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Effectuer des opérations entre des fractions simples.

Automatismes C10a

Ecrire sous forme irréductible:

  1. a = \frac{\ \ \frac{4}{3}\ \ }{12}, b = \frac{4}{\ \frac{3}{12}\ }, c = \frac{\ \ \frac{5}{8}\ \ }{\frac{3}{4}}
  2. d = \frac{2}{5} \times \left( \frac{-1}{2} +7 \times \frac{3}{14}\right)
  3. k = 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}.
  4. j = \left(\frac{2}{3}-1\right)-\left(2+\frac{1}{3}\right).

Attention

Calculatrices interdites pour les automatismes.

Question 1

a = \frac{\ \ \frac{4}{3}\ \ }{12} = \frac{\ \ \frac{4}{3}\ \ }{\frac{12}{1}} = \frac{4}{3}\times \frac{1}{12}= \frac{4\times 1}{3\times (4\times 3)}, soit a = \frac{1}{9}.

b = \frac{4}{\ \frac{3}{12}\ } = \frac{4}{\ \frac{1}{4}\ } = 4\times \frac{4}{1} = 16

c = \frac{\ \ \frac{5}{8}\ \ }{\frac{3}{4}} = \frac{5}{8}\times \frac{4}{3} = \frac{5\times 4}{(2\times 4)\times 3}, soit c = \frac{5}{6}.

Question 2

d = \frac{2}{5} \times \left( \frac{-1}{2} +7 \times \frac{3}{14}\right) = \frac{2}{5} \times \left( \frac{-1}{2} + \frac{7}{1}\times\frac{3}{2\times 7}\right), soit d = \frac{2}{5} \times \left( \frac{-1}{2} + \frac{7\times 3}{1\times 2\times 7}\right),
d = \frac{2}{5} \times \left( \frac{-1}{2} + \frac{3}{2}\right)
d = \frac{2}{5} \times \left( \frac{2}{2} \right)
d = \frac{2}{5} \times \left( 1 \right)
d = \frac{2}{5}

Question 3

k = 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4} =\frac{2}{2}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4} = \frac{3}{2}+\frac{1}{3}+\frac{1}{4}
k = \frac{6}{4}+\frac{1}{3}+\frac{1}{4}
k = \frac{7}{4}+\frac{1}{3} (en regroupant le premier terme et le dernier)
k = \frac{7\times 3}{4\times 3}+\frac{1\times 4}{3\times 4}
k = \frac{21}{12}+\frac{4}{12}
k = \frac{25}{12}

Question 4

j = \left(\frac{2}{3}-1\right)-\left(2+\frac{1}{3}\right)
j = \frac{2}{3}-1-2-\frac{1}{3}
j = \frac{1}{3}-3
j = \frac{1}{3}-\frac{9}{3}
j = \frac{-8}{3}