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1. What should be subtracted from -2/5 to get 11/35 .
2. Insert 3 rational number between -2/3 and 8/9
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Answer:
Step-by-step explanation:
Verified answer
Answer:
[tex] \:\boxed{\begin{aligned}& \:\sf \:(1). \: - \: \dfrac{5}{7} \: should \: be \: subtracted \: from \: \dfrac{ - 2}{5} \: to \: get \: \dfrac{11}{35} \: \\ \\& \:\sf \: (2). \: - \dfrac{2}{3}, \: - \dfrac{5}{9}, \: - \dfrac{4}{9}, \: - \dfrac{2}{9}, \: \dfrac{8}{9}\end{aligned}} \qquad \\ \\ [/tex]
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-1}}[/tex]
Let assume that x should be subtracted from -2/5 to get 11/35.
[tex]\sf \: - \dfrac{2}{5} - x = \dfrac{11}{35} \\ \\ [/tex]
[tex]\sf \: - x = \dfrac{11}{35} + \dfrac{2}{5} \\ \\ [/tex]
[tex]\sf \: - x = \dfrac{11}{35} + \dfrac{2 \times 7}{5 \times 7} \\ \\ [/tex]
[tex]\sf \: - x = \dfrac{11}{35} + \dfrac{14}{35} \\ \\ [/tex]
[tex]\sf \: - x = \dfrac{11 + 14}{35} \\ \\ [/tex]
[tex]\sf \: - x = \dfrac{25}{35} \\ \\ [/tex]
[tex]\sf \: - x = \dfrac{5}{7} \\ \\ [/tex]
[tex]\sf\implies \bf \: x \: = \: - \: \dfrac{5}{7} \\ \\ [/tex]
Hence,
[tex]\sf\implies \sf \: \: - \: \dfrac{5}{7} \: should \: be \: subtracted \: from \: \dfrac{ - 2}{5} \: to \: get \: \dfrac{11}{35} \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-2}}[/tex]
Given numbers are .
[tex]\sf \: - \dfrac{2}{3} \: and \: \dfrac{8}{9} \\ \\ [/tex]
can be rewritten as
[tex]\sf \: - \dfrac{2 \times 3}{3 \times 3} \: and \: \dfrac{8}{9} \\ \\ [/tex]
[tex]\sf \: - \dfrac{6}{9} \: and \: \dfrac{8}{9} \\ \\ [/tex]
We know, there are infinitely many rational number between two rational numbers.
So, three of them are
[tex]\sf \: - \dfrac{5}{9}, \: - \dfrac{4}{9}, \: - \dfrac{2}{9} \\ \\ [/tex]
Hence,
[tex]\sf \: - \dfrac{2}{3}, \: - \dfrac{5}{9}, \: - \dfrac{4}{9}, \: - \dfrac{2}{9}, \: \dfrac{8}{9} \\ \\ [/tex]