Solving word problems with integer subtraction
Solving word problems with integer subtraction is a Grade 7 skill in Big Ideas Math, Course 2 that applies the rule: subtracting an integer is equivalent to adding its opposite. The rule a − b = a + (−b) converts any subtraction into addition, which can then be handled with the signed addition rules. Real-world contexts include temperature change (−3 − (−8) = −3 + 8 = 5, meaning 5° rise), elevation differences, and financial changes. Key strategy: identify what is being subtracted, replace it with addition of the opposite, then apply the integer addition rules. The sign of the answer reflects whether the result is an increase or decrease.
Key Concepts
To solve word problems involving integer subtraction: 1. Identify the numbers and what operation is needed 2. Write the subtraction expression 3. Convert subtraction to addition: $a b = a + ( b)$ 4. Simplify using integer addition rules 5. State the answer with appropriate units.
Common Questions
What is the key rule for subtracting integers?
Subtracting an integer is the same as adding its opposite: a − b = a + (−b). Convert the subtraction to addition, then apply signed addition rules.
How do you compute −3 − (−8)?
Add the opposite: −3 + 8 = 5. The two negatives do not multiply; the minus sign in front changes −8 to +8.
A temperature drops from −3°C to −8°C. What is the change?
Change = −3 − (−8) = −3 + 8 = 5. The temperature changed by +5°C (it actually rose, but the problem context determines the interpretation).
How do you set up a word problem involving integer subtraction?
Identify the starting value and the value being subtracted. Write the expression, convert subtraction to adding the opposite, then compute.
What is the difference between −3 − 8 and −3 − (−8)?
−3 − 8 = −3 + (−8) = −11 (adding two negatives). −3 − (−8) = −3 + 8 = 5 (subtracting a negative becomes adding a positive).
Why is converting subtraction to addition useful in word problems?
It reduces two different operations (subtraction and addition of negatives) to a single rule, making it easier to apply consistent signed-number arithmetic.