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Answers
F A C T O R S. O F :
- 1.
- 2.
- 3.
- 4.
A N S W E R :
E X P L A I N T A T I O N :
_______________________
- 2.
_______________________
- 3.
_______________________
- 4.
_____________________
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!