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Applications of integer operations

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Applying Integer Operations

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.

Integer operations word problem: temperature change A thermometer word problem. The temperature starts at negative 4 degrees, drops 6 degrees, then rises 9 degrees. Computed as negative 4 minus 6 plus 9, the final temperature is negative 1 degree. Start: −4° Step 1: drops 6° −4 − 6 = −10 Step 2: rises 9° −10 + 9 = −1 Final temperature: −1°
Starting at −4°, a drop of 6° then a rise of 9° ends at −1°.

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°.

  1. Identify the starting value.
  2. Translate each change into a signed operation (a loss is subtraction or a negative addition; a gain is addition).
  3. Work through the operations in the order they happen.
  4. Check the sign of the final answer makes sense for the situation.

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.

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