Inicio › Matemáticas 2 › Operaciones con fracciones

Matemáticas 2 · Tema 1

Operaciones con fracciones

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Suma y resta ab±cd=ad±cbbd\dfrac{a}{b} \pm \dfrac{c}{d} = \dfrac{ad \pm cb}{bd}
Multiplicación ab(cd)=acbd\dfrac{a}{b}\left(\dfrac{c}{d}\right) = \dfrac{ac}{bd}
División ab÷cd=adbc\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc}  ó  abcd=adbc\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}} = \dfrac{ad}{bc}
Potencia (ab)n=anbn\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}
Raíces abn=anbn\sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}

Todas las fracciones se deben simplificar al menos: mitades, terceras y quintas.

Ejemplos

Suma y resta −34−86=−18−3224=−5024=−2512-\dfrac{3}{4} - \dfrac{8}{6} = \dfrac{-18-32}{24} = \dfrac{-50}{24} = \mathbf{-\dfrac{25}{12}}
Multiplicación −58(12)(410)=−20160=−1080=−18-\dfrac{5}{8}\left(\dfrac{1}{2}\right)\left(\dfrac{4}{10}\right) = \dfrac{-20}{160} = \dfrac{-10}{80} = \mathbf{-\dfrac{1}{8}}
División 34÷812=3632=1816=98oˊ34812=3632=98\dfrac{3}{4} \div \dfrac{8}{12} = \dfrac{36}{32} = \dfrac{18}{16} = \mathbf{\dfrac{9}{8}} \qquad \text{ó} \qquad \dfrac{\dfrac{3}{4}}{\dfrac{8}{12}} = \dfrac{36}{32} = \mathbf{\dfrac{9}{8}}
Potencia (5−3)3=(5)3(−3)3=125−27\left(\dfrac{5}{-3}\right)^3 = \dfrac{(5)^3}{(-3)^3} = \mathbf{\dfrac{125}{-27}}
Raíces 3625=3625=65\sqrt{\dfrac{36}{25}} = \dfrac{\sqrt{36}}{\sqrt{25}} = \mathbf{\dfrac{6}{5}}

Ejercicios

Bloque 1
−48+14=-\dfrac{4}{8} + \dfrac{1}{4} =
43(515)=\dfrac{4}{3}\left(\dfrac{5}{15}\right) =
34÷−26=\dfrac{3}{4} \div \dfrac{-2}{6} =
(25)2=\left(\dfrac{2}{5}\right)^2 =
2536=\sqrt{\dfrac{25}{36}} =
−24−53=-\dfrac{2}{4} - \dfrac{5}{3} =
24(714)(−13)=\dfrac{2}{4}\left(\dfrac{7}{14}\right)\left(\dfrac{-1}{3}\right) =
−12−46=\dfrac{-\frac{1}{2}}{-\frac{4}{6}} =
(1−5)3=\left(\dfrac{1}{-5}\right)^3 =
−810003=\sqrt[3]{\dfrac{-8}{1000}} =
Bloque 2
36−25=\dfrac{3}{6} - \dfrac{2}{5} =
−13(−24)=-\dfrac{1}{3}\left(-\dfrac{2}{4}\right) =
−12÷53=-\dfrac{1}{2} \div \dfrac{5}{3} =
(−14)2=\left(\dfrac{-1}{4}\right)^2 =
494=\sqrt{\dfrac{49}{4}} =
−35−210=-\dfrac{3}{5} - \dfrac{2}{10} =
−39(45)(13)=-\dfrac{3}{9}\left(\dfrac{4}{5}\right)\left(\dfrac{1}{3}\right) =
−25−43=\dfrac{-\frac{2}{5}}{-\frac{4}{3}} =
(−25)3=\left(-\dfrac{2}{5}\right)^3 =
−641253=\sqrt[3]{\dfrac{-64}{125}} =
Bloque 3
−35−24=-\dfrac{3}{5} - \dfrac{2}{4} =
−25(−46)=-\dfrac{2}{5}\left(-\dfrac{4}{6}\right) =
−23÷14=-\dfrac{2}{3} \div \dfrac{1}{4} =
(−13)2=\left(-\dfrac{1}{3}\right)^2 =
8149=\sqrt{\dfrac{81}{49}} =
710−610=\dfrac{7}{10} - \dfrac{6}{10} =
−23(−96)(−13)=-\dfrac{2}{3}\left(-\dfrac{9}{6}\right)\left(\dfrac{-1}{3}\right) =
−1326=\dfrac{-\frac{1}{3}}{\frac{2}{6}} =
(46)3=\left(\dfrac{4}{6}\right)^3 =
−183=\sqrt[3]{\dfrac{-1}{8}} =
Bloque 4
−28+69=-\dfrac{2}{8} + \dfrac{6}{9} =
−63(520)=-\dfrac{6}{3}\left(\dfrac{5}{20}\right) =
−64÷3−5=\dfrac{-6}{4} \div \dfrac{3}{-5} =
(−24)2=\left(-\dfrac{2}{4}\right)^2 =
449=\sqrt{\dfrac{4}{49}} =
−45−69=-\dfrac{4}{5} - \dfrac{6}{9} =
48(14)(−32)=\dfrac{4}{8}\left(\dfrac{1}{4}\right)\left(\dfrac{-3}{2}\right) =
23−54=\dfrac{\frac{2}{3}}{-\frac{5}{4}} =
(−35)3=\left(-\dfrac{3}{5}\right)^3 =
−12510003=\sqrt[3]{\dfrac{-125}{1000}} =

Respuestas

▼
Bloque 1
−48+14=−16+832=−832=−14-\dfrac{4}{8} + \dfrac{1}{4} = \dfrac{-16+8}{32} = \dfrac{-8}{32} = \mathbf{-\dfrac{1}{4}}
43(515)=2045=49\dfrac{4}{3}\left(\dfrac{5}{15}\right) = \dfrac{20}{45} = \mathbf{\dfrac{4}{9}}
34÷−26=18−8=−94\dfrac{3}{4} \div \dfrac{-2}{6} = \dfrac{18}{-8} = \mathbf{-\dfrac{9}{4}}
(25)2=(2)2(5)2=425\left(\dfrac{2}{5}\right)^2 = \dfrac{(2)^2}{(5)^2} = \mathbf{\dfrac{4}{25}}
2536=2536=56\sqrt{\dfrac{25}{36}} = \dfrac{\sqrt{25}}{\sqrt{36}} = \mathbf{\dfrac{5}{6}}
−24−53=−6−2012=−2612=−136-\dfrac{2}{4} - \dfrac{5}{3} = \dfrac{-6-20}{12} = \dfrac{-26}{12} = \mathbf{-\dfrac{13}{6}}
24(714)(−13)=−14168=−112\dfrac{2}{4}\left(\dfrac{7}{14}\right)\left(\dfrac{-1}{3}\right) = \dfrac{-14}{168} = \mathbf{-\dfrac{1}{12}}
−12−46=−6−8=34\dfrac{-\frac{1}{2}}{-\frac{4}{6}} = \dfrac{-6}{-8} = \mathbf{\dfrac{3}{4}}
(1−5)3=(1)3(−5)3=−1125\left(\dfrac{1}{-5}\right)^3 = \dfrac{(1)^3}{(-5)^3} = \mathbf{-\dfrac{1}{125}}
−810003=−8310003=−210\sqrt[3]{\dfrac{-8}{1000}} = \dfrac{\sqrt[3]{-8}}{\sqrt[3]{1000}} = \mathbf{-\dfrac{2}{10}}
Bloque 2
36−25=15−1230=330=110\dfrac{3}{6} - \dfrac{2}{5} = \dfrac{15-12}{30} = \dfrac{3}{30} = \mathbf{\dfrac{1}{10}}
−13(−24)=212=16-\dfrac{1}{3}\left(-\dfrac{2}{4}\right) = \dfrac{2}{12} = \mathbf{\dfrac{1}{6}}
−12÷53=−310-\dfrac{1}{2} \div \dfrac{5}{3} = \mathbf{-\dfrac{3}{10}}
(−14)2=(−1)2(4)2=116\left(\dfrac{-1}{4}\right)^2 = \dfrac{(-1)^2}{(4)^2} = \mathbf{\dfrac{1}{16}}
494=494=72\sqrt{\dfrac{49}{4}} = \dfrac{\sqrt{49}}{\sqrt{4}} = \mathbf{\dfrac{7}{2}}
−35−210=−30−1050=−4050=−45-\dfrac{3}{5} - \dfrac{2}{10} = \dfrac{-30-10}{50} = \dfrac{-40}{50} = \mathbf{-\dfrac{4}{5}}
−39(45)(13)=−12135=−445-\dfrac{3}{9}\left(\dfrac{4}{5}\right)\left(\dfrac{1}{3}\right) = \dfrac{-12}{135} = \mathbf{-\dfrac{4}{45}}
−25−43=−6−20=310\dfrac{-\frac{2}{5}}{-\frac{4}{3}} = \dfrac{-6}{-20} = \mathbf{\dfrac{3}{10}}
(−25)3=(−2)3(5)3=−8125\left(-\dfrac{2}{5}\right)^3 = \dfrac{(-2)^3}{(5)^3} = \mathbf{-\dfrac{8}{125}}
−641253=−6431253=−45\sqrt[3]{\dfrac{-64}{125}} = \dfrac{\sqrt[3]{-64}}{\sqrt[3]{125}} = \mathbf{-\dfrac{4}{5}}
Bloque 3
−35−24=−12−1020=−2220=−1110-\dfrac{3}{5} - \dfrac{2}{4} = \dfrac{-12-10}{20} = \dfrac{-22}{20} = \mathbf{-\dfrac{11}{10}}
−25(−46)=830=415-\dfrac{2}{5}\left(-\dfrac{4}{6}\right) = \dfrac{8}{30} = \mathbf{\dfrac{4}{15}}
−23÷14=−83-\dfrac{2}{3} \div \dfrac{1}{4} = \mathbf{-\dfrac{8}{3}}
(−13)2=(−1)2(3)2=19\left(-\dfrac{1}{3}\right)^2 = \dfrac{(-1)^2}{(3)^2} = \mathbf{\dfrac{1}{9}}
8149=8149=97\sqrt{\dfrac{81}{49}} = \dfrac{\sqrt{81}}{\sqrt{49}} = \mathbf{\dfrac{9}{7}}
710−610=70−60100=10100=110\dfrac{7}{10} - \dfrac{6}{10} = \dfrac{70-60}{100} = \dfrac{10}{100} = \mathbf{\dfrac{1}{10}}
−23(−96)(−13)=−1854=−13-\dfrac{2}{3}\left(-\dfrac{9}{6}\right)\left(\dfrac{-1}{3}\right) = \dfrac{-18}{54} = \mathbf{-\dfrac{1}{3}}
−1326=−66=−1\dfrac{-\frac{1}{3}}{\frac{2}{6}} = \dfrac{-6}{6} = \mathbf{-1}
(46)3=(4)3(6)3=64216=827\left(\dfrac{4}{6}\right)^3 = \dfrac{(4)^3}{(6)^3} = \dfrac{64}{216} = \mathbf{\dfrac{8}{27}}
−183=−1383=−12\sqrt[3]{\dfrac{-1}{8}} = \dfrac{\sqrt[3]{-1}}{\sqrt[3]{8}} = \mathbf{-\dfrac{1}{2}}
Bloque 4
−28+69=−18+4872=3072=512-\dfrac{2}{8} + \dfrac{6}{9} = \dfrac{-18+48}{72} = \dfrac{30}{72} = \mathbf{\dfrac{5}{12}}
−63(520)=−3060=−12-\dfrac{6}{3}\left(\dfrac{5}{20}\right) = \dfrac{-30}{60} = \mathbf{-\dfrac{1}{2}}
−64÷3−5=3012=156=52\dfrac{-6}{4} \div \dfrac{3}{-5} = \dfrac{30}{12} = \mathbf{\dfrac{15}{6}} = \mathbf{\dfrac{5}{2}}
(−24)2=(−2)2(4)2=416=14\left(-\dfrac{2}{4}\right)^2 = \dfrac{(-2)^2}{(4)^2} = \dfrac{4}{16} = \mathbf{\dfrac{1}{4}}
449=449=27\sqrt{\dfrac{4}{49}} = \dfrac{\sqrt{4}}{\sqrt{49}} = \mathbf{\dfrac{2}{7}}
−45−69=−36−3045=−6645=−2215-\dfrac{4}{5} - \dfrac{6}{9} = \dfrac{-36-30}{45} = \dfrac{-66}{45} = \mathbf{-\dfrac{22}{15}}
48(14)(−32)=−1264=−316\dfrac{4}{8}\left(\dfrac{1}{4}\right)\left(\dfrac{-3}{2}\right) = \dfrac{-12}{64} = \mathbf{-\dfrac{3}{16}}
23−54=−815\dfrac{\frac{2}{3}}{-\frac{5}{4}} = \mathbf{-\dfrac{8}{15}}
(−35)3=(−3)3(5)3=−27125\left(-\dfrac{3}{5}\right)^3 = \dfrac{(-3)^3}{(5)^3} = \mathbf{-\dfrac{27}{125}}
−12510003=−125310003=−510=−12\sqrt[3]{\dfrac{-125}{1000}} = \dfrac{\sqrt[3]{-125}}{\sqrt[3]{1000}} = \mathbf{-\dfrac{5}{10}} = \mathbf{-\dfrac{1}{2}}

Ejercicios extra

▼
Bloque 5
−714+37=-\dfrac{7}{14} + \dfrac{3}{7} =
−510−34=-\dfrac{5}{10} - \dfrac{3}{4} =
65(725)=\dfrac{6}{5}\left(\dfrac{7}{25}\right) =
49(515)(−38)=\dfrac{4}{9}\left(\dfrac{5}{15}\right)\left(-\dfrac{3}{8}\right) =
35÷−58=\dfrac{3}{5} \div -\dfrac{5}{8} =
−47÷−69=-\dfrac{4}{7} \div -\dfrac{6}{9} =
(23)2=\left(\dfrac{2}{3}\right)^2 =
(−38)3=\left(-\dfrac{3}{8}\right)^3 =
4981=\sqrt{\dfrac{49}{81}} =
−641253=\sqrt[3]{-\dfrac{64}{125}} =
Bloque 6
−816+510=-\dfrac{8}{16} + \dfrac{5}{10} =
−25−47=-\dfrac{2}{5} - \dfrac{4}{7} =
56(824)=\dfrac{5}{6}\left(\dfrac{8}{24}\right) =
79(312)(−45)=\dfrac{7}{9}\left(\dfrac{3}{12}\right)\left(-\dfrac{4}{5}\right) =
34÷−710=\dfrac{3}{4} \div -\dfrac{7}{10} =
−56÷−78=-\dfrac{5}{6} \div -\dfrac{7}{8} =
(58)2=\left(\dfrac{5}{8}\right)^2 =
(−49)3=\left(-\dfrac{4}{9}\right)^3 =
1649=\sqrt{\dfrac{16}{49}} =
−27643=\sqrt[3]{-\dfrac{27}{64}} =
Bloque 7
−918+49=-\dfrac{9}{18} + \dfrac{4}{9} =
−714−25=-\dfrac{7}{14} - \dfrac{2}{5} =
37(421)=\dfrac{3}{7}\left(\dfrac{4}{21}\right) =
511(214)(−59)=\dfrac{5}{11}\left(\dfrac{2}{14}\right)\left(-\dfrac{5}{9}\right) =
56÷−34=\dfrac{5}{6} \div -\dfrac{3}{4} =
−23÷−58=-\dfrac{2}{3} \div -\dfrac{5}{8} =
(49)2=\left(\dfrac{4}{9}\right)^2 =
(−58)3=\left(-\dfrac{5}{8}\right)^3 =
3649=\sqrt{\dfrac{36}{49}} =
−1252163=\sqrt[3]{-\dfrac{125}{216}} =
Bloque 8
−512+38=-\dfrac{5}{12} + \dfrac{3}{8} =
−37−14=-\dfrac{3}{7} - \dfrac{1}{4} =
89(527)=\dfrac{8}{9}\left(\dfrac{5}{27}\right) =
47(620)(−35)=\dfrac{4}{7}\left(\dfrac{6}{20}\right)\left(-\dfrac{3}{5}\right) =
710÷−25=\dfrac{7}{10} \div -\dfrac{2}{5} =
−49÷−37=-\dfrac{4}{9} \div -\dfrac{3}{7} =
(38)2=\left(\dfrac{3}{8}\right)^2 =
(−411)3=\left(-\dfrac{4}{11}\right)^3 =
2564=\sqrt{\dfrac{25}{64}} =
−8273=\sqrt[3]{-\dfrac{8}{27}} =
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