Question

Which number sentence is true?A) -1/12 x 6/7 = -1/14B) -1/12 x (-6/7) = -1/14C) 1/12 x 6/7 = 1/14D) 1/12 x (-6/7) = 1/14

Answer 1

Let's check each option:

a.

`\begin{gathered} (-1)/(12)\cdot(6)/(7)=(-1\cdot6)/(12\cdot7)=(6)/(84) \\ \text{We can rewrite the expresion:} \\ (6)/(84)=(6\cdot-1)/(6\cdot14) \\ \text{Simplify the common term }(6)/(6)=1,\text{ Then} \\ =(-1)/(14) \end{gathered}`

b.

`\begin{gathered} (-1)/(12)\cdot(-6)/(7)=((-1)(-6))/((12)(7))=(6)/(84) \\ \text{We can rewrite the expresion:} \\ (6\cdot1)/(6\cdot14) \\ \text{Simplify the common term }(6)/(6)=1,\text{ then:} \\ =(1)/(14) \end{gathered}`

c.

`\begin{gathered} (1)/(12)\cdot(6)/(7)=(1\cdot6)/(84) \\ \text{We can rewrite as:} \\ =(1\cdot6)/(6\cdot14) \\ \text{Simplify the common term }(6)/(6)=1,\text{ then:} \\ =(1)/(14) \end{gathered}`

d.

`\begin{gathered} (1)/(12)\cdot(-6)/(7)=((1)(-6))/(84) \\ \text{We can rewrite as:} \\ =(1\cdot-6)/(6\cdot14) \\ \text{Simplify the common term }(6)/(6)=1,\text{ then:} \\ =(-1)/(14) \end{gathered}`

Hence, the correct answers are options A and C.