Applying integer operations means turning a real situation into a sequence of signed-number steps, mixing addition, subtraction, multiplication, and division as needed. In a temperature problem starting at negative 4 degrees, a 6-degree drop then a 9-degree rise ends at negative 1 degree.
Combining integer operations in a word problem
Real problems rarely use just one integer operation at a time — they mix addition, subtraction, multiplication, and division in a single situation. Applying integer operations means translating the words into a sequence of signed-number steps and working through them in order.
Starting at −4°, a drop of 6° then a rise of 9° ends at −1°.
Reading the problem
Certain words signal certain operations: "drops" or "loses" means subtract; "rises" or "gains" means add. Starting at −4°, a drop of 6° is −4 − 6 = −10. A rise of 9° from there is −10 + 9 = −1, so the final temperature is −1°.
A general approach
Identify the starting value.
Translate each change into a signed operation (a loss is subtraction or a negative addition; a gain is addition).
Work through the operations in the order they happen.
Check the sign of the final answer makes sense for the situation.
Building on the basics
These problems combine the rules from multiplying integers and dividing integers with integer addition and subtraction. Once each operation is solid on its own, combining them is mostly a reading-comprehension skill.