Math, asked by Anonymous, 1 month ago

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Answered by Anonymous
73

F A C T O R S. O F :

  • 1. {\sf{\dfrac{1}{3} + \bigg(\dfrac{- 4}{5}\bigg) + \bigg(\dfrac{-3}{2}\bigg) + \dfrac{6}{7}}}

  • 2. {\sf{\dfrac{5}{14} × \dfrac{- 2}{11} × \dfrac{-7}{10} × \dfrac{33}{16}}}

  • 3. {\sf{\dfrac{2}{5} × \dfrac{4}{7} - \dfrac{1}{3} + \dfrac{4}{7} × \dfrac{8}{5}}}

  • 4. {\sf{\bigg(\dfrac{19}{16} × \dfrac{4}{12}\bigg) + \bigg(\dfrac{9}{16} × \dfrac{-3}{9}\bigg)}}

\\

A N S W E R :

  • {\sf{\dfrac{\bigg(-233\bigg)}{210}}}

  • {\sf{\bigg(\dfrac{3}{32}\bigg)}}

  • {\sf{\bigg(\dfrac{17}{21}\bigg)}}

  • {\sf{0}}

\\

E X P L A I N T A T I O N :

\begin{gathered}\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:1 \:)}}}\\\end{gathered}\end{gathered}\end{gathered}

  • {\sf{\dfrac{1}{3} + \bigg(\dfrac{- 4}{5}\bigg) + \bigg(\dfrac{-3}{2}\bigg) + \dfrac{6}{7}}}

{\sf{\dfrac{\bigg(70 - 4 × 42 - 3 × 105 + 6 × 30\bigg)}{210}}}

{\sf{\dfrac{\bigg(70 - 168 - 315 + 180\bigg)}{210}}}

{\sf{\dfrac{\bigg(250 - 483\bigg)}{210}}}

{\sf{\dfrac{\bigg(-233\bigg)}{210}}}

~~~~~~~~~~~~~~~ _______________________

\begin{gathered}\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:2 \:)}}}\\\end{gathered}\end{gathered}\end{gathered}

  • 2. {\sf{\dfrac{5}{14} × \dfrac{- 2}{11} × \dfrac{-7}{10} × \dfrac{33}{16}}}

{\sf{\dfrac{\bigg(5 × -2 × -7 × 33\bigg)}{\bigg(14 × 11 × 10 × 16\bigg)}}}

{\sf{\dfrac{\bigg(7 × 33\bigg)}{\bigg(14 × 11 × 16\bigg)}}}

{\sf{\dfrac{33}{\bigg(22 × 16\bigg)}}}

{\sf{\bigg(\dfrac{3}{32}\bigg)}}

~~~~~~~~~~~~~~~ _______________________

\begin{gathered}\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:3 \:)}}}\\\end{gathered}\end{gathered}\end{gathered}

  • 3. {\sf{\dfrac{2}{5} × \dfrac{4}{7} - \dfrac{1}{3} + \dfrac{4}{7} × \dfrac{8}{5}}}

{\sf{\bigg(\dfrac{8}{35}\bigg) - \bigg(\dfrac{1}{3}\bigg) + \bigg(\dfrac{32}{35}\bigg)}}

{\sf{\dfrac{\bigg(8 × 3 - 35 + 32 × 3\bigg)}{105}}}

{\sf{\dfrac{\bigg(24 - 35 + 96\bigg)}{105}}}

{\sf{\dfrac{\bigg(120 - 35\bigg)}{105}}}

{\sf{\dfrac{85}{105}}}

{\sf{\bigg(\dfrac{17}{21}\bigg)}}

~~~~~~~~~~~~~~~ _______________________

\begin{gathered}\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:4 \:)}}}\\\end{gathered}\end{gathered}\end{gathered}

  • 4. {\sf{\bigg(\dfrac{19}{16} × \dfrac{4}{12}\bigg) + \bigg(\dfrac{9}{16} × \dfrac{-3}{9}\bigg)}}

{\sf{\bigg(\dfrac{9}{16}\bigg) \bigg[\dfrac{4}{12} -  \dfrac{3}{9}\bigg]}}

{\sf{\bigg(\dfrac{9}{16}\bigg) \bigg[\dfrac{1}{3} -  \dfrac{1}{3}\bigg]}}

{\sf{\bigg(\dfrac{9}{16}\bigg) × 0}}

{\sf{0}}

\\

~~~~\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Proved!}}}}

~~~~~~~~~~~~~~ _____________________

Answered by ItzYourJaani
9

1. {\sf{\dfrac{1}{3} + \bigg(\dfrac{- 4}{5}\bigg) + \bigg(\dfrac{-3}{2}\bigg) + \dfrac{6}{7}}}

3

1

+(

5

−4

)+(

2

−3

)+

7

6

2. {\sf{\dfrac{5}{14} × \dfrac{- 2}{11} × \dfrac{-7}{10} × \dfrac{33}{16}}}

14

5

×

11

−2

×

10

−7

×

16

33

3. {\sf{\dfrac{2}{5} × \dfrac{4}{7} - \dfrac{1}{3} + \dfrac{4}{7} × \dfrac{8}{5}}}

5

2

×

7

4

3

1

+

7

4

×

5

8

4. {\sf{\bigg(\dfrac{19}{16} × \dfrac{4}{12}\bigg) + \bigg(\dfrac{9}{16} × \dfrac{-3}{9}\bigg)}}(

16

19

×

12

4

)+(

16

9

×

9

−3

)

\begin{gathered}\\\end{gathered}

A N S W E R :

{\sf{\dfrac{\bigg(-233\bigg)}{210}}}

210

(−233)

{\sf{\bigg(\dfrac{3}{32}\bigg)}}(

32

3

)

{\sf{\bigg(\dfrac{17}{21}\bigg)}}(

21

17

)

{\sf{0}}0

\begin{gathered}\\\end{gathered}

E X P L A I N T A T I O N :

\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:1 \:)}}}\\\end{gathered}\end{gathered}\end{gathered}\end{gathered}

(1)

{\sf{\dfrac{1}{3} + \bigg(\dfrac{- 4}{5}\bigg) + \bigg(\dfrac{-3}{2}\bigg) + \dfrac{6}{7}}}

3

1

+(

5

−4

)+(

2

−3

)+

7

6

{\sf{\dfrac{\bigg(70 - 4 × 42 - 3 × 105 + 6 × 30\bigg)}{210}}}

210

(70−4×42−3×105+6×30)

{\sf{\dfrac{\bigg(70 - 168 - 315 + 180\bigg)}{210}}}

210

(70−168−315+180)

{\sf{\dfrac{\bigg(250 - 483\bigg)}{210}}}

210

(250−483)

{\sf{\dfrac{\bigg(-233\bigg)}{210}}}

210

(−233)

~~~~~~~~~~~~~~~ _______________________

\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:2 \:)}}}\\\end{gathered}\end{gathered}\end{gathered}\end{gathered}

(2)

2. {\sf{\dfrac{5}{14} × \dfrac{- 2}{11} × \dfrac{-7}{10} × \dfrac{33}{16}}}

14

5

×

11

−2

×

10

−7

×

16

33

{\sf{\dfrac{\bigg(5 × -2 × -7 × 33\bigg)}{\bigg(14 × 11 × 10 × 16\bigg)}}}

(14×11×10×16)

(5×−2×−7×33)

{\sf{\dfrac{\bigg(7 × 33\bigg)}{\bigg(14 × 11 × 16\bigg)}}}

(14×11×16)

(7×33)

{\sf{\dfrac{33}{\bigg(22 × 16\bigg)}}}

(22×16)

33

{\sf{\bigg(\dfrac{3}{32}\bigg)}}(

32

3

)

~~~~~~~~~~~~~~~ _______________________

\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:3 \:)}}}\\\end{gathered}\end{gathered}\end{gathered}\end{gathered}

(3)

3. {\sf{\dfrac{2}{5} × \dfrac{4}{7} - \dfrac{1}{3} + \dfrac{4}{7} × \dfrac{8}{5}}}

5

2

×

7

4

3

1

+

7

4

×

5

8

{\sf{\bigg(\dfrac{8}{35}\bigg) - \bigg(\dfrac{1}{3}\bigg) + \bigg(\dfrac{32}{35}\bigg)}}(

35

8

)−(

3

1

)+(

35

32

)

{\sf{\dfrac{\bigg(8 × 3 - 35 + 32 × 3\bigg)}{105}}}

105

(8×3−35+32×3)

{\sf{\dfrac{\bigg(24 - 35 + 96\bigg)}{105}}}

105

(24−35+96)

{\sf{\dfrac{\bigg(120 - 35\bigg)}{105}}}

105

(120−35)

{\sf{\dfrac{85}{105}}}

105

85

{\sf{\bigg(\dfrac{17}{21}\bigg)}}(

21

17

)

~~~~~~~~~~~~~~~ _______________________

\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\large{\underline {\underline {\sf(\:4 \:)}}}\\\end{gathered}\end{gathered}\end{gathered}\end{gathered}

(4)

4. {\sf{\bigg(\dfrac{19}{16} × \dfrac{4}{12}\bigg) + \bigg(\dfrac{9}{16} × \dfrac{-3}{9}\bigg)}}(

16

19

×

12

4

)+(

16

9

×

9

−3

)

{\sf{\bigg(\dfrac{9}{16}\bigg) \bigg[\dfrac{4}{12} - \dfrac{3}{9}\bigg]}}(

16

9

)[

12

4

9

3

]

{\sf{\bigg(\dfrac{9}{16}\bigg) \bigg[\dfrac{1}{3} - \dfrac{1}{3}\bigg]}}(

16

9

)[

3

1

3

1

]

{\sf{\bigg(\dfrac{9}{16}\bigg) × 0}}(

16

9

)×0

{\sf{0}}0

\begin{gathered}\\\end{gathered}

~~~~ \qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Proved!}}}}∴

Hence, Proved!

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