Equation field guide
Addition and subtraction in an equation
Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.
Signed quantities
A plus sign can combine positive or negative values. For instance, 4 + (−6) = −2. The parentheses make clear that −6 is one signed quantity.
Subtraction is addition of an opposite: a − b means a + (−b). This rule explains why subtracting a negative increases a value: 4 − (−6) = 4 + 6 = 10.
Terms and grouping
In a + b − c, a, b, and c are terms joined by addition or subtraction. Addition and subtraction have equal precedence, so read left to right unless parentheses change the grouping.
In a formula such as y = mx + b, mx is one product and b is an added offset. Each operation describes a different relationship between the quantities.
Useful checks
Units can only be added or subtracted when they refer to the same kind of quantity: 2 metres + 30 centimetres is meaningful after converting units; 2 metres + 30 seconds is not.
If a result has the opposite sign from what the context allows, check whether a subtraction was reversed or a negative sign was lost.