Multiplication et Division de fractions

a) $-\dfrac{25 \times 4}{12 \times 5} = -\dfrac{(5 \times 5) \times 4}{(3 \times 4) \times 5} = $ $- \dfrac{5}{3}$

b) $\dfrac{7 \times 2}{8 \times 14} = \dfrac{7 \times 2}{(4 \times 2) \times (2 \times 7)} = \dfrac{1}{4 \times 2} = $ $\dfrac{1}{8}$

c) $+ \dfrac{9 \times 4}{16 \times 3} = \dfrac{(3 \times 3) \times 4}{(4 \times 4) \times 3} = $ $\dfrac{3}{4}$

d) $- \dfrac{15 \times 28}{7 \times 30} = - \dfrac{15 \times (4 \times 7)}{7 \times (2 \times 15)} = - \dfrac{4}{2} = $ $-2$

e) $+ \dfrac{3 \times 40}{10 \times 5} = \dfrac{3 \times (4 \times 10)}{10 \times 5} = \dfrac{12}{5} = $ $2,4$

a) L'inverse de $\dfrac{4}{7}$ est $\dfrac{7}{4}$.

b) L'inverse de $3$ (ou $\dfrac{3}{1}$) est $\dfrac{1}{3}$.

c) L'inverse de $\dfrac{1}{9}$ est $\dfrac{9}{1}$ ou $9$.

d) L'inverse de $-\dfrac{5}{2}$ est $-\dfrac{2}{5}$.

e) $\dfrac{-8}{-3} = \dfrac{8}{3}$. L'inverse est $\dfrac{3}{8}$.

a) $\dfrac{5}{3} \times \dfrac{2}{7} = \dfrac{10}{21}$

b) $\dfrac{1}{2} \times \dfrac{4}{3} = \dfrac{4}{6} = $ $\dfrac{2}{3}$

c) $\dfrac{8}{9} \times \dfrac{3}{2} = \dfrac{(4 \times 2) \times 3}{(3 \times 3) \times 2} = $ $\dfrac{4}{3}$

d) $\dfrac{5}{1} \times \dfrac{3}{1} = \dfrac{15}{1} = $ $15$

e) $\dfrac{-4}{7} \times \dfrac{3}{2} = -\dfrac{4 \times 3}{7 \times 2} = -\dfrac{(2 \times 2) \times 3}{7 \times 2} = $ $- \dfrac{6}{7}$

a) $\dfrac{2 \times 3 \times 4}{3 \times 4 \times 5} = $ $\dfrac{2}{5}$ (on simplifie par 3 et 4)

b) $\left( \dfrac{7}{8} \times \dfrac{4}{14} \right) \times \dfrac{1}{3} = \left( \dfrac{7 \times 4}{8 \times 14} \right) \times \dfrac{1}{3} = \left( \dfrac{1 \times 1}{2 \times 2} \right) \times \dfrac{1}{3} = \dfrac{1}{4} \times \dfrac{1}{3} = $ $\dfrac{1}{12}$

c) $\left( \dfrac{-1}{5} \times \dfrac{10}{3} \right) \times \dfrac{9}{2} = \left( \dfrac{-1 \times 10}{5 \times 3} \right) \times \dfrac{9}{2} = \dfrac{-2}{3} \times \dfrac{9}{2} = - \dfrac{2 \times 9}{3 \times 2} = $ $-3$

d) $\left( \dfrac{5 \times 3}{6 \times 10} \right) \div \dfrac{1}{4} = \left( \dfrac{1 \times 1}{2 \times 2} \right) \div \dfrac{1}{4} = \dfrac{1}{4} \times \dfrac{4}{1} = $ $1$

e) $\left( \dfrac{15}{4} \times \dfrac{8}{3} \right) \times \dfrac{-1}{2} = \left( \dfrac{(5 \times 3) \times (2 \times 4)}{4 \times 3} \right) \times \dfrac{-1}{2} = \dfrac{10}{1} \times \dfrac{-1}{2} = $ $-5$