Numbers: Negative numbers
Multiplying negative numbers
We know that: \[\orange{3} \times \red{5}= \underbrace{\red{5}+\red{5}+\red{5}}_{\orange{3} \text{ times}}=15\]
In the same way: \[\green 3 \times \blue{-5} =\underbrace{\blue{-5}+\blue{-5}+\blue{-5}}_{\green{3} \text{ times}}=\blue{-15}\]
Since the order of multiplication can be switched, we also have #\blue{-5} \times \green{3} =\blue{-15}#.
Generally said, the following holds:
A #\green{\textit{positive}}# number multiplied with a #\blue{\textit{negative}}# number equals a #\blue{\textit{negative}}# number.
Consider the pattern on the right. We see that the number by which we multiply decreases by one in every row. The outcome, therefore, always increases by #4#. Hence, we see that #-4 \times -1=4#.
Generally said, the following holds:
A #\blue{\textit{negative}}# number multiplied with a #\blue{\textit{negative}}# number equals a #\green{\textit{positive}}# number.
\[\begin{array}{rcrrr}-4 &\times& 2&=& -8 \\ -4 &\times& 1&=&-4 \\ -4 &\times& 0&=&0 \\ -4 &\times& -1&=&4 \\ -4 &\times& -2 &=&8 \end{array}\]
In general, we can state the following calculation rules for multiplication.
|
The calculation rules for multiplying positive and negative numbers are: \[\begin{array}{rclll} |
Examples \[\begin{array}{rcrrr} \\[1pt] |
We are multiplying two positive numbers, so the result is positive.
#2 \times 2=4#
Or visit omptest.org if jou are taking an OMPT exam.
