Question

How to multiply negative fractions

Answer 1

We have the following rules for the product of positive and negative numbers:

`\begin{gathered} (-)(+_{})=negative \\ (+_{})(-_{})=\text{negative} \\ (+)(+)=positive_{}_{} \\ (-)(-)=positive_{}_{} \end{gathered}`

This means that the product of two numbers with different sign will always be negative

And, the product of two numbers with equal sign will always be positive.

Now, given the general rule for the product of fractions:

`\begin{gathered} (a)/(b)\cdot(c)/(d)=(a\cdot c)/(b\cdot d) \\ b,d\\e0 \end{gathered}`

we have, for example:

`\begin{gathered} (-8)/(7)\cdot(-7)/(10)=((-8)(-7))/(7\cdot10)=(56)/(70) \\ \text{and} \\ -(2)/(3)\cdot(5)/(4)=(-2(5))/(3\cdot4)=(-10)/(20) \end{gathered}`