Order of operations
When calculations with negative numbers have more than one operation, we have to follow rules for the order of operations:
Do all operations that lie inside the parentheses first:
From left to right, do all multiplication and division.
From left to right, do all addition and subtraction.
Adding and subtracting negative numbers
If a number has no sign it means that it is a positive number (positive number are higher than 0). We can write it with a plus sign, e.g. 5=+5. We add and subtract, as we normally do. The sum of two positives numbers is always positive (higher than zero).
Subtraction of two positive numbers can take us beyond zero in some cases: 3−10=(−7) To add and subtract with negative numbers, at first add positive signs to positive numbers, e.g. 20−5=20−+5
For each combination of two signs follow these rules:
Two like signs (++ or −−) become a positive sign.
Two unlike signs (+− or −+) become a negative sign.
Multiplying and dividing negative numbers
To multiply and divide two numbers follow these rules:
When the signs are different the result is negative:
When the signs are the same the result is positive:
At first count up the minus signs: seven minus signs.
So there are three pairs that can be eliminated, with one left over. As a result, the final answer will be negative: (−48)
In other words, if there is an even number of negative factors (2 factors, 4 factors, 6 factors, etc.) , the result is positive. If there is an odd number of factors with negative sign, the result is negative.
There are four negative numbers → result will be positive: