Vidéo explicative
Exercice 1
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 1
$$\frac{5}{3} + \frac{4}{3}$$
$$\frac{5}{3} + \frac{4}{3}$$
Question 2
$$\frac{11}{6} + \frac{1}{6}$$
$$\frac{11}{6} + \frac{1}{6}$$
Question 3
$$3 + \frac{6}{9}$$
$$3 + \frac{6}{9}$$
Question 4
$$\frac{7}{12} + \frac{5}{6}$$
$$\frac{7}{12} + \frac{5}{6}$$
Question 5
$$\frac{4}{10} + \frac{6}{5}$$
$$\frac{4}{10} + \frac{6}{5}$$
Question 6
$$\frac{8}{4} + \frac{6}{8}$$
$$\frac{8}{4} + \frac{6}{8}$$
Correction
Question 1
$$\frac{\textcolor{red}{5}}{3} + \frac{\textcolor{red}{4}}{3}$$
$$\frac{\textcolor{red}{5}}{3} + \frac{\textcolor{red}{4}}{3}$$
$$= \frac{\textcolor{red}{9}}{3}$$
$$= \textcolor{goldenrod}{3}$$
Question 2
$$\frac{\textcolor{red}{11}}{6} + \frac{\textcolor{red}{1}}{6}$$
$$\frac{\textcolor{red}{11}}{6} + \frac{\textcolor{red}{1}}{6}$$
$$= \frac{\textcolor{red}{12}}{6}$$
$$= \textcolor{goldenrod}{2}$$
Question 3
$$3 + \textcolor{limegreen}{\frac{6}{9}}$$
$$3 + \textcolor{limegreen}{\frac{6}{9}}$$
$$= \textcolor{red}{3} + \textcolor{limegreen}{\frac{2}{3}}$$
$$= \textcolor{red}{\frac{3}{1}} + \frac{2}{3}$$
$$= \textcolor{red}{\frac{9}{3}} + \frac{2}{3}$$
$$= \textcolor{goldenrod}{\frac{11}{3}}$$
Question 4
$$\frac{7}{12} + \textcolor{limegreen}{\frac{5}{6}}$$
$$\frac{7}{12} + \textcolor{limegreen}{\frac{5}{6}}$$
$$= \frac{7}{12} + \textcolor{limegreen}{\frac{10}{12}}$$
$$= \textcolor{goldenrod}{\frac{17}{12}}$$
Question 5
$$\textcolor{limegreen}{\frac{4}{10}} + \frac{6}{5}$$
$$\textcolor{limegreen}{\frac{4}{10}} + \frac{6}{5}$$
$$= \textcolor{limegreen}{\frac{2}{5}} + \frac{6}{5}$$
$$= \textcolor{goldenrod}{\frac{8}{5}}$$
Question 6
$$\frac{8}{4} + \textcolor{limegreen}{\frac{6}{8}}$$
$$\frac{8}{4} + \textcolor{limegreen}{\frac{6}{8}}$$
$$= \frac{8}{4} + \textcolor{limegreen}{\frac{3}{4}}$$
$$= \textcolor{goldenrod}{\frac{11}{4}}$$
Exercice 2
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 7
$$\frac{3}{4} + \frac{5}{6}$$
$$\frac{3}{4} + \frac{5}{6}$$
Question 8
$$\frac{2}{5} + \frac{3}{8}$$
$$\frac{2}{5} + \frac{3}{8}$$
Question 9
$$\frac{5}{7} + \frac{2}{3}$$
$$\frac{5}{7} + \frac{2}{3}$$
Question 10
$$\frac{1}{6} + \frac{2}{5}$$
$$\frac{1}{6} + \frac{2}{5}$$
Question 11
$$\frac{4}{9} + \frac{7}{10}$$
$$\frac{4}{9} + \frac{7}{10}$$
Question 12
$$\frac{3}{8} + \frac{5}{12}$$
$$\frac{3}{8} + \frac{5}{12}$$
Correction
Question 7
$$\textcolor{limegreen}{\frac{3}{4}} + \textcolor{red}{\frac{5}{6}}$$
$$\textcolor{limegreen}{\frac{3}{4}} + \textcolor{red}{\frac{5}{6}}$$
$$= \textcolor{limegreen}{\frac{9}{12}} + \textcolor{red}{\frac{10}{12}}$$
$$= \textcolor{goldenrod}{\frac{19}{12}}$$
Question 8
$$\textcolor{limegreen}{\frac{2}{5}} + \textcolor{red}{\frac{3}{8}}$$
$$\textcolor{limegreen}{\frac{2}{5}} + \textcolor{red}{\frac{3}{8}}$$
$$= \textcolor{limegreen}{\frac{16}{40}} + \textcolor{red}{\frac{15}{40}}$$
$$= \textcolor{goldenrod}{\frac{31}{40}}$$
Question 9
$$\textcolor{limegreen}{\frac{5}{7}} + \textcolor{red}{\frac{2}{3}}$$
$$\textcolor{limegreen}{\frac{5}{7}} + \textcolor{red}{\frac{2}{3}}$$
$$= \textcolor{limegreen}{\frac{15}{21}} + \textcolor{red}{\frac{14}{21}}$$
$$= \textcolor{goldenrod}{\frac{29}{21}}$$
Question 10
$$\textcolor{limegreen}{\frac{1}{6}} + \textcolor{red}{\frac{2}{5}}$$
$$\textcolor{limegreen}{\frac{1}{6}} + \textcolor{red}{\frac{2}{5}}$$
$$= \textcolor{limegreen}{\frac{5}{30}} + \textcolor{red}{\frac{12}{30}}$$
$$= \textcolor{goldenrod}{\frac{17}{30}}$$
Question 11
$$\textcolor{limegreen}{\frac{4}{9}} + \textcolor{red}{\frac{7}{10}}$$
$$\textcolor{limegreen}{\frac{4}{9}} + \textcolor{red}{\frac{7}{10}}$$
$$= \textcolor{limegreen}{\frac{40}{90}} + \textcolor{red}{\frac{63}{90}}$$
$$= \textcolor{goldenrod}{\frac{103}{90}}$$
Question 12
$$\textcolor{limegreen}{\frac{3}{8}} + \textcolor{red}{\frac{5}{12}}$$
$$\textcolor{limegreen}{\frac{3}{8}} + \textcolor{red}{\frac{5}{12}}$$
$$= \textcolor{limegreen}{\frac{9}{24}} + \textcolor{red}{\frac{10}{24}}$$
$$= \textcolor{goldenrod}{\frac{19}{24}}$$
Exercice 3
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 13
$$\frac{1}{2} + \frac{1}{3} - \frac{1}{6}$$
$$\frac{1}{2} + \frac{1}{3} - \frac{1}{6}$$
Question 14
$$\frac{5}{8} + \frac{3}{4} - \frac{1}{2}$$
$$\frac{5}{8} + \frac{3}{4} - \frac{1}{2}$$
Question 15
$$\frac{7}{10} - \frac{2}{5} + \frac{1}{2}$$
$$\frac{7}{10} - \frac{2}{5} + \frac{1}{2}$$
Question 16
$$\frac{3}{4} + \frac{5}{6} - \frac{1}{3}$$
$$\frac{3}{4} + \frac{5}{6} - \frac{1}{3}$$
Question 17
$$\frac{4}{5} - \frac{2}{3} + \frac{1}{6}$$
$$\frac{4}{5} - \frac{2}{3} + \frac{1}{6}$$
Question 18
$$\frac{2}{3} + \frac{3}{10} - \frac{1}{2}$$
$$\frac{2}{3} + \frac{3}{10} - \frac{1}{2}$$
Correction
Question 13
$$\frac{1}{2} + \textcolor{limegreen}{\frac{1}{3}} - \frac{1}{6}$$
$$\frac{1}{2} + \textcolor{limegreen}{\frac{1}{3}} - \frac{1}{6}$$
$$= \frac{3}{6} + \textcolor{limegreen}{\frac{2}{6}} - \frac{1}{6}$$
$$= \frac{4}{6}$$
$$= \textcolor{goldenrod}{\frac{2}{3}}$$
Question 14
$$\frac{5}{8} + \textcolor{limegreen}{\frac{3}{4}} - \textcolor{red}{\frac{1}{2}}$$
$$\frac{5}{8} + \textcolor{limegreen}{\frac{3}{4}} - \textcolor{red}{\frac{1}{2}}$$
$$= \frac{5}{8} + \textcolor{limegreen}{\frac{6}{8}} - \textcolor{red}{\frac{4}{8}}$$
$$= \textcolor{goldenrod}{\frac{7}{8}}$$
Question 15
$$\frac{7}{10} - \textcolor{limegreen}{\frac{2}{5}} + \textcolor{red}{\frac{1}{2}}$$
$$\frac{7}{10} - \textcolor{limegreen}{\frac{2}{5}} + \textcolor{red}{\frac{1}{2}}$$
$$= \frac{7}{10} - \textcolor{limegreen}{\frac{4}{10}} + \textcolor{red}{\frac{5}{10}}$$
$$= \frac{8}{10}$$
$$= \textcolor{goldenrod}{\frac{4}{5}}$$
Question 16
$$\textcolor{limegreen}{\frac{3}{4}} + \textcolor{red}{\frac{5}{6}} - \frac{1}{3}$$
$$\textcolor{limegreen}{\frac{3}{4}} + \textcolor{red}{\frac{5}{6}} - \frac{1}{3}$$
$$= \textcolor{limegreen}{\frac{9}{12}} + \textcolor{red}{\frac{10}{12}} - \frac{4}{12}$$
$$= \frac{15}{12}$$
$$= \textcolor{goldenrod}{\frac{5}{4}}$$
Question 17
$$\textcolor{limegreen}{\frac{4}{5}} - \textcolor{red}{\frac{2}{3}} + \frac{1}{6}$$
$$\textcolor{limegreen}{\frac{4}{5}} - \textcolor{red}{\frac{2}{3}} + \frac{1}{6}$$
$$= \textcolor{limegreen}{\frac{24}{30}} - \textcolor{red}{\frac{20}{30}} + \frac{5}{30}$$
$$= \frac{9}{30}$$
$$= \textcolor{goldenrod}{\frac{3}{10}}$$
Question 18
$$\textcolor{limegreen}{\frac{2}{3}} + \frac{3}{10} - \textcolor{red}{\frac{1}{2}}$$
$$\textcolor{limegreen}{\frac{2}{3}} + \frac{3}{10} - \textcolor{red}{\frac{1}{2}}$$
$$= \textcolor{limegreen}{\frac{20}{30}} + \frac{9}{30} - \textcolor{red}{\frac{15}{30}}$$
$$= \frac{14}{30}$$
$$= \textcolor{goldenrod}{\frac{7}{15}}$$
Exercice 4
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 19
$$\frac{5}{6} - \frac{1}{4} + \frac{3}{8}$$
$$\frac{5}{6} - \frac{1}{4} + \frac{3}{8}$$
Question 20
$$\frac{1}{3} + \frac{1}{5} - \frac{1}{10}$$
$$\frac{1}{3} + \frac{1}{5} - \frac{1}{10}$$
Question 21
$$\frac{3}{7} + \frac{4}{9} - \frac{2}{3}$$
$$\frac{3}{7} + \frac{4}{9} - \frac{2}{3}$$
Question 22
$$\frac{5}{12} - \frac{1}{6} + \frac{1}{4}$$
$$\frac{5}{12} - \frac{1}{6} + \frac{1}{4}$$
Question 23
$$\frac{7}{10} + \frac{2}{3} - \frac{4}{5}$$
$$\frac{7}{10} + \frac{2}{3} - \frac{4}{5}$$
Question 24
$$\frac{3}{5} - \frac{2}{9} + \frac{1}{3}$$
$$\frac{3}{5} - \frac{2}{9} + \frac{1}{3}$$
Correction
Correction Théorème de thalès Exercice 4.
Question 19
$$\frac{5}{6} - \textcolor{limegreen}{\frac{1}{4}} + \textcolor{red}{\frac{3}{8}}$$
$$\frac{5}{6} - \textcolor{limegreen}{\frac{1}{4}} + \textcolor{red}{\frac{3}{8}}$$
$$= \frac{20}{24} - \textcolor{limegreen}{\frac{6}{24}} + \textcolor{red}{\frac{9}{24}}$$
$$= \textcolor{goldenrod}{\frac{23}{24}}$$
Question 20
$$\textcolor{limegreen}{\frac{1}{3}} + \frac{1}{5} - \textcolor{red}{\frac{1}{10}}$$
$$\textcolor{limegreen}{\frac{1}{3}} + \frac{1}{5} - \textcolor{red}{\frac{1}{10}}$$
$$= \textcolor{limegreen}{\frac{10}{30}} + \frac{6}{30} - \textcolor{red}{\frac{3}{30}}$$
$$= \textcolor{goldenrod}{\frac{13}{30}}$$
Question 21
$$\textcolor{limegreen}{\frac{3}{7}} + \textcolor{red}{\frac{4}{9}} - \frac{2}{3}$$
$$\textcolor{limegreen}{\frac{3}{7}} + \textcolor{red}{\frac{4}{9}} - \frac{2}{3}$$
$$= \textcolor{limegreen}{\frac{27}{63}} + \textcolor{red}{\frac{28}{63}} - \frac{42}{63}$$
$$= \textcolor{goldenrod}{\frac{13}{63}}$$
Question 22
$$\frac{5}{12} - \textcolor{red}{\frac{1}{6}} + \textcolor{limegreen}{\frac{1}{4}}$$
$$\frac{5}{12} - \textcolor{red}{\frac{1}{6}} + \textcolor{limegreen}{\frac{1}{4}}$$
$$= \frac{5}{12} - \textcolor{red}{\frac{2}{12}} + \textcolor{limegreen}{\frac{3}{12}}$$
$$= \frac{6}{12}$$
$$= \textcolor{goldenrod}{\frac{1}{2}}$$
Question 23
$$\frac{7}{10} + \textcolor{limegreen}{\frac{2}{3}} - \textcolor{red}{\frac{4}{5}}$$
$$\frac{7}{10} + \textcolor{limegreen}{\frac{2}{3}} - \textcolor{red}{\frac{4}{5}}$$
$$= \frac{21}{30} + \textcolor{limegreen}{\frac{20}{30}} - \textcolor{red}{\frac{24}{30}}$$
$$= \textcolor{goldenrod}{\frac{17}{30}}$$
Question 24
$$\frac{3}{5} - \textcolor{limegreen}{\frac{2}{9}} + \textcolor{red}{\frac{1}{3}}$$
$$\frac{3}{5} - \textcolor{limegreen}{\frac{2}{9}} + \textcolor{red}{\frac{1}{3}}$$
$$= \frac{27}{45} - \textcolor{limegreen}{\frac{10}{45}} + \textcolor{red}{\frac{15}{45}}$$
$$= \textcolor{goldenrod}{\frac{32}{45}}$$
Exercice 5
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 25
$$\frac{2}{3} \times \left( \frac{-4}{5} \right)$$
$$\frac{2}{3} \times \left( \frac{-4}{5} \right)$$
Question 26
$$\left( \frac{-5}{6} \right) \times \frac{3}{8}$$
$$\left( \frac{-5}{6} \right) \times \frac{3}{8}$$
Question 27
$$2 \times \left( \frac{-3}{4} \right)$$
$$2 \times \left( \frac{-3}{4} \right)$$
Question 28
$$\left( \frac{-7}{10} \right) \times \frac{5}{6}$$
$$\left( \frac{-7}{10} \right) \times \frac{5}{6}$$
Question 29
$$\frac{1}{2} \times (-6)$$
$$\frac{1}{2} \times (-6)$$
Question 30
$$\left( \frac{-3}{7} \right) \times \left( \frac{-4}{9} \right)$$
$$\left( \frac{-3}{7} \right) \times \left( \frac{-4}{9} \right)$$
Correction
Correction Théorème de thalès Exercice 5.
Question 25
$$\frac{2}{3} \times \left( \frac{-4}{5} \right)$$
$$\frac{2}{3} \times \left( \frac{-4}{5} \right)$$
$$= \frac{\textcolor{cyan}{2 \times -4}}{\textcolor{violet}{3 \times 5}}$$
$$= \frac{\textcolor{cyan}{-8}}{\textcolor{violet}{15}}$$
$$= \textcolor{goldenrod}{\frac{-8}{15}}$$
Question 26
$$\left( \frac{-5}{6} \right) \times \frac{3}{8}$$
$$\left( \frac{-5}{6} \right) \times \frac{3}{8}$$
$$= \frac{\textcolor{cyan}{-5 \times 3}}{\textcolor{violet}{6 \times 8}}$$
$$= \frac{\textcolor{cyan}{-15}}{\textcolor{violet}{48}}$$
$$= \textcolor{goldenrod}{\frac{-5}{16}}$$
Question 27
$$2 \times \left( \frac{-3}{4} \right)$$
$$2 \times \left( \frac{-3}{4} \right)$$
$$= \frac{\textcolor{cyan}{2 \times -3}}{\textcolor{violet}{1 \times 4}}$$
$$= \frac{\textcolor{cyan}{-6}}{\textcolor{violet}{4}}$$
$$= \textcolor{goldenrod}{\frac{-3}{2}}$$
Question 28
$$\left( \frac{-7}{10} \right) \times \frac{5}{6}$$
$$\left( \frac{-7}{10} \right) \times \frac{5}{6}$$
$$= \frac{\textcolor{cyan}{-7 \times 5}}{\textcolor{violet}{10 \times 6}}$$
$$= \frac{\textcolor{cyan}{-35}}{\textcolor{violet}{60}}$$
$$= \textcolor{goldenrod}{\frac{-7}{12}}$$
Question 29
$$\frac{1}{2} \times (-6)$$
$$\frac{1}{2} \times (-6)$$
$$= \frac{\textcolor{cyan}{1 \times -6}}{\textcolor{violet}{2 \times 1}}$$
$$= \frac{\textcolor{cyan}{-6}}{\textcolor{violet}{2}}$$
$$= \textcolor{goldenrod}{-3}$$
Question 30
$$\left( \frac{-3}{7} \right) \times \left( \frac{-4}{9} \right)$$
$$\left( \frac{-3}{7} \right) \times \left( \frac{-4}{9} \right)$$
$$= \frac{\textcolor{cyan}{(-3) \times (-4)}}{\textcolor{violet}{7 \times 9}}$$
$$= \frac{\textcolor{cyan}{12}}{\textcolor{violet}{63}}$$
$$= \textcolor{goldenrod}{\frac{4}{21}}$$
Exercice 6
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 31
$$\left( \frac{-2}{5} \right) \times \frac{7}{3}$$
$$\left( \frac{-2}{5} \right) \times \frac{7}{3}$$
Question 32
$$\frac{4}{9} \times \left( \frac{-3}{8} \right)$$
$$\frac{4}{9} \times \left( \frac{-3}{8} \right)$$
Question 33
$$(-5) \times \frac{2}{7}$$
$$(-5) \times \frac{2}{7}$$
Question 34
$$\left( \frac{-6}{11} \right) \times \left( \frac{-5}{2} \right)$$
$$\left( \frac{-6}{11} \right) \times \left( \frac{-5}{2} \right)$$
Question 35
$$\frac{3}{10} \times \left( \frac{-15}{4} \right)$$
$$\frac{3}{10} \times \left( \frac{-15}{4} \right)$$
Question 36
$$\left( \frac{-8}{9} \right) \times (-3)$$
$$\left( \frac{-8}{9} \right) \times (-3)$$
Correction
Correction Théorème de thalès Exercice 6.
Question 31
$$\left( \frac{-2}{5} \right) \times \frac{7}{3}$$
$$\left( \frac{-2}{5} \right) \times \frac{7}{3}$$
$$= \frac{\textcolor{cyan}{-2 \times 7}}{\textcolor{violet}{5 \times 3}}$$
$$= \frac{\textcolor{cyan}{-14}}{\textcolor{violet}{15}}$$
$$= \textcolor{goldenrod}{\frac{-14}{15}}$$
Question 32
$$\frac{4}{9} \times \left( \frac{-3}{8} \right)$$
$$\frac{4}{9} \times \left( \frac{-3}{8} \right)$$
$$= \frac{\textcolor{cyan}{4 \times -3}}{\textcolor{violet}{9 \times 8}}$$
$$= \frac{\textcolor{cyan}{-12}}{\textcolor{violet}{72}}$$
$$= \textcolor{goldenrod}{\frac{-1}{6}}$$
Question 33
$$(-5) \times \frac{2}{7}$$
$$(-5) \times \frac{2}{7}$$
$$= \frac{\textcolor{cyan}{-5 \times 2}}{\textcolor{violet}{1 \times 7}}$$
$$= \frac{\textcolor{cyan}{-10}}{\textcolor{violet}{7}}$$
$$= \textcolor{goldenrod}{\frac{-10}{7}}$$
Question 34
$$\left( \frac{-6}{11} \right) \times \left( \frac{-5}{2} \right)$$
$$\left( \frac{-6}{11} \right) \times \left( \frac{-5}{2} \right)$$
$$= \frac{\textcolor{cyan}{(-6) \times (-5)}}{\textcolor{violet}{11 \times 2}}$$
$$= \frac{\textcolor{cyan}{30}}{\textcolor{violet}{22}}$$
$$= \textcolor{goldenrod}{\frac{15}{11}}$$
Question 35
$$\frac{3}{10} \times \left( \frac{-15}{4} \right)$$
$$\frac{3}{10} \times \left( \frac{-15}{4} \right)$$
$$= \frac{\textcolor{cyan}{3 \times -15}}{\textcolor{violet}{10 \times 4}}$$
$$= \frac{\textcolor{cyan}{-45}}{\textcolor{violet}{40}}$$
$$= \textcolor{goldenrod}{\frac{-9}{8}}$$
Question 36
$$\left( \frac{-8}{9} \right) \times (-3)$$
$$\left( \frac{-8}{9} \right) \times (-3)$$
$$= \frac{\textcolor{cyan}{-8 \times -3}}{\textcolor{violet}{9 \times 1}}$$
$$= \frac{\textcolor{cyan}{24}}{\textcolor{violet}{9}}$$
$$= \textcolor{goldenrod}{\frac{8}{3}}$$
Exercice 7
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 37
$$(-3) \div \frac{4}{5}$$
$$(-3) \div \frac{4}{5}$$
Question 38
$$\frac{-9}{10} \div \frac{3}{5}$$
$$\frac{-9}{10} \div \frac{3}{5}$$
Question 39
$$\frac{-7}{12} \div \left( \frac{-2}{3} \right)$$
$$\frac{-7}{12} \div \left( \frac{-2}{3} \right)$$
Question 40
$$\frac{4}{9} \div \left( \frac{-5}{6} \right)$$
$$\frac{4}{9} \div \left( \frac{-5}{6} \right)$$
Question 41
$$\frac{-6}{7} \div (-2)$$
$$\frac{-6}{7} \div (-2)$$
Question 42
$$(-5) \div \frac{2}{3}$$
$$(-5) \div \frac{2}{3}$$
Correction
Correction Théorème de thalès Exercice 7.
Question 37
$$(-3) \div \frac{4}{5}$$
$$(-3) \div \frac{4}{5}$$
$$= \frac{-3}{1} \times \frac{\textcolor{violet}{5}}{\textcolor{cyan}{4}}$$
$$= \frac{\textcolor{cyan}{-15}}{\textcolor{violet}{4}}$$
$$= \textcolor{goldenrod}{\frac{-15}{4}}$$
Question 38
$$\frac{-9}{10} \div \frac{3}{5}$$
$$\frac{-9}{10} \div \frac{3}{5}$$
$$= \frac{-9}{10} \times \frac{\textcolor{violet}{5}}{\textcolor{cyan}{3}}$$
$$= \frac{\textcolor{cyan}{-45}}{\textcolor{violet}{30}}$$
$$= \textcolor{goldenrod}{\frac{-3}{2}}$$
Question 39
$$\frac{-7}{12} \div \left( \frac{-2}{3} \right)$$
$$\frac{-7}{12} \div \left( \frac{-2}{3} \right)$$
$$= \frac{-7}{12} \times \frac{\textcolor{violet}{3}}{\textcolor{cyan}{-2}}$$
$$= \frac{\textcolor{cyan}{21}}{\textcolor{violet}{-24}}$$
$$= \textcolor{goldenrod}{\frac{-7}{8}}$$
Question 40
$$\frac{4}{9} \div \left( \frac{-5}{6} \right)$$
$$\frac{4}{9} \div \left( \frac{-5}{6} \right)$$
$$= \frac{4}{9} \times \frac{\textcolor{violet}{6}}{\textcolor{cyan}{-5}}$$
$$= \frac{\textcolor{cyan}{24}}{\textcolor{violet}{-45}}$$
$$= \textcolor{goldenrod}{\frac{-8}{15}}$$
Question 41
$$\frac{-6}{7} \div (-2)$$
$$\frac{-6}{7} \div (-2)$$
$$= \frac{-6}{7} \times \frac{\textcolor{violet}{1}}{\textcolor{cyan}{-2}}$$
$$= \frac{\textcolor{cyan}{6}}{\textcolor{violet}{14}}$$
$$= \textcolor{goldenrod}{\frac{3}{7}}$$
Question 42
$$(-5) \div \frac{2}{3}$$
$$(-5) \div \frac{2}{3}$$
$$= \frac{-5}{1} \times \frac{\textcolor{violet}{3}}{\textcolor{cyan}{2}}$$
$$= \frac{\textcolor{cyan}{-15}}{\textcolor{violet}{2}}$$
$$= \textcolor{goldenrod}{\frac{-15}{2}}$$
Exercice 8
Énoncé Théorème de thalès Exercice 8.
Correction
Correction Théorème de thalès Exercice 8.
Exercice 9
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 25
$$\left( \frac{-3}{4} + \frac{2}{5} \right) - \frac{7}{6}$$
$$\left( \frac{-3}{4} + \frac{2}{5} \right) - \frac{7}{6}$$
Question 26
$$\frac{-6}{10} + \left( \frac{-3}{8} - \frac{5}{-12} \right)$$
$$\frac{-6}{10} + \left( \frac{-3}{8} - \frac{5}{-12} \right)$$
Question 27
$$\frac{5}{-8} - \left( \frac{3}{4} + \frac{-1}{2} \right)$$
$$\frac{5}{-8} - \left( \frac{3}{4} + \frac{-1}{2} \right)$$
Question 28
$$\left( \frac{7}{-15} - \frac{-2}{9} \right) + \frac{-1}{3}$$
$$\left( \frac{7}{-15} - \frac{-2}{9} \right) + \frac{-1}{3}$$
Question 29
$$\left( \frac{-2}{7} + \frac{-3}{5} \right) + \frac{4}{9}$$
$$\left( \frac{-2}{7} + \frac{-3}{5} \right) + \frac{4}{9}$$
Question 30
$$\left( \frac{-5}{12} + \frac{4}{-9} \right) - \frac{2}{3}$$
$$\left( \frac{-5}{12} + \frac{4}{-9} \right) - \frac{2}{3}$$
Correction
Correction Théorème de thalès Exercice 9.
Question 25
$$\left( \textcolor{limegreen}{\frac{-3}{4}} + \textcolor{red}{\frac{2}{5}} \right) - \textcolor{skyblue}{\frac{7}{6}}$$
$$\left( \textcolor{limegreen}{\frac{-3}{4}} + \textcolor{red}{\frac{2}{5}} \right) - \textcolor{skyblue}{\frac{7}{6}}$$
$$= \left( \textcolor{limegreen}{\frac{-15}{20}} + \textcolor{red}{\frac{8}{20}} \right) - \textcolor{skyblue}{\frac{7}{6}}$$
$$= \frac{-7}{20} - \textcolor{skyblue}{\frac{7}{6}}$$
$$= \frac{-21}{60} - \textcolor{skyblue}{\frac{70}{60}}$$
$$= \textcolor{goldenrod}{\frac{-91}{60}}$$
Question 26
$$\textcolor{skyblue}{\frac{-6}{10}} + \left( \textcolor{limegreen}{\frac{-3}{8}} - \textcolor{red}{\frac{5}{-12}} \right)$$
$$\textcolor{skyblue}{\frac{-6}{10}} + \left( \textcolor{limegreen}{\frac{-3}{8}} - \textcolor{red}{\frac{5}{-12}} \right)$$
$$= \textcolor{skyblue}{\frac{-3}{5}} + \left( \textcolor{limegreen}{\frac{-9}{24}} - \textcolor{red}{\frac{-10}{24}} \right)$$
$$= \textcolor{skyblue}{\frac{-3}{5}} + \textcolor{magenta}{\frac{1}{24}}$$
$$= \textcolor{skyblue}{\frac{-72}{120}} + \textcolor{magenta}{\frac{5}{120}}$$
$$= \textcolor{goldenrod}{\frac{-67}{120}}$$
Question 27
$$\frac{5}{-8} - \left( \textcolor{limegreen}{\frac{3}{4}} + \textcolor{red}{\frac{-1}{2}} \right)$$
$$\frac{5}{-8} - \left( \textcolor{limegreen}{\frac{3}{4}} + \textcolor{red}{\frac{-1}{2}} \right)$$
$$= \frac{-5}{8} - \left( \textcolor{limegreen}{\frac{6}{8}} + \textcolor{red}{\frac{-4}{8}} \right)$$
$$= \frac{-5}{8} - \frac{2}{8}$$
$$= \textcolor{goldenrod}{\frac{-7}{8}}$$
Question 28
$$\left( \textcolor{limegreen}{\frac{7}{-15}} - \textcolor{red}{\frac{-2}{9}} \right) + \textcolor{magenta}{\frac{-1}{3}}$$
$$\left( \textcolor{limegreen}{\frac{7}{-15}} - \textcolor{red}{\frac{-2}{9}} \right) + \textcolor{magenta}{\frac{-1}{3}}$$
$$= \left( \textcolor{limegreen}{\frac{-21}{45}} - \textcolor{red}{\frac{-10}{45}} \right) + \textcolor{magenta}{\frac{-1}{3}}$$
$$= \frac{-11}{45} + \textcolor{magenta}{\frac{-15}{45}}$$
$$= \textcolor{goldenrod}{\frac{-26}{45}}$$
Question 29
$$\left( \textcolor{limegreen}{\frac{-2}{7}} + \textcolor{red}{\frac{-3}{5}} \right) + \textcolor{magenta}{\frac{4}{9}}$$
$$\left( \textcolor{limegreen}{\frac{-2}{7}} + \textcolor{red}{\frac{-3}{5}} \right) + \textcolor{magenta}{\frac{4}{9}}$$
$$= \left( \textcolor{limegreen}{\frac{-10}{35}} + \textcolor{red}{\frac{-21}{35}} \right) + \textcolor{magenta}{\frac{4}{9}}$$
$$= \textcolor{skyblue}{\frac{-31}{35}} + \textcolor{magenta}{\frac{4}{9}}$$
$$= \textcolor{skyblue}{\frac{-279}{315}} + \textcolor{magenta}{\frac{140}{315}}$$
$$= \textcolor{goldenrod}{\frac{-139}{315}}$$
Question 30
$$\left( \textcolor{limegreen}{\frac{-5}{12}} + \textcolor{red}{\frac{4}{-9}} \right) - \textcolor{magenta}{\frac{2}{3}}$$
$$\left( \textcolor{limegreen}{\frac{-5}{12}} + \textcolor{red}{\frac{4}{-9}} \right) - \textcolor{magenta}{\frac{2}{3}}$$
$$= \left( \textcolor{limegreen}{\frac{-15}{36}} + \textcolor{red}{\frac{-16}{36}} \right) - \textcolor{magenta}{\frac{2}{3}}$$
$$= \frac{-31}{36} - \textcolor{magenta}{\frac{24}{36}}$$
$$= \textcolor{goldenrod}{\frac{-55}{36}}$$
Exercice 10
Énoncé Théorème de thalès Exercice 10.
Correction
Correction Théorème de thalès Exercice 10.
Exercice 11
Énoncé Théorème de thalès Exercice 10.
Correction
Correction Théorème de thalès Exercice 10.
Exercice 12
Énoncé Théorème de thalès Exercice 10.
Correction
Correction Théorème de thalès Exercice 10.
Exercice 13
Énoncé Théorème de thalès Exercice 10.
Correction
Correction Théorème de thalès Exercice 10.
Exercice 14
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 79
$$\left( \frac{-2}{3} + \frac{5}{6} \right) \times 3$$
$$\left( \frac{-2}{3} + \frac{5}{6} \right) \times 3$$
Question 80
$$\frac{2}{3} \div \left( \frac{1}{2} - \frac{1}{6} \right)$$
$$\frac{2}{3} \div \left( \frac{1}{2} - \frac{1}{6} \right)$$
Question 81
$$\frac{-3}{5} + \left( 4 \times \frac{2}{3} \right)$$
$$\frac{-3}{5} + \left( 4 \times \frac{2}{3} \right)$$
Question 82
$$\left( \frac{7}{10} - \frac{3}{4} \right) \div \frac{2}{5}$$
$$\left( \frac{7}{10} - \frac{3}{4} \right) \div \frac{2}{5}$$
Question 83
$$\left( \frac{-3}{4} \div \frac{2}{3} \right) + \frac{1}{2}$$
$$\left( \frac{-3}{4} \div \frac{2}{3} \right) + \frac{1}{2}$$
Question 84
$$\frac{2}{3} - \left( \frac{1}{4} \times 5 \right)$$
$$\frac{2}{3} - \left( \frac{1}{4} \times 5 \right)$$
Correction
Correction Théorème de thalès Exercice 10.
Question 79
$$\left( \textcolor{limegreen}{\frac{-2}{3}} + \frac{5}{6} \right) \times 3$$
$$\left( \textcolor{limegreen}{\frac{-2}{3}} + \frac{5}{6} \right) \times 3$$
$$= \left( \textcolor{limegreen}{\frac{-4}{6}} + \frac{5}{6} \right) \times 3$$
$$= \frac{1}{6} \times 3$$
$$= \frac{3}{6}$$
$$= \textcolor{goldenrod}{\frac{1}{2}}$$
Question 80
$$\frac{2}{3} \div \left( \textcolor{limegreen}{\frac{1}{2}} - \textcolor{red}{\frac{1}{6}} \right)$$
$$\frac{2}{3} \div \left( \textcolor{limegreen}{\frac{1}{2}} - \textcolor{red}{\frac{1}{6}} \right)$$
$$= \frac{2}{3} \div \left( \textcolor{limegreen}{\frac{3}{6}} - \textcolor{red}{\frac{1}{6}} \right)$$
$$= \frac{2}{3} \textcolor{skyblue}{\div} \textcolor{skyblue}{\frac{2}{6}}$$
$$= \frac{2}{3} \textcolor{skyblue}{\times} \textcolor{skyblue}{\frac{6}{2}}$$
$$= \frac{12}{6}$$
$$= \textcolor{goldenrod}{2}$$
Question 81
$$\textcolor{red}{\frac{-3}{5}} + \textcolor{limegreen}{\left( 4 \times \frac{2}{3} \right)}$$
$$\textcolor{red}{\frac{-3}{5}} + \textcolor{limegreen}{\left( 4 \times \frac{2}{3} \right)}$$
$$= \textcolor{red}{\frac{-3}{5}} + \textcolor{limegreen}{\frac{8}{3}}$$
$$= \textcolor{red}{\frac{-9}{15}} + \textcolor{limegreen}{\frac{40}{15}}$$
$$= \textcolor{goldenrod}{\frac{31}{15}}$$
Question 82
$$\left( \textcolor{limegreen}{\frac{7}{10}} - \textcolor{red}{\frac{3}{4}} \right) \div \frac{2}{5}$$
$$\left( \textcolor{limegreen}{\frac{7}{10}} - \textcolor{red}{\frac{3}{4}} \right) \div \frac{2}{5}$$
$$= \left( \textcolor{limegreen}{\frac{14}{20}} - \textcolor{red}{\frac{15}{20}} \right) \div \frac{2}{5}$$
$$= \frac{-1}{20} \textcolor{skyblue}{\div \frac{2}{5}}$$
$$= \frac{-1}{20} \textcolor{skyblue}{\times \frac{5}{2}}$$
$$= \frac{-5}{40}$$
$$= \textcolor{goldenrod}{\frac{-1}{8}}$$
Question 83
$$\left( \frac{-3}{4} \textcolor{skyblue}{\div \frac{2}{3}} \right) + \textcolor{red}{\frac{1}{2}}$$
$$\left( \frac{-3}{4} \textcolor{skyblue}{\div \frac{2}{3}} \right) + \textcolor{red}{\frac{1}{2}}$$
$$= \left( \frac{-3}{4} \textcolor{skyblue}{\times \frac{3}{2}} \right) + \textcolor{red}{\frac{1}{2}}$$
$$= \frac{-9}{8} + \textcolor{red}{\frac{1}{2}}$$
$$= \frac{-9}{8} + \textcolor{red}{\frac{4}{8}}$$
$$= \textcolor{goldenrod}{\frac{-5}{8}}$$
Question 84
$$\textcolor{red}{\frac{2}{3}} - \textcolor{limegreen}{\left( \frac{1}{4} \times 5 \right)}$$
$$\textcolor{red}{\frac{2}{3}} - \textcolor{limegreen}{\left( \frac{1}{4} \times 5 \right)}$$
$$= \textcolor{red}{\frac{2}{3}} - \textcolor{limegreen}{\frac{5}{4}}$$
$$= \textcolor{red}{\frac{8}{12}} - \textcolor{limegreen}{\frac{15}{12}}$$
$$= \textcolor{goldenrod}{\frac{-7}{12}}$$
Exercice 15
Calcule les fractions suivantes et donne le résultat sous forme simplifiée.
Question 85
$$\left( \frac{2}{5} + \frac{3}{10} \right) \times \left( \frac{-3}{4} \right)$$
$$\left( \frac{2}{5} + \frac{3}{10} \right) \times \left( \frac{-3}{4} \right)$$
Question 86
$$\frac{-5}{6} + \left( \frac{4}{5} \div \frac{2}{3} \right)$$
$$\frac{-5}{6} + \left( \frac{4}{5} \div \frac{2}{3} \right)$$
Question 87
$$\left( \frac{1}{2} + \frac{3}{4} \right) \times \left( \frac{5}{6} - \frac{2}{3} \right)$$
$$\left( \frac{1}{2} + \frac{3}{4} \right) \times \left( \frac{5}{6} - \frac{2}{3} \right)$$
Question 88
$$\left( \frac{-3}{5} + \frac{2}{3} \right) \div \frac{4}{7}$$
$$\left( \frac{-3}{5} + \frac{2}{3} \right) \div \frac{4}{7}$$
Question 89
$$\frac{4}{9} - \left( 2 \times \frac{5}{8} \right)$$
$$\frac{4}{9} - \left( 2 \times \frac{5}{8} \right)$$
Question 90
$$\left( \frac{7}{12} + \frac{1}{4} \right) \div \left( \frac{3}{10} \right)$$
$$\left( \frac{7}{12} + \frac{1}{4} \right) \div \left( \frac{3}{10} \right)$$
Correction
Correction Théorème de thalès Exercice 10.
Question 85
$$\left( \textcolor{limegreen}{\frac{2}{5}} + \frac{3}{10} \right) \times \left( \frac{-3}{4} \right)$$
$$\left( \textcolor{limegreen}{\frac{2}{5}} + \frac{3}{10} \right) \times \left( \frac{-3}{4} \right)$$
$$= \left( \textcolor{limegreen}{\frac{4}{10}} + \frac{3}{10} \right) \times \frac{-3}{4}$$
$$= \frac{7}{10} \times \frac{-3}{4}$$
$$= \textcolor{goldenrod}{\frac{-21}{40}}$$
Question 86
$$\textcolor{limegreen}{\frac{-5}{6}} + \left( \frac{4}{5} \textcolor{skyblue}{\div \frac{2}{3}} \right)$$
$$\textcolor{limegreen}{\frac{-5}{6}} + \left( \frac{4}{5} \textcolor{skyblue}{\div \frac{2}{3}} \right)$$
$$= \textcolor{limegreen}{\frac{-5}{6}} + \left( \frac{4}{5} \textcolor{skyblue}{\times \frac{3}{2}} \right)$$
$$= \textcolor{limegreen}{\frac{-5}{6}} + \frac{12}{10}$$
$$= \textcolor{limegreen}{\frac{-25}{30}} + \frac{36}{30}$$
$$= \textcolor{goldenrod}{\frac{11}{30}}$$
Question 87
$$\left( \textcolor{limegreen}{\frac{1}{2}} + \frac{3}{4} \right) \times \left( \frac{5}{6} - \textcolor{red}{\frac{2}{3}} \right)$$
$$\left( \textcolor{limegreen}{\frac{1}{2}} + \frac{3}{4} \right) \times \left( \frac{5}{6} - \textcolor{red}{\frac{2}{3}} \right)$$
$$= \left( \textcolor{limegreen}{\frac{2}{4}} + \frac{3}{4} \right) \times \left( \frac{5}{6} - \textcolor{red}{\frac{4}{6}} \right)$$
$$= \frac{5}{4} \times \frac{1}{6}$$
$$= \textcolor{goldenrod}{\frac{5}{24}}$$
Question 88
$$\left( \textcolor{limegreen}{\frac{-3}{5}} + \textcolor{red}{\frac{2}{3}} \right) \textcolor{skyblue}{\div \frac{4}{7}}$$
$$\left( \textcolor{limegreen}{\frac{-3}{5}} + \textcolor{red}{\frac{2}{3}} \right) \textcolor{skyblue}{\div \frac{4}{7}}$$
$$= \left( \textcolor{limegreen}{\frac{-9}{15}} + \textcolor{red}{\frac{10}{15}} \right) \textcolor{skyblue}{\div \frac{4}{7}}$$
$$= \frac{1}{15} \textcolor{skyblue}{\div \frac{4}{7}}$$
$$= \frac{1}{15} \textcolor{skyblue}{\times \frac{7}{4}}$$
$$= \textcolor{goldenrod}{\frac{7}{60}}$$
Question 89
$$\textcolor{red}{\frac{4}{9}} - \textcolor{limegreen}{\left( 2 \times \frac{5}{8} \right)}$$
$$\textcolor{red}{\frac{4}{9}} - \textcolor{limegreen}{\left( 2 \times \frac{5}{8} \right)}$$
$$= \textcolor{red}{\frac{4}{9}} - \textcolor{limegreen}{\frac{10}{8}}$$
$$= \textcolor{red}{\frac{16}{36}} - \textcolor{limegreen}{\frac{45}{36}}$$
$$= \textcolor{goldenrod}{\frac{-29}{36}}$$
Question 90
$$\left( \textcolor{limegreen}{\frac{7}{12}} + \textcolor{red}{\frac{1}{4}} \right) \textcolor{skyblue}{\div \frac{3}{10}}$$
$$\left( \textcolor{limegreen}{\frac{7}{12}} + \textcolor{red}{\frac{1}{4}} \right) \textcolor{skyblue}{\div \frac{3}{10}}$$
$$= \left( \textcolor{limegreen}{\frac{7}{12}} + \textcolor{red}{\frac{3}{12}} \right) \textcolor{skyblue}{\div \frac{3}{10}}$$
$$= \frac{10}{12} \textcolor{skyblue}{\div \frac{3}{10}}$$
$$= \frac{5}{6} \textcolor{skyblue}{\times \frac{10}{3}}$$
$$= \frac{50}{18}$$
$$= \textcolor{goldenrod}{\frac{25}{9}}$$
Exercice 1
Énoncé Réciproque Exercice 1.
Correction
Correction Réciproque Exercice 1.
Exercice 2
Énoncé Réciproque Exercice 2.
Correction
Correction Réciproque Exercice 2.
Exercice 1
Énoncé Réciproque Exercice 1.
Correction
Correction Réciproque Exercice 1.
Exercice 2
Énoncé Réciproque Exercice 2.
Correction
Correction Réciproque Exercice 2.
Exercice 1
Énoncé Réciproque Exercice 1.
Correction
Correction Réciproque Exercice 1.
Exercice 2
Énoncé Réciproque Exercice 2.
Correction
Correction Réciproque Exercice 2.
Exercice 1
Énoncé Réciproque Exercice 1.
Correction
Correction Réciproque Exercice 1.
Exercice 2
Énoncé Réciproque Exercice 2.
Correction
Correction Réciproque Exercice 2.
Exercice 1
Énoncé Réciproque Exercice 1.
Correction
Correction Réciproque Exercice 1.
Exercice 2
Énoncé Réciproque Exercice 2.
Correction
Correction Réciproque Exercice 2.
Exercice 1
Énoncé Réciproque Exercice 1.
Correction
Correction Réciproque Exercice 1.
Exercice 2
Énoncé Réciproque Exercice 2.
Correction
Correction Réciproque Exercice 2.
Exercice 1
Énoncé Réciproque Exercice 1.
Correction
Correction Réciproque Exercice 1.
Exercice 2
Énoncé Réciproque Exercice 2.
Correction
Correction Réciproque Exercice 2.
Exercice 1
Énoncé Réciproque Exercice 1.
Correction
Correction Réciproque Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.
Exercice 1
Énoncé Problème Exercice 1.
Correction
Correction Problème Exercice 1.