Question

-1/2 divided by ? = -7/3
1/7 divided by ? = 14

Answer 1

`-(1)/(2) \textsf{ divided by } \boxed{(3)/(14)} = -(7)/(3)`

`(1)/(7) \textsf{ divided by } \boxed{(1)/(98)} = 14`

Explanation:

Let x be the unknown number.

`\begin{aligned}&\textsf{Given}: \quad&(-(1)/(2))/(x)&=-(7)/(3)\\\\&\textsf{Multiply both sides by $x$}: & (-(1)/(2)x)/(x) & = -(7)/(3)x\\\\& \textsf{Simplify}: & -(1)/(2) & = -(7)/(3)x\\\\& \textsf{Multiply both sides by 3}: & -(1 \cdot 3)/(2) & = (-7 \cdot 3)/(3)x\\\\& \textsf{Simplify}: & -(3)/(2) & = -7x\\\\& \textsf{Divide both sides by -7}: \quad & -(3)/(2 \cdot -7)& = (-7x)/(-7)\\\\& \textsf{Simplify}: &(3)/(14) & = x\end{aligned}`

`\textsf{Therefore, }-(1)/(2) \textsf{ divided by } \boxed{(3)/(14)} = -(7)/(3)`

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Let x be the unknown number.

`\begin{aligned}& \textsf{Given}: & ((1)/(7))/(x) & = 14\\\\& \textsf{Multiply both sides by $x$}: & ((1)/(7)x)/(x) & = 14x\\\\& \textsf{Simplify}: & (1)/(7) & = 14x\\\\& \textsf{Divide both sides by 14}: & (1)/(7 \cdot 14) & = (14x)/(14)\\\\ & \textsf{Simplify}: & (1)/(98) & = x\end{aligned}`

`\textsf{Therefore, }(1)/(7) \textsf{ divided by } \boxed{(1)/(98)} = 14`