Add and subtract integers: word problems

Learning Objectives Identify keywords in word problems that indicate addition or subtraction of integers. Translate real-world scenarios involving gains, losses, temperatures, and elevations into mathematical expressions using integers. Accurately add integers with the same and different signs to solve word problems. Accurately subtract integers by converting subtraction to addition of the opposite in word problems. Interpret the integer solution in the context of the original word problem. Check the reasonableness of their answers for integer word problems. Ever wondered how meteorologists track temperature changes 🌡️ or how a submarine's depth is calculated? These real-world situations often involve adding and subtracting integers! In this tutorial, you'll learn...

TermDefinitionExample IntegerA whole number (not a fraction) that can be positive, negative, or zero. Integers include numbers like -3, -2, -1, 0, 1, 2, 3.In a game, gaining 5 points is +5, losing 3 points is -3. Positive IntegerAn integer greater than zero. Often represents gains, increases, above zero, or forward movement.A temperature rise of 7 degrees is +7. A deposit of $50 is +50. Negative IntegerAn integer less than zero. Often represents losses, decreases, below zero, or backward movement.A temperature drop of 10 degrees is -10. A withdrawal of $25 is -25. Word ProblemA mathematical problem presented in a narrative or descriptive form, requiring translation into a mathematical expression or equation to solve.If the temperature was -5°C and rose by 12°C, what is the new temperature...

Adding Integers with the Same Sign $$a + b = \text{sign}(a) \cdot (|a| + |b|)$$ When adding two integers with the same sign (both positive or both negative), add their absolute values and keep the common sign. For example, $3 + 5 = 8$ and $(-3) + (-5) = -8$. Adding Integers with Different Signs $$a + b = \text{sign of larger absolute value} \cdot (| |a| - |b| |)$$ When adding two integers with different signs (one positive, one negative), subtract the smaller absolute value from the larger absolute value. The result takes the sign of the integer with the larger absolute value. For example, $7 + (-3) = 4$ and $(-7) + 3 = -4$. Subtracting Integers (Keep, Change, Flip) $$a - b = a + (-b)$$ To subtract an integer, add its opposite. This means 'Keep' the first n...