- 小数・分数を含む四則計算
- 小数と分数、どちらが計算しやすいか考えよう！
かけ算・わり算 ⇒ 分数のほうが計算しやすい
たし算・引き算 ⇒ 小数のほうが計算しやすいこともある
※悩んだら、分数に変換する
問１
\(（１）\dfrac{2}{5} + 1.35\ =\)
- 答え（１）
- 1.75 ( または、\(1\dfrac{3}{4}\) )
- 解き方（１）
- \(\dfrac{2}{5}\) + 1.35
= 0.4 + 1.35 = 1.75
※覚えておこう！
\(\dfrac{1}{5}\) = \(\dfrac{2}{10}\) = 0.2
\(\dfrac{2}{5}\) = \(\dfrac{4}{10}\) = 0.4
\(\dfrac{3}{5}\) = \(\dfrac{6}{10}\) = 0.6
\(\dfrac{4}{5}\) = \(\dfrac{8}{10}\) = 0.8
\(（２）\dfrac{7}{9}\ ÷\ \dfrac{14}{15}\ ×\ 2.1\ ×\ \dfrac{2}{3}\ =\)
- 答え（２）
- \(1\dfrac{1}{6}\)
- 解き方（２）
- \(\dfrac{7}{9}\) ÷ \(\dfrac{14}{15}\) × 2.1 × \(\dfrac{2}{3}\)
⇒ かけ算・わり算は分数同士の方が計算しやすいので、小数は分数に変換
= \(\dfrac{7}{9}\) × \(\dfrac{15}{14}\) × \(\dfrac{21}{10}\) × \(\dfrac{2}{3}\)
= \(\dfrac{7}{9}\) × \(\dfrac{3}{2}\) × \(\dfrac{3}{2}\) × \(\dfrac{2}{3}\)
= \(\dfrac{7}{9}\) × \(\dfrac{3}{2}\) = \(\dfrac{7}{6}\) = \(1\dfrac{1}{6}\)
\(（３）1\dfrac{1}{8}\ ×\ \dfrac{2}{5}\ ×\ 0.75\ ×\ 3.5\ ×\ 2\dfrac{2}{3}\ ×\ \dfrac{6}{7}\ ×\ \dfrac{1}{9}\ ×\ \dfrac{5}{6}\ ×\ 4\ =\)
- 答え（３）
- 1
- 解き方（３）
- \(1\dfrac{1}{8}\) × \(\dfrac{2}{5}\) × 0.75 × 3.5 × \(2\dfrac{2}{3}\) × \(\dfrac{6}{7}\) × \(\dfrac{1}{9}\) × \(\dfrac{5}{6}\) × 4
⇒ かけ算は分数同士の方が計算しやすいので、小数は分数に変換
= \(\dfrac{9}{8}\) × \(\dfrac{2}{5}\) × \(\dfrac{3}{4}\) × \(\dfrac{7}{2}\) × \(\dfrac{8}{3}\) × \(\dfrac{6}{7}\) × \(\dfrac{1}{9}\) × \(\dfrac{5}{6}\) × 4 = 1
※覚えておこう！
0.25 = \(\dfrac{1}{4}\)
0.75 = 3 × 0.25 = \(\dfrac{3}{4}\)
1.25 = 5 × 0.25 = \(\dfrac{5}{4}\)
\(（４）2\dfrac{3}{4}\ ÷\ 2.5\ ×\ \dfrac{2}{7}\ =\)
- 答え（４）
- \(\dfrac{11}{35}\)
- 解き方（４）
- \(2\dfrac{3}{4}\) ÷ 2.5 × \(\dfrac{2}{7}\)
⇒ かけ算/わり算は分数同士の方が計算しやすいので、小数は分数に変換
= \(\dfrac{11}{4}\) ÷ \(\dfrac{5}{2}\) × \(\dfrac{2}{7}\)
= \(\dfrac{11}{4}\) × \(\dfrac{2}{5}\) × \(\dfrac{2}{7}\) = \(\dfrac{11}{35}\)
問２
\(（１）1.36\ ×\ 0.5\ -\ \dfrac{2}{25}\ =\)
- 答え（１）
- \(\dfrac{3}{5}\) ( または、0.6 )
- 解き方（１）
- 1.36 × 0.5 － \(\dfrac{2}{25}\)
⇒ 小数は分数に変換
= \(\dfrac{136}{100}\) × \(\dfrac{5}{10}\) － \(\dfrac{2}{25}\)
= \(\dfrac{34}{25}\) × \(\dfrac{1}{2}\) － \(\dfrac{2}{25}\)
= \(\dfrac{17}{25}\) － \(\dfrac{2}{25}\)
= \(\dfrac{15}{25}\) = \(\dfrac{3}{5}\)
\(（２）1.25\ -\ 0.4\ ÷\ 1\dfrac{3}{5}\ =\)
- 答え（２）
- 1
- 解き方（２）
- 1.25 － 0.4 ÷ \(1\dfrac{3}{5}\)
⇒ わり算は分数同士の方が計算しやすいので、小数は分数に変換、帯分数は仮分数に変換
= 1.25 － \(\dfrac{4}{10}\) ÷ \(\dfrac{8}{5}\)
= 1.25 － \(\dfrac{2}{5}\) × \(\dfrac{5}{8}\)
= 1.25 － \(\dfrac{1}{4}\)
= 1.25 － 0.25 = 1
※覚えておこう！
\(\dfrac{1}{4}\) = \(\dfrac{25}{4\ ×\ 25}\) = \(\dfrac{25}{100}\) = 0.25
\(\dfrac{2}{4}\) ( = \(\dfrac{1}{2}\) ) = \(\dfrac{2\ ×\ 25}{4\ ×\ 25}\) = \(\dfrac{50}{100}\) = 0.5
\(\dfrac{3}{4}\) = \(\dfrac{3\ ×\ 25}{4\ ×\ 25}\) = \(\dfrac{75}{100}\) = 0.75
\(\dfrac{5}{4}\) = \(\dfrac{5\ ×\ 25}{4\ ×\ 25}\) = \(\dfrac{125}{100}\) = 1.25
\(（３）4\dfrac{3}{4}\ -\ 6\ ÷\ 3\dfrac{3}{7}\ +\ 3.25\ =\)
- 答え（３）
- 6.25 ( または、\(6\dfrac{1}{4}\) )
- 解き方（３）
- \(4\dfrac{3}{4}\) － 6 ÷ \(3\dfrac{3}{7}\) + 3.25
⇒ 帯分数は仮分数に変換
= \(\dfrac{19}{4}\) － 6 ÷ \(\dfrac{24}{7}\) + 3.25
= \(\dfrac{19}{4}\) － 6 × \(\dfrac{7}{24}\) + 3.25
= \(\dfrac{19}{4}\) － \(\dfrac{7}{4}\) + 3.25
= \(\dfrac{12}{4}\) + 3.25
= 3 + 3.25 = 6.25
\(（４）84\ ÷\ 0.28\ -\ 1.6\ ÷\ \dfrac{1}{5}\ =\)
- 答え（４）
- 292
- 解き方（４）
- 84 ÷ 0.28 － 1.6 ÷ \(\dfrac{1}{5}\)
⇒ わり算は分数同士の方が計算しやすいので、小数は分数に変換
= 84 ÷ \(\dfrac{28}{100}\) － \(\dfrac{16}{10}\) ÷ \(\dfrac{1}{5}\)
= 84 ÷ \(\dfrac{7}{25}\) － \(\dfrac{8}{5}\) × 5
= 84 × \(\dfrac{25}{7}\) － 8
= 12 × 25 － 8
= 300 － 8 = 292
\(（５）\dfrac{3}{5}\ +\ 0.4\ -\ \dfrac{4}{15}\ ÷\ 1.8\ ÷\ \dfrac{8}{27}\ =\)
- 答え（５）
- \(\dfrac{1}{2}\) ( または、0.5 )
- 解き方（５）
- \(\dfrac{3}{5}\) + 0.4 － \(\dfrac{4}{15}\) ÷ 1.8 ÷ \(\dfrac{8}{27}\)
⇒ わり算は分数同士の方が計算しやすいので、小数は分数に変換
= \(\dfrac{3}{5}\) + \(\dfrac{2}{5}\) － \(\dfrac{4}{15}\) ÷ \(\dfrac{9}{5}\) ÷ \(\dfrac{8}{27}\)
= 1 － \(\dfrac{4}{15}\) × \(\dfrac{5}{9}\) × \(\dfrac{27}{8}\)
= 1 － \(\dfrac{1}{2}\) = \(\dfrac{1}{2}\)
\(（６）1.2\ ÷\ \dfrac{2}{5}\ ×\ 0.75\ -\ 0.25\ =\)
- 答え（６）
- 2
- 解き方（６）
- 1.2 ÷ \(\dfrac{2}{5}\) × 0.75 － 0.25
⇒ かけ算・わり算は分数同士の方が計算しやすいので、小数は分数に変換
= \(\dfrac{6}{5}\) ÷ \(\dfrac{2}{5}\) × \(\dfrac{3}{4}\) － 0.25
= \(\dfrac{6}{5}\) × \(\dfrac{5}{2}\) × \(\dfrac{3}{4}\) － 0.25
= \(\dfrac{9}{4}\) － \(\dfrac{1}{4}\) = \(\dfrac{8}{4}\) = 2
\(（７）4.8\ ×\ 2\ -\ 0.9\ ÷\ \dfrac{1}{2}\ =\)
- 答え（７）
- 7.8
- 解き方（７）
- 4.8 × 2 － 0.9 ÷ \(\dfrac{1}{2}\)
= 4.8 × 2 － 0.9 × 2
= ( 4.8 － 0.9 ) × 2
= 3.9 × 2 = 7.8
\(（８）4.5\ -\ 1\dfrac{1}{7}\ ×\ 1\dfrac{5}{16}\ =\)
- 答え（８）
- 3
- 解き方（８）
- 4.5 － \(1\dfrac{1}{7}\) × \(1\dfrac{5}{16}\)
= \(\dfrac{9}{2}\) － \(\dfrac{8}{7}\) × \(\dfrac{21}{16}\)
= \(\dfrac{9}{2}\) － \(\dfrac{3}{2}\) = \(\dfrac{6}{2}\) = 3
\(（９）24\ ×\ \dfrac{7}{8}\ -\ 7\dfrac{1}{2}\ ×\ 2.4\ =\)
- 答え（９）
- 3
- 解き方（９）
- 24 × \(\dfrac{7}{8}\) － \(7\dfrac{1}{2}\) × 2.4
= 21 － \(\dfrac{15}{2}\) × \(\dfrac{12}{5}\)
= 21 – 18 = 3
\(（１０）\dfrac{1}{7}\ ÷\ 0.4\ +\ 1\dfrac{1}{7}\ ×\ 0.75\ -\ \dfrac{2}{3}\ =\)
- 答え（１０）
- \(\dfrac{23}{42}\)
- 解き方（１０）
- \(\dfrac{1}{7}\) ÷ 0.4 + \(1\dfrac{1}{7}\) × 0.75 － \(\dfrac{2}{3}\)
= \(\dfrac{1}{7}\) ÷ \(\dfrac{2}{5}\) + \(\dfrac{8}{7}\) × \(\dfrac{3}{4}\) － \(\dfrac{2}{3}\)
= \(\dfrac{1}{7}\) × \(\dfrac{5}{2}\) + \(\dfrac{6}{7}\) － \(\dfrac{2}{3}\)
= \(\dfrac{5}{14}\) + \(\dfrac{6}{7}\) － \(\dfrac{2}{3}\)
= \(\dfrac{10}{42}\) + \(\dfrac{36}{42}\) － \(\dfrac{28}{42}\) = \(\dfrac{23}{42}\)
問３
\(（１）(\ 2\dfrac{2}{5}\ +\ 0.6\ )\ ÷\ \dfrac{1}{8}\ ÷\ 2\dfrac{2}{5}\ +\ 10\ =\)
- 答え（１）
- 20
- 解き方（１）
- ( \(2\dfrac{2}{5}\) + 0.6 ) ÷ \(\dfrac{1}{8}\) ÷ \(2\dfrac{2}{5}\) + 10
⇒ わり算は分数同士の方が計算しやすいので、小数は分数に変換
= ( \(2\dfrac{2}{5}\) + \(\dfrac{3}{5}\) ) ÷ \(\dfrac{1}{8}\) ÷ \(\dfrac{12}{5}\) + 10
= 3 × 8 × \(\dfrac{5}{12}\) + 10
= 10 + 10 = 20
\(（２）(\ 0.625\ ÷\ 1\dfrac{2}{3}\ +\ 0.25\ )\ ×\ \dfrac{2}{5}\ =\)
- 答え（２）
- \(\dfrac{1}{4}\) ( または、0.25 )
- 解き方（２）
- ( 0.625 ÷ \(1\dfrac{2}{3}\) + 0.25 ) × \(\dfrac{2}{5}\)
⇒ かけ算・わり算は分数同士の方が計算しやすいので、小数は分数に変換
= ( \(\dfrac{625}{1000}\) ÷ \(\dfrac{5}{3}\) + \(\dfrac{25}{100}\) ) × \(\dfrac{2}{5}\)
⇒ \(\dfrac{625}{1000}\) = \(\dfrac{25\ × \ 25}{25\ ×\ 40}\), \(\dfrac{25}{100}\) = \(\dfrac{25}{25\ ×\ 4}\)
= ( \(\dfrac{5}{8}\) × \(\dfrac{3}{5}\) + \(\dfrac{1}{4}\) ) × \(\dfrac{2}{5}\)
= ( \(\dfrac{3}{8}\) + \(\dfrac{2}{8}\) ) × \(\dfrac{2}{5}\)
= \(\dfrac{5}{8}\) × \(\dfrac{2}{5}\) = \(\dfrac{1}{4}\)
\(（３）(\ 1\dfrac{2}{7}\ -\ 0.8\ )\ ×\ 35\ =\)
- 答え（３）
- 17
- 解き方（３）
- ( \(1\dfrac{2}{7}\) － 0.8 ) × 35
⇒ かけ算は分数同士の方が計算しやすいので、小数は分数に変換
= ( \(\dfrac{9}{7}\) － \(\dfrac{4}{5}\) ) × 35
= \(\dfrac{9}{7}\) × 35 － \(\dfrac{4}{5}\) × 35 ( 分配法則 )
= 45 － 28 = 17
\(（４）0.75\ +\ \dfrac{2}{3}\ ×\ (\ 1.25\ -\ \dfrac{5}{8}\ )\ =\)
- 答え（４）
- \(1\dfrac{1}{6}\)
- 解き方（４）
- 0.75 + \(\dfrac{2}{3}\) × ( 1.25 － \(\dfrac{5}{8}\) )
⇒ かけ算は分数同士の方が計算しやすいので、小数は分数に変換
= \(\dfrac{3}{4}\) + \(\dfrac{2}{3}\) × ( \(\dfrac{5}{4}\) － \(\dfrac{5}{8}\) )
= \(\dfrac{3}{4}\) + \(\dfrac{2}{3}\) × \(\dfrac{5}{8}\)
= \(\dfrac{3}{4}\) + \(\dfrac{5}{12}\)
= \(\dfrac{9}{12}\) + \(\dfrac{5}{12}\)
= \(\dfrac{14}{12}\) = \(\dfrac{7}{6}\) = \(1\dfrac{1}{6}\)
※覚えておこう！
0.25 = \(\dfrac{1}{4}\)
0.75 = 3 × 0.25 = 3 × \(\dfrac{1}{4}\) = \(\dfrac{3}{4}\)
1.25 = 5 × 0.25 = 5 × \(\dfrac{1}{4}\) = \(\dfrac{5}{4}\)
\(（５）\dfrac{4}{7}\ ×\ (\ 1\dfrac{2}{3}\ -\ 1.25\ )\ ÷\ 1\dfrac{2}{3}\ +\ \dfrac{3}{4}\ =\)
- 答え（５）
- \(\dfrac{25}{28}\)
- 解き方（５）
- \(\dfrac{4}{7}\) × ( \(1\dfrac{2}{3}\) － 1.25 ) ÷ \(1\dfrac{2}{3}\) + \(\dfrac{3}{4}\)
⇒ かけ算・わり算は分数同士の方が計算しやすいので、小数は分数に変換
= \(\dfrac{4}{7}\) × ( \(\dfrac{5}{3}\) － \(\dfrac{5}{4}\) ) ÷ \(\dfrac{5}{3}\) + \(\dfrac{3}{4}\)
= \(\dfrac{4}{7}\) × ( \(\dfrac{5}{3}\) － \(\dfrac{5}{4}\) ) × \(\dfrac{3}{5}\) + \(\dfrac{3}{4}\)
= \(\dfrac{4}{7}\) × ( \(\dfrac{5}{3}\) × \(\dfrac{3}{5}\) － \(\dfrac{5}{4}\) × \(\dfrac{3}{5}\) ) + \(\dfrac{3}{4}\) ( 分配法則 )
= \(\dfrac{4}{7}\) × ( 1 － \(\dfrac{3}{4}\) ) + \(\dfrac{3}{4}\)
= \(\dfrac{4}{7}\) × \(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)
= \(\dfrac{1}{7}\) + \(\dfrac{3}{4}\)
= \(\dfrac{4}{28}\) + \(\dfrac{21}{28}\) = \(\dfrac{25}{28}\)
\(（６）2.4\ ÷\ 1\dfrac{3}{5}\ +\ (\ \dfrac{5}{6}\ -\ 0.6\ )\ ÷\ 0.7\ =\)
- 答え（６）
- \(1\dfrac{5}{6}\)
- 解き方（６）
- 2.4 ÷ \(1\dfrac{3}{5}\) + ( \(\dfrac{5}{6}\) － 0.6 ) ÷ 0.7
⇒ わり算は分数同士の方が計算しやすいので、小数は分数に変換
= \(\dfrac{24}{10}\) ÷ \(\dfrac{8}{5}\) + ( \(\dfrac{5}{6}\) － \(\dfrac{3}{5}\) ) ÷ \(\dfrac{7}{10}\)
= \(\dfrac{12}{5}\) × \(\dfrac{5}{8}\) + ( \(\dfrac{25}{30}\) － \(\dfrac{18}{30}\) ) × \(\dfrac{10}{7}\)
= \(\dfrac{3}{2}\) + \(\dfrac{7}{30}\) × \(\dfrac{10}{7}\)
= \(\dfrac{3}{2}\) + \(\dfrac{1}{3}\)
= \(\dfrac{9}{6}\) + \(\dfrac{2}{6}\) = \(\dfrac{11}{6}\) = \(1\dfrac{5}{6}\)
\(（７）\{\ (\ 0.75\ -\ \dfrac{3}{8}\ )\ ÷\ \dfrac{3}{5}\ +\ 1.625\ \}\ ×\ \dfrac{8}{19}\ =\)
- 答え（７）
- 1
- 解き方（７）
- { ( 0.75 － \(\dfrac{1}{8}\) ) ÷ \(\dfrac{5}{6}\) + 1.625 } × \(\dfrac{8}{19}\)
⇒ かけ算・わり算は分数同士の方が計算しやすいので、小数は分数に変換
= { ( \(\dfrac{3}{4}\) － \(\dfrac{1}{8}\) ) ÷ \(\dfrac{5}{6}\) + \(\dfrac{1625}{1000}\) } × \(\dfrac{8}{19}\)
= { ( \(\dfrac{6}{8}\) － \(\dfrac{1}{8}\) ) × \(\dfrac{6}{5}\) + \(\dfrac{13}{8}\) } × \(\dfrac{8}{19}\)
= ( \(\dfrac{5}{8}\) × \(\dfrac{6}{5}\) + \(\dfrac{13}{8}\) ) × \(\dfrac{8}{19}\)
= ( \(\dfrac{6}{8}\) + \(\dfrac{13}{8}\) ) × \(\dfrac{8}{19}\)
= \(\dfrac{19}{8}\) × \(\dfrac{8}{19}\) = 1
\(（８）\{\ 5.9\ -\ (\ \dfrac{2}{5}\ +\ 2\dfrac{1}{3}\ ×\ 0.3\ )\ \}\ ÷\ 1\dfrac{1}{5}\ =\)
- ‘
- 答え（８）
- 4
- 解き方（８）
- { 5.9 － ( \(\dfrac{2}{5}\) + \(2\dfrac{1}{3}\) × 0.3 ) } ÷ \(1\dfrac{1}{5}\)
⇒ かけ算だが、小数のほうが計算しやすそう
= { 5.9 － ( 0.4 + \(\dfrac{7}{3}\) × 0.3 ) } ÷ \(\dfrac{6}{5}\)
= { 5.9 － ( 0.4 + 0.7 ) } × \(\dfrac{5}{6}\)
= ( 5.9 － 1.1 ) × \(\dfrac{5}{6}\)
= 4.8 × \(\dfrac{5}{6}\)
= 0.8 × 5 = 4
\(（９）(\ 3\dfrac{3}{5}\ -\ \dfrac{3}{4}\ )\ ÷\ 0.75\ -\ 2\dfrac{1}{4}\ ×\ 1\dfrac{7}{27}\ =\)
- 答え（９）
- \(\dfrac{29}{30}\)
- 解き方（９）
- ( \(3\dfrac{3}{5}\) － \(\dfrac{3}{4}\) ) ÷ 0.75 － \(2\dfrac{1}{4}\) × \(1\dfrac{7}{27}\)
⇒ わり算は分数同士の方が計算しやすいので、小数は分数に変換
= ( \(\dfrac{18}{5}\) － \(\dfrac{3}{4}\) ) ÷ \(\dfrac{3}{4}\) － \(\dfrac{9}{4}\) × \(\dfrac{34}{27}\)
= ( \(\dfrac{18}{5}\) － \(\dfrac{3}{4}\) ) × \(\dfrac{4}{3}\) － \(\dfrac{17}{6}\)
= ( \(\dfrac{18}{5}\) × \(\dfrac{4}{3}\) － \(\dfrac{3}{4}\) × \(\dfrac{4}{3}\) ) － \(\dfrac{17}{6}\) ( 分配法則 )
= ( \(\dfrac{24}{5}\) － 1 ) － \(\dfrac{17}{6}\)
= ( \(\dfrac{24}{5}\) － \(\dfrac{5}{5}\) ) － \(\dfrac{17}{6}\)
= \(\dfrac{19}{5}\) － \(\dfrac{17}{6}\)
= \(\dfrac{114}{30}\) － \(\dfrac{85}{30}\) = \(\dfrac{29}{30}\)
\(（１０）(\ 2.8\ +\ 3.25\ ÷\ \dfrac{5}{8}\ )\ ×\ 1.25\ =\)
- 答え（１０）
- 10
- 解き方（１０）
- ( 2.8 + 3.25 ÷ \(\dfrac{5}{8}\) ) × 1.25
= ( 2.8 + 3.25 × \(\dfrac{8}{5}\) ) × \(\dfrac{5}{4}\)
= 2.8 × \(\dfrac{5}{4}\) + 3.25 × \(\dfrac{8}{5}\) × \(\dfrac{5}{4}\) ( 分配法則 )
= 0.7 × 5 + 3.25 × 2
= 3.5 + 6.5 = 10
\(（１１）\dfrac{4}{3}\ ×\ 2.7\ -\ (\ \dfrac{7}{8}\ -\ 0.75\ )\ ÷\ 1.25\ =\)
- 答え（１１）
- 3.5 ( または、 \(3\dfrac{1}{2}\))
- 解き方（１１）
- \(\dfrac{4}{3}\) × 2.7 － ( \(\dfrac{7}{8}\) － 0.75 ) ÷ 1.25
= 4 × 0.9 － ( \(\dfrac{7}{8}\) － \(\dfrac{3}{4}\) ) ÷ \(\dfrac{5}{4}\)
= 3.6 － ( \(\dfrac{7}{8}\) － \(\dfrac{3}{4}\) ) × \(\dfrac{4}{5}\)
= 3.6 － ( \(\dfrac{7}{8}\) × \(\dfrac{4}{5}\) － \(\dfrac{3}{4}\) × \(\dfrac{4}{5}\) ) ( 分配法則 )
= 3.6 － ( \(\dfrac{7}{10}\) － \(\dfrac{3}{5}\) )
⇒ 分数が小数に変換しやすい、引き算は小数同士の方が計算しやすい
= 3.6 － ( 0.7 － 0.6 )
= 3.6 － 0.1 = 3.5
\(（１２）(\ 1\ -\ \dfrac{3}{4}\ )\ ×\ 6\ +\ 0.25\ ×\ 4\ =\)
- 答え（１２）
- \(2\dfrac{1}{2}\) ( または、2.5 )
- 解き方（１２）
- ( 1 － \(\dfrac{3}{4}\) ) × 6 + 0.25 × 4
= \(\dfrac{1}{4}\) × 6 + 1
= \(\dfrac{3}{2}\) + 1
= \(1\dfrac{1}{2}\) + 1 = \(2\dfrac{1}{2}\)
【別解】
( 1 － \(\dfrac{3}{4}\) ) × 6 + 0.25 × 4
= \(\dfrac{1}{4}\) × 6 + 0.25 × 4
= 0.25 × 6 + 0.25 × 4
= 0.25 × ( 6 + 4 )
= 0.25 × 10 = 2.5
※0.25の倍数は、「小数 ⇔ 分数」の変換を覚えておくと便利！
\(（１３）4\dfrac{1}{6}\ ÷\ (\ 1\dfrac{7}{8}\ -\ 0.25\ )\ ×\ 0.26\ =\)
- 答え（１３）
- \(\dfrac{2}{3}\)
- 解き方（１３）
- \(4\dfrac{1}{6}\) ÷ ( \(1\dfrac{7}{8}\) － 0.25 ) × 0.26
⇒ かけ算・わり算は分数同士の方が計算しやすいので、小数は分数に変換= \(\dfrac{25}{6}\) ÷ ( \(\dfrac{15}{8}\) － \(\dfrac{1}{4}\) ) × \(\dfrac{26}{100}\)
= \(\dfrac{25}{6}\) ÷ ( \(\dfrac{15}{8}\) － \(\dfrac{2}{8}\) ) × \(\dfrac{13}{50}\)
= \(\dfrac{25}{6}\) ÷ \(\dfrac{13}{8}\) × \(\dfrac{13}{50}\)
= \(\dfrac{25}{6}\) × \(\dfrac{8}{13}\) × \(\dfrac{13}{50}\) = \(\dfrac{2}{3}\)
\(（１４）(\ 4\dfrac{1}{2}\ -\ \dfrac{5}{19}\ ×\ 3\dfrac{4}{5}\ )\ ÷\ 1.25\ -\ \dfrac{4}{5}\ =\)
- 答え（１４）
- 2
- 解き方（１４）
- ( \(4\dfrac{1}{2}\) － \(\dfrac{5}{19}\) × \(3\dfrac{4}{5}\) ) ÷ 1.25 – \(\dfrac{4}{5}\)
= ( \(\dfrac{9}{2}\) － \(\dfrac{5}{19}\) × \(\dfrac{19}{5}\) ) ÷ \(\dfrac{5}{4}\) – \(\dfrac{4}{5}\)
= ( \(\dfrac{9}{2}\) － 1 ) × \(\dfrac{4}{5}\) – \(\dfrac{4}{5}\)
= \(\dfrac{7}{2}\) × \(\dfrac{4}{5}\) – \(\dfrac{4}{5}\)
= \(\dfrac{14}{5}\) – \(\dfrac{4}{5}\)
= \(\dfrac{10}{5}\) = 2
\(（１５）135\ ÷\ (\ 34\ -\ 25\ )\ ×\ (\ 4.6\ -\ \dfrac{3}{5}\ ×\ 3\ )\ =\)
- 答え（１５）
- 42
- 解き方（１５）
- 135 ÷ ( 34 － 25 ) × ( 4.6 － \(\dfrac{3}{5}\) × 3 )
= 135 ÷ 9 × ( \(\dfrac{23}{5}\) － \(\dfrac{9}{5}\) )
= 135 × \(\dfrac{1}{9}\) × \(\dfrac{14}{5}\)
= 42
\(（１６） (\ 3.5\ -\ \dfrac{4}{5}\ )\ ×\ \dfrac{2}{9}\ +\ (\ 0.8\ -\ \dfrac{2}{3}\ )\ ×\ 1\dfrac{7}{8}\ =\)
- 答え（１６）
- 0.85 ( または、\(\dfrac{17}{20}\) )
- 解き方（１６）
- ( 3.5 － \(\dfrac{4}{5}\)) × \(\dfrac{2}{9}\) + ( 0.8 － \(\dfrac{2}{3}\) ) × \(1\dfrac{7}{8}\)
= ( 3.5 － 0.8) × \(\dfrac{2}{9}\) + ( \(\dfrac{4}{5}\) － \(\dfrac{2}{3}\) ) × \(\dfrac{15}{8}\)
= 2.7 × \(\dfrac{2}{9}\) + ( \(\dfrac{12}{15}\) － \(\dfrac{10}{15}\) ) × \(\dfrac{15}{8}\)
= 0.3 × 2 + \(\dfrac{2}{15}\) × \(\dfrac{15}{8}\)
= 0.6 + \(\dfrac{1}{4}\)
= 0.6 + 0.25 = 0.85
\(（１７）\dfrac{12}{25}\ ×\ (\ 1.25\ -\ \dfrac{7}{8}\ )\ +\ 0.96\ ÷\ 5\dfrac{1}{3}\ =\)
- 答え（１７）
- \(\dfrac{9}{25}\)
- 解き方（１７）
- \(\dfrac{12}{25}\) × ( 1.25 － \(\dfrac{7}{8}\) ) + 0.96 ÷ \(5\dfrac{1}{3}\)
= \(\dfrac{12}{25}\) × ( \(\dfrac{5}{4}\) － \(\dfrac{7}{8}\) ) + \(\dfrac{24}{25}\) ÷ \(\dfrac{16}{3}\)
= \(\dfrac{12}{25}\) × ( \(\dfrac{10}{8}\) － \(\dfrac{7}{8}\) ) + \(\dfrac{24}{25}\) × \(\dfrac{3}{16}\)
= \(\dfrac{12}{25}\) × \(\dfrac{3}{8}\) + \(\dfrac{9}{50}\)
= \(\dfrac{9}{50}\) + \(\dfrac{9}{50}\) = \(\dfrac{18}{50}\) = \(\dfrac{9}{25}\)
\(（１８）3\ -\ (\ 1\ -\ 0.8\ ÷\ 1\dfrac{5}{7}\ )\ =\)
- 答え（１８）
- \(2\dfrac{7}{15}\)
- 解き方（１８）
- 3 － ( 1 － 0.8 ÷ \(1\dfrac{5}{7}\) )
= 3 － ( 1 － \(\dfrac{4}{5}\) ÷ \(\dfrac{12}{7}\) )
= 3 － ( 1 － \(\dfrac{4}{5}\) × \(\dfrac{7}{12}\) )
= 3 － ( 1 － \(\dfrac{7}{15}\) )
= 3 － \(\dfrac{8}{15}\)
= \(2\dfrac{15}{15}\) － \(\dfrac{8}{15}\) = \(2\dfrac{7}{15}\)
\(（１９）(\ \dfrac{4}{5}\ +\ 0.4\ ×\ \dfrac{1}{6}\ )\ ×\ 45\ -\ 6\ =\)
- 答え（１９）
- 33
- 解き方（１９）
- ( \(\dfrac{4}{5}\) + 0.4 × \(\dfrac{1}{6}\) ) × 45 － 6
= ( \(\dfrac{4}{5}\) + \(\dfrac{2}{5}\) × \(\dfrac{1}{6}\) ) × 45 － 6
= ( \(\dfrac{4}{5}\) + \(\dfrac{1}{15}\) ) × 45 － 6
= ( \(\dfrac{4}{5}\) × 45 + \(\dfrac{1}{15}\) × 45 ) － 6 ( 分配法則 )
= ( 36 + 3 ) － 6 = 33
\(（２０）(\ 3\ +\ 3\dfrac{3}{4}\ ÷\ 0.25\ )\ ÷\ 9\ =\)
- 答え（２０）
- 2
- 解き方（２０）
- ( 3 + \(3\dfrac{3}{4}\) ÷ 0.25 ) ÷ 9
= ( 3 + \(\dfrac{15}{4}\) ÷ \(\dfrac{1}{4}\) ) ÷ 9
= ( 3 + \(\dfrac{15}{4}\) × 4 ) ÷ 9
= ( 3 + 15 ) ÷ 9
= 18 ÷ 9 = 2
\(（２１）2\dfrac{3}{8}\ ÷\ 1.25\ -\ (\ 0.825\ -\ \dfrac{3}{8}\ )\ ×\ 3\dfrac{1}{3}\ =\)
- 答え（２１）
- \(\dfrac{2}{5}\) ( または、0.4 )
- 解き方（２１）
- \(2\dfrac{3}{8}\) ÷ 1.25 － ( 0.825 － \(\dfrac{3}{8}\) ) × \(3\dfrac{1}{3}\)
= \(\dfrac{19}{8}\) ÷ \(\dfrac{5}{4}\) － ( \(\dfrac{33}{40}\) － \(\dfrac{3}{8}\) ) × \(\dfrac{10}{3}\)
= \(\dfrac{19}{10}\) － ( \(\dfrac{33}{40}\) × \(\dfrac{10}{3}\) － \(\dfrac{3}{8}\) × \(\dfrac{10}{3}\) ) ( 分配法則 )
= \(\dfrac{19}{10}\) － ( \(\dfrac{11}{4}\) － \(\dfrac{5}{4}\) )
= \(\dfrac{19}{10}\) － \(\dfrac{6}{4}\)
= \(\dfrac{19}{10}\) － \(\dfrac{3}{2}\)
= \(\dfrac{19}{10}\) － \(\dfrac{15}{10}\) = \(\dfrac{4}{10}\) = \(\dfrac{2}{5}\)
\(（２２）(\ \dfrac{7}{24}\ ÷\ 0.125\ -\ 1\dfrac{8}{9}\ )\ ÷\ \dfrac{8}{3}\ =\)
- 答え（２２）
- \(\dfrac{1}{6}\)
- 解き方（２２）
- ( \(\dfrac{7}{24}\) ÷ 0.125 － \(1\dfrac{8}{9}\) ) ÷ \(\dfrac{8}{3}\)
= ( \(\dfrac{7}{24}\) ÷ \(\dfrac{1}{8}\) － \(\dfrac{17}{9}\) ) ÷ \(\dfrac{8}{3}\)
= ( \(\dfrac{7}{24}\) × 8 － \(\dfrac{17}{9}\) ) × \(\dfrac{3}{8}\)
= ( \(\dfrac{7}{3}\) － \(\dfrac{17}{9}\) ) × \(\dfrac{3}{8}\)
= ( \(\dfrac{21}{9}\) － \(\dfrac{17}{9}\) ) × \(\dfrac{3}{8}\)
= \(\dfrac{4}{9}\) × \(\dfrac{3}{8}\) = \(\dfrac{1}{6}\)
\(（２３）\dfrac{3}{8}\ ×\ (\ 3\dfrac{1}{8}\ ÷\ 0.375\ +\ 2\dfrac{1}{3}\ )\ =\)
- 答え（２３）
- 4
- 解き方（２３）
- \(\dfrac{3}{8}\) × ( \(3\dfrac{1}{8}\) ÷ 0.375 + \(2\dfrac{1}{3}\) )
= \(\dfrac{3}{8}\) × ( \(\dfrac{25}{8}\) ÷ \(\dfrac{3}{8}\) + \(\dfrac{7}{3}\) )
= \(\dfrac{3}{8}\) × ( \(\dfrac{25}{8}\) × \(\dfrac{8}{3}\) + \(\dfrac{7}{3}\) )
= \(\dfrac{3}{8}\) × ( \(\dfrac{25}{3}\) + \(\dfrac{7}{3}\) )
= \(\dfrac{3}{8}\) × \(\dfrac{32}{3}\) = 4
※覚えておこう！
0.125 = \(\dfrac{1}{8}\)
0.375 = 3 × 0.125 = \(\dfrac{3}{8}\)
0.625 = 5 × 0.125 = \(\dfrac{5}{8}\)
0.875 = 7 × 0.125 = \(\dfrac{7}{8}\)
\(（２４）41\ -\ (\ 31\ -\ 16\ )\ ×\ 1\dfrac{1}{3}\ ×\ 1.8\ =\)
- 答え（２４）
- 5
- 解き方（２４）
- 41 － ( 31 － 16 ) × \(1\dfrac{1}{3}\) × 1.8
= 41 － 15 × \(\dfrac{4}{3}\) × \(\dfrac{9}{5}\)
= 41 － 36 = 5
\(（２５）\dfrac{1}{3}\ ÷\ (\ \dfrac{3}{4}\ +\ \dfrac{7}{4}\ ÷\ 0.2\ )\ =\)
- 答え（２５）
- \(\dfrac{2}{57}\)
- 解き方（２５）
- \(\dfrac{1}{3}\) ÷ ( \(\dfrac{3}{4}\) + \(\dfrac{7}{4}\) ÷ 0.2 )
= \(\dfrac{1}{3}\) ÷ ( \(\dfrac{3}{4}\) + \(\dfrac{7}{4}\) ÷ \(\dfrac{1}{5}\) )
= \(\dfrac{1}{3}\) ÷ ( \(\dfrac{3}{4}\) + \(\dfrac{7}{4}\) × 5 )
= \(\dfrac{1}{3}\) ÷ ( \(\dfrac{3}{4}\) + \(\dfrac{35}{4}\) )
= \(\dfrac{1}{3}\) ÷ \(\dfrac{38}{4}\)
= \(\dfrac{1}{3}\) ÷ \(\dfrac{19}{2}\)
= \(\dfrac{1}{3}\) × \(\dfrac{2}{19}\) = \(\dfrac{2}{57}\)
\(（２６）1\ ÷\ \{\ 1\ ÷\ (\ 2\dfrac{7}{20}\ -\ 1.05\ )\ -\ \dfrac{85}{169}\ \}\ ×\ 1\dfrac{2}{13}\ =\)
- 答え（２６）
- \(4\dfrac{1}{3}\)
- 解き方（２６）
- 1 ÷ { 1 ÷ ( \(2\dfrac{7}{20}\) － 1.05 ) － \(\dfrac{85}{169}\) } × \(1\dfrac{2}{13}\)
= 1 ÷ { 1 ÷ ( \(\dfrac{47}{20}\) － \(\dfrac{21}{20}\) ) － \(\dfrac{85}{169}\) } × \(\dfrac{15}{13}\)
= 1 ÷ ( 1 ÷ \(\dfrac{13}{10}\) － \(\dfrac{85}{169}\) ) × \(\dfrac{15}{13}\)
= 1 ÷ ( \(\dfrac{10}{13}\) － \(\dfrac{85}{169}\) ) × \(\dfrac{15}{13}\)
= 1 ÷ ( \(\dfrac{130}{169}\) － \(\dfrac{85}{169}\) ) × \(\dfrac{15}{13}\)
= 1 ÷ \(\dfrac{45}{169}\) × \(\dfrac{15}{13}\)
= \(\dfrac{169}{45}\) × \(\dfrac{15}{13}\) = \(\dfrac{13}{3}\) = \(4\dfrac{1}{3}\)
\(（２７）(\ 3.76\ +\ 4.16\ )\ ÷\ 0.6\ -\ 3\dfrac{1}{5}\ =\)
- 答え（２７）
- 10
- 解き方（２７）
- ( 3.76 + 4.16 ) ÷ 0.6 － \(3\dfrac{1}{5}\)
= 7.92 ÷ \(\dfrac{3}{5}\) － \(\dfrac{16}{5}\)
= \(\dfrac{198}{25}\) × \(\dfrac{5}{3}\) － \(\dfrac{16}{5}\)
= \(\dfrac{66}{5}\) － \(\dfrac{16}{5}\) = \(\dfrac{50}{5}\) = 10
\(（２８）(\ 1.25\ ×\ 3.6\ -\ 1\dfrac{5}{6}\ )\ ÷\ 2\dfrac{2}{3}\ -\ 0.375\ =\)
- 答え（２８）
- \(\dfrac{5}{8}\)
- 解き方（２８）
- ( 1.25 × 3.6 － \(1\dfrac{5}{6}\) ) ÷ \(2\dfrac{2}{3}\) － 0.375
= ( \(\dfrac{5}{4}\) × \(\dfrac{18}{5}\) － \(\dfrac{11}{6}\) ) ÷ \(\dfrac{8}{3}\) － \(\dfrac{3}{8}\)
= ( \(\dfrac{9}{2}\) － \(\dfrac{11}{6}\) ) × \(\dfrac{3}{8}\) － \(\dfrac{3}{8}\)
= ( \(\dfrac{27}{6}\) － \(\dfrac{11}{6}\) ) × \(\dfrac{3}{8}\) － \(\dfrac{3}{8}\)
= \(\dfrac{8}{3}\) × \(\dfrac{3}{8}\) － \(\dfrac{3}{8}\)
= 1 － \(\dfrac{3}{8}\) = \(\dfrac{5}{8}\)
\(（２９）3\dfrac{1}{2}\ -\ (\ 1.25\ -\ 0.5\ ×\ \dfrac{1}{6}\ )\ ÷\ 1\dfrac{1}{6}\ =\)
- 答え（２９）
- \(2\dfrac{1}{2}\) ( または、2.5 )
- 解き方（２９）
- \(3\dfrac{1}{2}\) － ( 1.25 － 0.5 × \(\dfrac{1}{6}\) ) ÷ \(1\dfrac{1}{6}\)
= \(\dfrac{7}{2}\) － ( \(\dfrac{5}{4}\) － \(\dfrac{1}{2}\) × \(\dfrac{1}{6}\) ) ÷ \(\dfrac{7}{6}\)
= \(\dfrac{7}{2}\) － ( \(\dfrac{5}{4}\) － \(\dfrac{1}{12}\) ) × \(\dfrac{6}{7}\)
= \(\dfrac{7}{2}\) － ( \(\dfrac{5}{4}\) × \(\dfrac{6}{7}\) － \(\dfrac{1}{12}\) × \(\dfrac{6}{7}\) )
= \(\dfrac{7}{2}\) － ( \(\dfrac{15}{14}\) － \(\dfrac{1}{14}\) )
= \(\dfrac{7}{2}\) － 1 = \(\dfrac{5}{2}\) = \(2\dfrac{1}{2}\)
\(（３０）0.25\ ÷\ (\ 2\ -\ 0.75\ )\ +\ \dfrac{1}{2}\ ×\ (\ 2 -\ 1\dfrac{1}{5}\ )\ =\)
- 答え（３０）
- 0.6 ( または、\(\dfrac{3}{5}\) )
- 解き方（３０）
- 0.25 ÷ ( 2 － 0.75 ) + \(\dfrac{1}{2}\) × ( 2 － \(1\dfrac{1}{5}\) )
= 0.25 ÷ 1.25 + \(\dfrac{1}{2}\) × ( 2 － \(\dfrac{6}{5}\) )
= \(\dfrac{1}{4}\) ÷ \(\dfrac{5}{4}\) + \(\dfrac{1}{2}\) × ( 2 － 1.2 )
= \(\dfrac{1}{4}\) × \(\dfrac{4}{5}\) + \(\dfrac{1}{2}\) × 0.8
= \(\dfrac{1}{5}\) + 0.4
= 0.2 + 0.4 = 0.6
\(（３１）(\ 1\dfrac{1}{5}\ ×\ 0.125\ -\ 0.05\ )\ ×\ 200\ +\ 28\ =\)
- 答え（３１）
- 48
- 解き方（３１）
- ( \(1\dfrac{1}{5}\) × 0.125 －0.05 ) × 200 + 28
= ( \(\dfrac{6}{5}\) × 0.125 －0.05 ) × 200 + 28
= ( 6 × 0.125 －0.05 ) × 200 + 28
= ( 0.15 －0.05 ) × 200 + 28
= 0.1 × 200 + 28
= 20 + 28 = 48<