Question

solve it for 50 points.

Answer 1

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: QUESTION \: \: \red{ \mid}}}}}}}}$

$\bold{6. \: Which \: \: rational \: \: number \: \: should \: \: be} \\ \bold{added \: \: to \: \: \frac{ - 7}{8} \: \: to \: \: get \: \: \frac{5}{9} }$

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \:SOLUTION \: \: \red{ \mid}}}}}}}} \:$

$\bold{Let , \: \: } \\ \\ \bold{The \: \: number \: \: should \: \: be \: \: added = x} \\ \\ \underline{ \underline{ \bold{ \: \: According \: \: To \: \: Question, \: \: }}} \\ \\ \bold{x +( \frac{ - 7}{8} ) = \frac{5}{9} } \\ \\ \bold{ = > x - \frac{7}{8} = \frac{5}{9} } \\ \\ \bold{ = > x = \frac{5}{9} + \frac{7}{8} } \\ \\ \bold{ = > x = \frac{40 + 63}{72} } \\ \\ \bold{ = > x = \boxed{ \bold{ \frac{103}{72} }}}$

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: VERIFICATION \: \: \red{ \mid}}}}}}}}$

$\bold{x + \frac{ - 7}{8} = \frac{5}{9} } \\ \\ \\ \underline{ \underline{\bold{ \: \: Putting \: \: the \: \: value \: \: of \: \: \red{x} \: \: : }}} \\ \\ \\ \bold{ \underline{ \: \: \frac{103}{72} \:} + ( \frac{ - 7}{8} ) } \\ \\ \bold{= \frac{103 - 63}{72} } \\ \\ \bold{ = \frac{40}{72} } \\ \\ \bold{ = \frac{5}{9} }$



$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: ANSWER\: \: \red{ \mid}}}}}}}} \:$


$\bold{ \:The \: \: rational \: \: number \: \: should \: \: be\: \: \boxed{ \bold{ \frac{103}{72} }}} \\ \bold{added \: \: to \: \: \frac{ - 7}{8} \: \: to \: \: get \: \: \frac{5}{9} .}$


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$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: QUESTION\: \: \red{ \mid}}}}}}}} \:$

$\bold{7 .\: Which \: \: rational \: \: number \: \: should \: \: be} \\ \bold{added \: \: to \: \: \frac{ - 5}{9} \: \: to \: \: get \: \: \frac{ - 2}{3} }$

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \:SOLUTION \: \: \red{ \mid}}}}}}}}$

$\bold{Let,} \\ \\ \bold{The \: \: number \: \: should \: \: be \: \: added= x} \\ \\ \underline{ \underline{\bold{ \: \: According \: \: To \: \: Question, \: \: }}} \\ \\ \bold{x + ( \frac{ - 5}{9} ) = \frac{ - 2}{3} } \\ \\ \bold{ = > x - \frac{5}{9} = \frac{ - 2}{3} } \\ \\ \bold{ = > x = \frac{ - 2}{3} + \frac{5}{9} } \\ \\ \bold{ = > x = \frac{ - 6 + 5}{9} } \\ \\ \bold{ = > x = \boxed{ \bold{ \frac{ - 1}{9} }}}$

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: VERIFICATION \: \: \red{ \mid}}}}}}}} \:$

$\bold{x + \frac{ - 5}{9} = \frac{ -2 }{3} } \\ \\ \\ \underline{ \underline{\bold{ \: \: Putting \: \: the \: \: value \: \: of \: \: \red{x} \: \: : }}} \\ \\ \bold{ \underline{ \: \: ( \frac{ - 1}{9} ) \: \: }+ ( \frac{ - 5}{9} ) } \\ \\ \bold{ = \frac{ - 1 + ( - 5)}{9} } \\ \\ \bold{ = \frac{ - 1 - 5}{9} } \\ \\ \bold{ = \frac{ \times 6}{9} } \\ \\ \bold{ = \frac{ - 2}{3} }$


$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: ANSWER \: \: \red{ \mid}}}}}}}} \:$


$\bold{ The \: \: rational \: \: number \: \: should \: \: be \: \:\boxed{ \bold{ \frac{ - 1}{9} }} } \\ \bold{added \: \: to \: \: \frac{ - 5}{9} \: \: to \: \: get \: \: \frac{ - 2}{3} }$

Answer 2

1.

x+(-7/8) = 5/9

x = 5/9 + 7/8

x = 103 / 72

2.

x+(-5/9)= -2/3

x = 5/9 - 2/3

x = -1/9