfrac{9}{10}\)
□ + \(\dfrac{1}{3}\) = \(\dfrac{\cancelto{3}{9}}{\cancelto{5}{10}}\) × \(\dfrac{\cancelto{4}{8}}{\cancel{3}}\) = \(\dfrac{12}{5}\)
□ = \(\dfrac{12}{5}\) – \(\dfrac{1}{3}\) = \(\dfrac{36\ -\ 5}{15}\) = \(\dfrac{31}{15}\) = \(2\dfrac{1}{15}\)
※覚えておこう！
0.375 = \(\dfrac{375}{1000}\) = \(\dfrac{125\ ×\ 3}{125\ ×\ 8}\) = \(\dfrac{3}{8}\)
問１６
{ ( □ – \(1\dfrac{1}{4}\) ) ÷ 3 + \(1\dfrac{3}{10}\) } × 0.375 = \(\dfrac{3}{5}\)
- 答え
- 2.15 ( または \(2\dfrac{3}{20}\) )
- 解き方
- { ( □ – \(1\dfrac{1}{4}\) ) ÷ 3 + \(1\dfrac{3}{10}\) } × 0.375 = \(\dfrac{3}{5}\)
{ ( □ – \(\dfrac{5}{4}\) ) ÷ 3 + \(\dfrac{13}{10}\) } × \(\dfrac{3}{8}\) = \(\dfrac{3}{5}\)
( □ – \(\dfrac{5}{4}\) ) ÷ 3 + \(\dfrac{13}{10}\) = \(\dfrac{\cancel{3}}{5}\) × \(\dfrac{8}{\cancel{3}}\) = \(\dfrac{8}{5}\)
( □ – \(\dfrac{5}{4}\) ) ÷ 3 = \(\dfrac{8}{5}\) – \(\dfrac{13}{10}\) = \(\dfrac{16\ -\ 13}{10}\) = \(\dfrac{3}{10}\)
□ – \(\dfrac{5}{4}\) = \(\dfrac{3}{10}\) × 3 = \(\dfrac{9}{10}\)
□ = \(\dfrac{9}{10}\) + \(\dfrac{5}{4}\) = 0.9 + 1.25 = 2.15
問１７
\(1\dfrac{3}{4}\) × 1.6 ÷ ( 0.25 × 3 + □ ) – \(1\dfrac{1}{2}\) = 1.3
- 答え
- \(\dfrac{1}{4}\) ( または 0.25 )
- 解き方
- \(1\dfrac{3}{4}\) × 1.6 ÷ ( 0.25 × 3 + □ ) – \(1\dfrac{1}{2}\) = 1.3
\(\dfrac{7}{\cancel{4}}\) × \(\dfrac{\cancelto{2}{8}}{5}\) ÷ ( \(\dfrac{1}{4}\) × 3 + □ ) – \(\dfrac{3}{2}\) = \(\dfrac{13}{10}\)
\(\dfrac{14}{5}\) ÷ ( \(\dfrac{3}{4}\) + □ ) = \(\dfrac{13}{10}\) + \(\dfrac{3}{2}\) = \(\dfrac{13\ +\ 15}{10}\) = \(\dfrac{28}{10}\) = \(\dfrac{14}{5}\)
\(\dfrac{14}{5}\) × ( \(\dfrac{3}{4}\) + □ ) = \(\dfrac{14}{5}\)
\(\dfrac{3}{4}\) + □ = 1
□ = 1 – \(\dfrac{3}{4}\) = \(\dfrac{1}{4}\)
問１８
{ ( □ + 6.4 ) ÷ \(1\dfrac{3}{5}\) – \(1\dfrac{8}{15}\) } × 3.5 = 10.5
- 答え
- \(\dfrac{64}{75}\)
- 解き方
- { ( □ + 6.4 ) ÷ \(1\dfrac{3}{5}\) – \(1\dfrac{8}{15}\) } × 3.5 = 10.5
( □ + \(\dfrac{32}{5}\) ) ÷ \(\dfrac{8}{5}\) – \(1\dfrac{8}{15}\) = 10.5 ÷ 3.5 = 3
( □ + \(\dfrac{32}{5}\) ) ÷ \(\dfrac{8}{5}\) = 3 + \(1\dfrac{8}{15}\) = \(4\dfrac{8}{15}\)
□ = \(\dfrac{68}{15}\) × \(\dfrac{8}{5}\) = \(\dfrac{544}{75}\)
□ = \(\dfrac{544}{75}\) – \(\dfrac{32}{5}\) = \(\dfrac{544\ -\ 480}{75}\) = \(\dfrac{64}{75}\)
問１９
{ \(19\dfrac{1}{7}\) – ( □ + \(5\dfrac{2}{7}\) ) × 0.5 } ÷ \(\dfrac{3}{28}\) = 56
- 答え
- 21
- 解き方
- { \(19\dfrac{1}{7}\) – ( □ + \(5\dfrac{2}{7}\) ) × 0.5 } ÷ \(\dfrac{3}{28}\) = 56
\(\dfrac{134}{7}\) – ( □ + \(\dfrac{37}{7}\) ) × \(\dfrac{1}{2}\) = \(\cancelto{2}{56}\) × \(\dfrac{3}{\cancel{28}}\) = 6
( □ + \(\dfrac{37}{7}\) ) × \(\dfrac{1}{2}\) = \(\dfrac{134}{7}\) – 6 = \(\dfrac{92}{7}\)
□ + \(\dfrac{37}{7}\) = \(\dfrac{92}{7}\) × 2 = \(\dfrac{184}{7}\)
□ = \(\dfrac{184}{7}\) – \(\dfrac{37}{7}\) = \(\dfrac{147}{7}\) = 21
問２０
[ { ( □ ÷ 0.125 + 10 ) ÷ \(1\dfrac{2}{3}\) – 6 } × 0.75 + 3 ] ÷ \(2\dfrac{1}{2}\) = 9
- 答え
- \(5\dfrac{5}{12}\)
- 解き方
[ { ( □ ÷ 0.125 + 10 ) ÷ \(1\dfrac{2}{3}\) – 6 } × 0.75 + 3 ] ÷ \(2\dfrac{1}{2}\) = 9
[ { ( □ ÷ \(\dfrac{1}{8}\) + 10 ) ÷ \(\dfrac{5}{3}\) – 6 } × \(\dfrac{3}{4}\) + 3 ] ÷ \(\dfrac{5}{2}\) = 9
{ ( □ ÷ \(\dfrac{1}{8}\) + 10 ) ÷ \(\dfrac{5}{3}\) – 6 } × \(\dfrac{3}{4}\) + 3 = 9 × \(\dfrac{5}{2}\) = \(\dfrac{45}{2}\)
{ ( □ ÷ \(\dfrac{1}{8}\) + 10 ) ÷ \(\dfrac{5}{3}\) – 6 } × \(\dfrac{3}{4}\) = \(\dfrac{45}{2}\) – 3 = \(\dfrac{39}{2}\)
( □ ÷ \(\dfrac{1}{8}\) + 10 ) ÷ \(\dfrac{5}{3}\) – 6 = \(\dfrac{\cancelto{13}{39}}{\cancel{2}}\) × \(\dfrac{\cancelto{2}{4}}{\cancel{3}}\) = 26
( □ ÷ \(\dfrac{1}{8}\) + 10 ) ÷ \(\dfrac{5}{3}\) = 26 + 6 = 32
□ ÷ \(\dfrac{1}{8}\) + 10 = 32 × \(\dfrac{5}{3}\) = \(\dfrac{160}{3}\)
□ ÷ \(\dfrac{1}{8}\) = \(\dfrac{160}{3}\) – 10 = \(\dfrac{130}{3}\)
□ = \(\dfrac{\cancelto{65}{130}}{3}\) × \(\dfrac{1}{\cancelto{4}{8}}\) = \(5\dfrac{5}{12}\)
問２１
8.4 ÷ \(1\dfrac{2}{5}\) – { 6 × ( □ – \(\dfrac{1}{6}\) ) + 1 ÷ \(\dfrac{2}{3}\) } = \(2\dfrac{1}{2}\)
- 答え
- \(\dfrac{1}{2}\) ( または 0.5 )
- 解き方
- 8.4 ÷ \(1\dfrac{2}{5}\) – { 6 × ( □ – \(\dfrac{1}{6}\) ) + 1 ÷ \(\dfrac{2}{3}\) } = \(2\dfrac{1}{2}\)
\(\dfrac{42}{5}\) ÷ \(\dfrac{7}{5}\) – { 6 × ( □ – \(\dfrac{1}{6}\) ) + 1 × \(\dfrac{3}{2}\) } = \(\dfrac{5}{2}\)
\(\dfrac{\cancelto{6}{42}}{\cancel{5}}\) × \(\dfrac{\cancel{5}}{\cancel{7}}\) – { 6 × ( □ – \(\dfrac{1}{6}\) ) + \(\dfrac{3}{2}\) } = \(\dfrac{5}{2}\)
6 × ( □ – \(\dfrac{1}{6}\) ) + \(\dfrac{3}{2}\) = 6 – \(\dfrac{5}{2}\) = \(\dfrac{7}{2}\)
6 × ( □ – \(\dfrac{1}{6}\) ) = \(\dfrac{7}{2}\) – \(\dfrac{3}{2}\) = \(\dfrac{4}{2}\) = 2
□ – \(\dfrac{1}{6}\) = 2 ÷ 6 = \(\dfrac{1}{3}\)
□ = \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) = \(\dfrac{2\ +\ 1}{6}\) = \(\dfrac{3}{6}\) = \(\dfrac{1}{2}\)
問２２
8 ÷ ( □ – 0.375 ) × ( \(\dfrac{1}{36}\) + \(\dfrac{2}{27}\) ) = \(2\dfrac{4}{9}\) ÷ ( 1 – 0.25 )
- 答え
- \(\dfrac{5}{8}\) ( または 0.625 )
- 解き方
- 8 ÷ ( □ – 0.375 ) × ( \(\dfrac{1}{36}\) + \(\dfrac{2}{27}\) ) = \(2\dfrac{4}{9}\) ÷ ( 1 – 0.25 )
8 ÷ ( □ – \(\dfrac{3}{8}\) ) × ( \(\dfrac{3}{108}\) + \(\dfrac{8}{108}\) ) = \(\dfrac{22}{9}\) ÷ ( 1 – \(\dfrac{1}{4}\) )
8 ÷ ( □ – \(\dfrac{3}{8}\) ) × \(\dfrac{11}{108}\) = \(\dfrac{22}{9}\) × \(\dfrac{4}{3}\)
8 ÷ ( □ – \(\dfrac{3}{8}\) ) × \(\dfrac{11}{108}\) = \(\dfrac{88}{27}\)
8 ÷ ( □ – \(\dfrac{3}{8}\) ) = \(\dfrac{\cancelto{8}{88}}{\cancel{27}}\) × \(\dfrac{\cancelto{4}{108}}{\cancel{11}}\) = 32
32 × ( □ – \(\dfrac{3}{8}\) ) = 8
□ – \(\dfrac{3}{8}\) = 8 ÷ 32 = \(\dfrac{1}{4}\)
□ = \(\dfrac{1}{4}\) + \(\dfrac{3}{8}\) = \(\dfrac{2\ +\ 3}{8}\) = \(\dfrac{5}{8}\)