Răspuns:
Explicație pas cu pas:
a) 9/10:3/5=3/2 proba 9/10:3/2=9/10×2/3=3/5
b)1/8:(-5/8)=-1/8×8/5=-1/5 proba 1/8:(-1/5)=(-5/8)
c)(2/3):11/12 =2/3×12/11=8/11 proba 2/3:8/11=11/12
d) 7/9:9=7/9×1/9=7/49 proba 7/9:7/49=9
a)
[tex] \bf \dfrac{9}{10} \div \dfrac{3}{5} [/tex]
[tex]\bf \dfrac{9}{10} \times \dfrac{5}{3}[/tex]
[tex]\bf \dfrac{ \not9}{ \not10} \times \dfrac{ \not5}{ \not3}[/tex]
[tex]\bf \dfrac{3}{2} \times \dfrac{1}{1}[/tex]
[tex]\boxed{ \bf \dfrac{3}{2}}[/tex]
Verificare:
[tex]\it \dfrac{9}{10} = \dfrac{3}{5} \times \dfrac{3}{2}[/tex]
[tex]\it\dfrac{9}{10} = \dfrac{9}{10} \: (adevarat)[/tex]
b)
[tex]\bf \dfrac{1}{8} \div \big( - \dfrac{5}{8} \big)[/tex]
[tex]\bf \dfrac{1}{8} \times \big( - \dfrac{8}{5} \big)[/tex]
[tex]\bf \dfrac{1}{ \not8} \times \big( - \dfrac{ \not8}{5} \big)[/tex]
[tex] \boxed{\bf - \dfrac{1}{5}}[/tex]
Verificare:
[tex]\it \dfrac{1}{8} = - \dfrac{1}{5} \times ( - \dfrac{5}{8})[/tex]
[tex]\it \dfrac{1}{8} = - \dfrac{1}{ \not5} \times ( - \dfrac{ \not5}{8})[/tex]
[tex]\it \dfrac{1}{8} =\dfrac{1}{8} \: (adevarat)[/tex]
c)
[tex]\bf \dfrac{2}{3} \div \dfrac{11}{12}[/tex]
[tex]\bf \dfrac{2}{3} \times \dfrac{12}{11}[/tex]
[tex]\bf \dfrac{2}{\not3}\times \dfrac{ \not 12}{11}[/tex]
[tex] \boxed{\bf \dfrac{8}{11}}[/tex]
Verificare:
[tex]\it \dfrac{2}{3} = \dfrac{11}{12} \times\dfrac{8}{11}[/tex]
[tex]\it \dfrac{2}{3} = \dfrac{ \not11}{ \not12} \times\dfrac{ \not8}{ \not11}[/tex]
[tex]\it \dfrac{2}{3} = \dfrac{2}{3} \: (adevarat)[/tex]
d)
[tex]\bf \dfrac{7}{9} \div \dfrac{9}{1}[/tex]
[tex]\bf \dfrac{7}{9} \times \dfrac{1}{9}[/tex]
[tex] \boxed{\bf \dfrac{7}{81}}[/tex]
Verificare:
[tex]\it \dfrac{7}{9} = \dfrac{9}{1} \times\dfrac{7}{81}[/tex]
[tex]\it \dfrac{7}{9} = \dfrac{ \not9}{1} \times\dfrac{7}{ \not81}[/tex]
[tex]\it \dfrac{7}{9} = \dfrac{7}{9} \: (adevarat)[/tex]