Here’s the step-by-step solution to each of the 5 integer word problems:
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Problem 1:
> How cold will it get if it is 7°C outside and the temperature drops by 19°C in the next six hours?
Solution:
Start at 7°C and subtract 19°C (since it’s a drop).
7 – 19 =
–12
✔ Answer: –12°C
*Explanation:* When temperature drops, we subtract. Since 19 is greater than 7, the result is negative — meaning it gets below zero.
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Problem 2:
> Cara has $4,000 in her bank account. She spends $1,000 for her admission and $200 for buying accessories. How much money is left with her?
Solution:
Start with $4,000.
Subtract $1,000 → 4,000 – 1,000 = 3,000
Then subtract $200 → 3,000 – 200 =
2,800
Or combine the expenses: 1,000 + 200 = 1,200
Then: 4,000 – 1,200 =
2,800
✔ Answer: $2,800
*Explanation:* Spending money means subtracting from the total. We can do it step by step or add all expenses first.
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Problem 3:
> Suppose your office elevator was initially on the 12th floor. It goes down 11 floors and then goes up 5 floors. Find on which floor one can find the elevator.
Solution:
Start at 12.
Go down 11 → 12 – 11 =
1
Then go up 5 → 1 + 5 =
6
✔ Answer: 6th floor
*Explanation:* “Down” means subtract, “up” means add. We follow the sequence of movements.
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Problem 4:
> Mr. Roberts makes 4 withdrawals of $10 each. How much has he withdrawn in total?
Solution:
Each withdrawal is $10, and he does this 4 times.
4 × 10 =
40
✔ Answer: $40
*Explanation:* Total withdrawal = number of withdrawals × amount per withdrawal. Even though it’s money leaving his account, the question asks for the *total amount withdrawn*, so we give the positive value.
*(Note: If the problem asked for his net change, it would be –$40, but here it just asks “how much has he withdrawn,” so $40 is correct.)*
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Problem 5:
> A number added to 5 is equal to –11. Find the number.
Solution:
Let the unknown number be
x.
Equation: x + 5 = –11
To solve, subtract 5 from both sides:
x = –11 – 5
x =
–16
✔ Answer: –16
*Explanation:* We isolate the variable by doing the inverse operation. Since 5 is added, we subtract 5 from both sides to find x.
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✔ Final Answers:
1.
–12°C
2.
$2,800
3.
6th floor
4.
$40
5.
–16
Let me know if you’d like these explained with number lines or diagrams!
Parent Tip: Review the logic above to help your child master the concept of dividing integers word problems worksheet.
