約分、通分
分数の約分と通分について学びます。分母と分子を同じ数で割る約分や、分母をそろえる通分の方法を理解し、分数の計算に生かせるようにします。
【小学5年算数】分数のたし算、ひき算｜通分・帯分数の練習問題
このページは、小学5年生算数「分数のたし算・ひき算」の練習問題です。通分や約分を使った分数の計算、帯分数のたし算・ひき算、かっこを含む計算、文章問題まで、段階的に練習できます。分数の計算の復習や確認にご利用ください。
小学5年算数で学ぶ「分数のたし算、ひき算」とは？
分数のたし算やひき算では、分母が異なる分数の分母をそろえて計算する必要があります。 このときに使うのが「通分」です。また、計算した答えを簡単な分数にするときには「約分」を使います。 分数のたし算やひき算を正しく計算するために、通分や約分の考え方を身につけることが大切です。
分数のたし算、ひき算の計算問題
分数のたし算、ひき算の計算問題に取り組みましょう。
(1)\(\displaystyle \frac{2}{3}+\frac{1}{6}\)
\(\displaystyle \frac{5}{6}\)
(2)\(\displaystyle \frac{3}{5}+\frac{3}{10}\)
\(\displaystyle \frac{9}{10}\)
(3)\(\displaystyle \frac{1}{4}+\frac{2}{5}\)
\(\displaystyle \frac{13}{20}\)
(4)\(\displaystyle \frac{1}{12}+\frac{11}{30}\)
\(\displaystyle \frac{9}{20}\)
(5)\(\displaystyle \frac{5}{6}+\frac{1}{4}\)
\(\displaystyle \frac{13}{12}\)
(6)\(\displaystyle \frac{1}{2}+\frac{6}{7}\)
\(\displaystyle 1\frac{5}{14}\)
(7)\(\displaystyle \frac{9}{10}+2\frac{7}{12}\)
\(\displaystyle 3\frac{29}{60}\)
(8)\(\displaystyle 2\frac{1}{4}+1\frac{2}{5}\)
\(\displaystyle 3\frac{13}{20}\)
(9)\(\displaystyle \frac{4}{5}+6\frac{7}{10}\)
\(\displaystyle 7\frac{1}{2}\)
(10)\(\displaystyle 1\frac{3}{4}+3\frac{5}{12}\)
\(\displaystyle 5\frac{1}{6}\)
(11)\(\displaystyle 2\frac{8}{15}+1\frac{3}{10}\)
\(\displaystyle 3\frac{5}{6}\)
(12)\(\displaystyle 2\frac{5}{18}+1\frac{2}{9}\)
\(\displaystyle 3\frac{1}{2}\)
(13)\(\displaystyle \frac{1}{3}-\frac{1}{6}\)
\(\displaystyle \frac{1}{6}\)
(14)\(\displaystyle \frac{2}{3}-\frac{1}{12}\)
\(\displaystyle \frac{7}{12}\)
(15)\(\displaystyle \frac{5}{6}-\frac{2}{3}\)
\(\displaystyle \frac{1}{6}\)
(16)\(\displaystyle \frac{3}{4}-\frac{3}{5}\)
\(\displaystyle \frac{3}{20}\)
(17)\(\displaystyle \frac{7}{8}-\frac{5}{6}\)
\(\displaystyle \frac{1}{24}\)
(18)\(\displaystyle \frac{11}{12}-\frac{7}{15}\)
\(\displaystyle \frac{9}{20}\)
(19)\(\displaystyle \frac{13}{15}-\frac{7}{10}\)
\(\displaystyle \frac{1}{6}\)
(20)\(\displaystyle 1\frac{5}{6}-\frac{4}{15}\)
\(\displaystyle 1\frac{17}{30}\)
(21)\(\displaystyle 1\frac{1}{3}-\frac{1}{2}\)
\(\displaystyle \frac{5}{6}\)
(22)\(\displaystyle 4\frac{2}{3}-2\frac{4}{5}\)
\(\displaystyle 1\frac{13}{15}\)
(23)\(\displaystyle 3\frac{1}{3}-1\frac{2}{5}\)
\(\displaystyle 1\frac{14}{15}\)
(24)\(\displaystyle 2\frac{5}{24}-1\frac{1}{8}\)
\(\displaystyle 1\frac{1}{12}\)
(25)\(\displaystyle \frac{7}{6}+\frac{8}{21}\)
\(\displaystyle 1\frac{23}{42}\)
(26)\(\displaystyle \frac{4}{7}+\frac{3}{14}\)
\(\displaystyle \frac{11}{14}\)
(27)\(\displaystyle \frac{7}{16}+\frac{5}{24}\)
\(\displaystyle \frac{31}{48}\)
(28)\(\displaystyle \frac{3}{4}+\frac{5}{16}\)
\(\displaystyle 1\frac{1}{16}\)
(29)\(\displaystyle \frac{3}{8}+\frac{5}{6}\)
\(\displaystyle 1\frac{5}{24}\)
(30)\(\displaystyle \frac{2}{9}+\frac{1}{6}\)
\(\displaystyle \frac{7}{18}\)
(31)\(\displaystyle \frac{3}{4}+\frac{1}{6}\)
\(\displaystyle \frac{11}{12}\)
(32)\(\displaystyle \frac{3}{14}+\frac{5}{21}\)
\(\displaystyle \frac{19}{42}\)
(33)\(\displaystyle \frac{7}{12}+\frac{1}{18}\)
\(\displaystyle \frac{23}{36}\)
(34)\(\displaystyle \frac{5}{12}+\frac{7}{18}\)
\(\displaystyle \frac{29}{36}\)
(35)\(\displaystyle \frac{1}{6}+\frac{1}{2}\)
\(\displaystyle \frac{2}{3}\)
(36)\(\displaystyle \frac{3}{4}+\frac{1}{8}\)
\(\displaystyle \frac{7}{8}\)
(37)\(\displaystyle \frac{1}{6}+\frac{9}{10}\)
\(\displaystyle 1\frac{1}{15}\)
(38)\(\displaystyle \frac{5}{8}+\frac{3}{20}\)
\(\displaystyle \frac{31}{40}\)
(39)\(\displaystyle \frac{4}{3}+\frac{2}{5}\)
\(\displaystyle 1\frac{11}{15}\)
(40)\(\displaystyle \frac{3}{5}+\frac{1}{3}\)
\(\displaystyle \frac{14}{15}\)
(41)\(\displaystyle \frac{2}{3}-\frac{3}{8}\)
\(\displaystyle \frac{7}{24}\)
(42)\(\displaystyle \frac{5}{6}-\frac{3}{4}\)
\(\displaystyle \frac{1}{12}\)
(43)\(\displaystyle \frac{5}{9}-\frac{1}{6}\)
\(\displaystyle \frac{7}{18}\)
(44)\(\displaystyle \frac{5}{8}-\frac{1}{6}\)
\(\displaystyle \frac{11}{24}\)
(45)\(\displaystyle \frac{7}{10}-\frac{7}{15}\)
\(\displaystyle \frac{7}{30}\)
(46)\(\displaystyle \frac{17}{18}-\frac{19}{24}\)
\(\displaystyle \frac{11}{72}\)
(47)\(\displaystyle \frac{13}{16}-\frac{7}{12}\)
\(\displaystyle \frac{11}{48}\)
(48)\(\displaystyle \frac{11}{14}-\frac{8}{35}\)
\(\displaystyle \frac{39}{70}\)
(49)\(\displaystyle \frac{5}{6}-\frac{7}{9}\)
\(\displaystyle \frac{1}{18}\)
(50)\(\displaystyle \frac{6}{7}-\frac{1}{2}\)
\(\displaystyle \frac{5}{14}\)
(51)\(\displaystyle \frac{2}{3}-\frac{4}{15}\)
\(\displaystyle \frac{2}{5}\)
(52)\(\displaystyle \frac{7}{6}-\frac{5}{12}\)
\(\displaystyle \frac{3}{4}\)
(53)\(\displaystyle \frac{1}{2}-\frac{2}{7}\)
\(\displaystyle \frac{3}{14}\)
(54)\(\displaystyle \frac{5}{6}-\frac{4}{27}\)
\(\displaystyle \frac{37}{54}\)
(55)\(\displaystyle \frac{5}{12}-\frac{4}{15}\)
\(\displaystyle \frac{3}{20}\)
(56)\(\displaystyle 3-\frac{3}{8}\)
\(\displaystyle 2\frac{5}{8}\)
(57)\(\displaystyle \frac{7}{36}+\frac{5}{9}\)
\(\displaystyle \frac{3}{4}\)
(58)\(\displaystyle \frac{9}{14}+\frac{1}{2}\)
\(\displaystyle 1\frac{1}{7}\)
(59)\(\displaystyle \frac{5}{6}+\frac{3}{10}\)
\(\displaystyle 1\frac{2}{15}\)
(60)\(\displaystyle \frac{7}{15}+\frac{5}{6}\)
\(\displaystyle 1\frac{3}{10}\)
(61)\(\displaystyle \frac{7}{10}+\frac{2}{15}\)
\(\displaystyle \frac{5}{6}\)
(62)\(\displaystyle 1\frac{13}{30}+\frac{3}{20}\)
\(\displaystyle 1\frac{7}{12}\)
(63)\(\displaystyle \frac{7}{18}+2\frac{13}{30}\)
\(\displaystyle 2\frac{37}{45}\)
(64)\(\displaystyle 1\frac{11}{20}+3\frac{5}{12}\)
\(\displaystyle 4\frac{29}{30}\)
(65)\(\displaystyle 2\frac{5}{12}+4\frac{11}{15}\)
\(\displaystyle 7\frac{3}{20}\)
(66)\(\displaystyle 2\frac{5}{8}+3\frac{7}{12}\)
\(\displaystyle 6\frac{5}{24}\)
(67)\(\displaystyle 1\frac{3}{10}+3\frac{1}{5}\)
\(\displaystyle 4\frac{1}{2}\)
(68)\(\displaystyle 1\frac{2}{5}+2\frac{3}{4}\)
\(\displaystyle 4\frac{3}{20}\)
(69)\(\displaystyle 3\frac{5}{6}+\frac{3}{10}\)
\(\displaystyle 4\frac{2}{15}\)
(70)\(\displaystyle 2\frac{11}{18}+3\frac{5}{9}\)
\(\displaystyle 6\frac{1}{6}\)
(71)\(\displaystyle \frac{9}{10}-\frac{2}{5}\)
\(\displaystyle \frac{1}{2}\)
(72)\(\displaystyle \frac{5}{6}-\frac{8}{15}\)
\(\displaystyle \frac{3}{10}\)
(73)\(\displaystyle \frac{3}{4}-\frac{7}{20}\)
\(\displaystyle \frac{2}{5}\)
(74)\(\displaystyle \frac{13}{18}-\frac{5}{9}\)
\(\displaystyle \frac{1}{6}\)
(75)\(\displaystyle \frac{11}{12}-\frac{4}{15}\)
\(\displaystyle \frac{13}{20}\)
(76)\(\displaystyle \frac{11}{14}-\frac{13}{21}\)
\(\displaystyle \frac{1}{6}\)
(77)\(\displaystyle 1\frac{1}{2}-\frac{7}{10}\)
\(\displaystyle \frac{4}{5}\)
(78)\(\displaystyle 1\frac{1}{12}-\frac{9}{20}\)
\(\displaystyle \frac{19}{30}\)
(79)\(\displaystyle 2\frac{5}{12}-1\frac{4}{15}\)
\(\displaystyle 1\frac{3}{20}\)
(80)\(\displaystyle 4\frac{3}{10}-2\frac{1}{6}\)
\(\displaystyle 2\frac{2}{15}\)
(81)\(\displaystyle 3\frac{3}{10}-1\frac{4}{5}\)
\(\displaystyle 1\frac{1}{2}\)
(82)\(\displaystyle 4-3\frac{5}{8}\)
\(\displaystyle \frac{3}{8}\)
(83)\(\displaystyle 5-1\frac{5}{6}\)
\(\displaystyle 3\frac{1}{6}\)
(84)\(\displaystyle 4\frac{1}{6}-2\frac{4}{5}\)
\(\displaystyle 1\frac{11}{30}\)
(85)\(\displaystyle \frac{1}{3}+\frac{1}{6}+\frac{5}{12}\)
\(\displaystyle \frac{11}{12}\)
(86)\(\displaystyle \frac{1}{4}+\frac{2}{5}+\frac{3}{10}\)
\(\displaystyle \frac{19}{20}\)
(87)\(\displaystyle \frac{7}{15}+\frac{1}{3}-\frac{3}{5}\)
\(\displaystyle \frac{1}{5}\)
(88)\(\displaystyle \frac{9}{8}-\frac{1}{6}+\frac{5}{12}\)
\(\displaystyle 1\frac{3}{8}\)
(89)\(\displaystyle 3-1\frac{4}{5}-\frac{7}{10}\)
\(\displaystyle \frac{1}{2}\)
(90)\(\displaystyle \frac{5}{6}-\left(\frac{1}{2}+\frac{2}{9}\right)\)
\(\displaystyle \frac{1}{9}\)
(91)\(\displaystyle 1\frac{2}{3}-\left(1\frac{1}{4}-\frac{5}{6}\right)\)
\(\displaystyle 1\frac{1}{4}\)
分数のたし算、ひき算の文章問題
分数のたし算、ひき算を使って、文章問題を解いてみましょう。
(1)\(\displaystyle \frac{2}{3}\)mの縄と\(\displaystyle \frac{5}{6}\)mの縄がある。合わせて何mか求めなさい。
\(\displaystyle \frac{2}{3}+\frac{5}{6}=\frac{3}{2}=1\frac{1}{2}\)
【答】\(\displaystyle 1\frac{1}{2}\)m
【答】\(\displaystyle 1\frac{1}{2}\)m
(2)りんごと容器の重さが\(\displaystyle \frac{5}{8}\)kg、りんごの重さが\(\displaystyle \frac{2}{9}\)kgだった。容器の重さは何kgか求めなさい。
\(\displaystyle \frac{5}{8}-\frac{2}{9}=\frac{29}{72}\)
【答】\(\displaystyle \frac{29}{72}\)kg
【答】\(\displaystyle \frac{29}{72}\)kg
(3)家から公園まで\(\displaystyle \frac{4}{5}\)km、公園から学校まで\(\displaystyle \frac{2}{3}\)kmだった。家から公園を通って学校までは何kmか求めなさい。
\(\displaystyle \frac{4}{5}+\frac{2}{3}=\frac{22}{15}=1\frac{7}{15}\)
【答】\(\displaystyle 1\frac{7}{15}\)km
【答】\(\displaystyle 1\frac{7}{15}\)km
練習問題・次の単元
分数のたし算、ひき算の学習が終わったら、要点の復習や次の単元にも挑戦してみましょう。
関連する学習内容
「分数のたし算、ひき算」では、通分や約分の考え方を使います。通分や約分のもとになる倍数や約数についても復習し、分数の計算への理解を深めましょう。
分数と整数、小数の関係
分数と小数の関係を理解し、数の表し方や大きさについて学びます。小数の仕組みを理解することで、数の大きさや計算への理解を深めます。
よくある質問
【小学5年算数】分数のたし算、ひき算について、よくある質問をまとめています。
分数のたし算では何に気をつければいいですか？
分数のたし算では、分母を通分してから分子をたし合わせる必要があります。同じ分母にそろえることが大切です。
帯分数のたし算はどうやって解きますか？
帯分数は仮分数に直してからたし算を行い、最後に帯分数に戻すのが一般的な解き方です。
分数のひき算で注意する点はありますか？
たし算と同様に、分母を通分してから分子をひきます。また、帯分数のひき算では繰り下がりに注意が必要です。