Operations with integers
Adding and subtracting negative numbers, multiplying and dividing, the order of operations and powers with a minus. Problem after problem, checked and explained.
How to solve it
A negative number is a move in the opposite direction, or a debt. The sign rules come from there: adding a debt is the same as subtracting, and multiplying by a minus turns the direction around.
Step by step
- Replace subtraction with adding the opposite number: $a - b = a + (-b)$.
- Same signs: add the absolute values and keep the common sign: $-16 + (-9) = -25$.
- Different signs: subtract the smaller absolute value from the larger and take the sign of the number with the larger one: $-19 + 10 = -9$.
- Multiplying and dividing: the sign first (an even number of minuses gives plus, an odd number gives minus), then multiply the absolute values.
- In an expression keep the order: powers, then multiplication and division, then addition and subtraction.
Common mistakes
- Mixing up $-2^2$ and $(-2)^2$. In $-2^2$ the power comes first, then the minus: $-4$. And $(-2)^2 = 4$.
- Adding the absolute values when the signs differ: $-19 + 10$ is not $-29$ but $-9$.
- Losing the minus when subtracting a negative: $5 - (-3) = 5 + 3 = 8$.
- Working left to right without the order of operations: in $-3 \cdot 2 - 4 \cdot 7$ both multiplications come first.