Dividing negative numbers

Numbers: Negative numbers

Dividing negative numbers

Since we can write a division as a product, we can use the same calculation rules for multiplication of negative numbers, for division.

We can write a division as a product with a fraction. In the chapter about fractions we will elaborate on this. This results in:

\[\begin{array}{rcrcrcrcr}\green6&:&\green2&=&\green6 &\times& \green{\frac{1}{2}}&=&\green3 \\ \green6&:&\blue{-2}&=&\green6 &\times& \blue{-\frac{1}{2}}&=&\blue{-3} \\ \blue{-6}&:&\green2&=&\blue{-6} &\times& \green{\frac{1}{2}}&=&\blue{-3} \\ \blue{-6}&:&\blue{-2}&=&\blue{-6} &\times& \blue{-\frac{1}{2}}&=&\green3 \end{array}\]

Using this example, we can state the general calculation rules for division.

Dividing negative numbers

The calculation rules for division of positive and negative numbers are:

\[\begin{array}{rclll}
\green{\text{positive}}&:& \green{\text{positive}} &=& \green{\text{positive}} \\
\green{\text{positive}}&:& \blue{\text{negative}}&=&\blue{\text{negative}} \\
\blue{\text{negative}}&:& \green{\text{positive}} &=& \blue{\text{negative}} \\
\blue{\text{negative}}&:& \blue{\text{negative}}&=& \green{\text{positive}}
\end{array}\]

Examples

\[\begin{array}{rrrrr} \\[1pt]
\green{20} &:&\green4 &=&\green{5} \\[2pt]
\green{20} &:& \blue{-4} &=&\blue{-5} \\[2pt]
\blue{-20} &:& \green4&=&\blue{-5} \\[2pt]
\blue{-20} &:& \blue{-4}&=&\green{5}
\end{array}\]

Calculate #4 : 1#.

#4 : 1=# #4#

We divide two positive numbers by each other, so the result is positive.
#4 : 1=4#

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