Problems with whole numbers
Bank balance, degrees on the thermometer, floor in the lift, year BC. All these problems look alike: there is a starting point and a series of movements, positive or negative, that must be added in order.
Money and temperatures
Salma has $34\ €$ in her money box. She decides to buy a book that costs $15\ €$ and a backpack that costs $25\ €$. As she does not have enough money, her parents tell…
Salma has $34\ €$ in her money box. She decides to buy a book that costs $15\ €$ and a backpack that costs $25\ €$. As she does not have enough money, her parents tell her she can owe them the remainder. What integer represents Salma's final balance with respect to her parents?
In a video game tournament, "The Gamers" team has a total of $-150$ points accumulated for committing fouls. If in the final round they get a bonus of $225$ points, how…
In a video game tournament, "The Gamers" team has a total of $-150$ points accumulated for committing fouls. If in the final round they get a bonus of $225$ points, how many points do they have on their scoreboard now?
Marta has $45€$ in her bank account. Over the weekend, she makes the following transactions: she pays for a streaming platform subscription for $12€$, receives a bank…
Marta has $45€$ in her bank account. Over the weekend, she makes the following transactions: she pays for a streaming platform subscription for $12€$, receives a bank transfer (Bizum) of $20€$ from her father and buys a book costing $15€$. If at the end of Sunday her bank charges her an account maintenance fee of $3€$, what is the final balance of her account?
Floors, heights and depths
Lifts, divers and drones move "upwards" (positive) or "downwards" (negative) from a level $0$.
A food delivery courier gets into the elevator of a large shopping mall on the third basement floor, which is labelled floor $-3$. First he goes up $7$ floors to deliver…
A food delivery courier gets into the elevator of a large shopping mall on the third basement floor, which is labelled floor $-3$. First he goes up $7$ floors to deliver an order and, right after that, he goes down $2$ floors to pick up another order. On which floor is the courier after these movements?
In the figure you can see the floors of the elevator and the starting point.
A diver is submerged in the ocean at a depth of $18$ metres below sea level ($-18\ m$). If he ascends $7$ metres to observe a coral reef and then descends another $4$…
A diver is submerged in the ocean at a depth of $18$ metres below sea level ($-18\ m$). If he ascends $7$ metres to observe a coral reef and then descends another $4$ metres, at what depth is he finally? Express the result as an integer.
The summit of Mount Everest is at an altitude of $+8.848$ metres above sea level, while the deepest point of the Mariana Trench is at $-11.034$ metres. What is the total…
The summit of Mount Everest is at an altitude of $+8.848$ metres above sea level, while the deepest point of the Mariana Trench is at $-11.034$ metres. What is the total vertical distance between the highest point and the lowest point on the planet?
Dates before and after Christ
The year $0$ (approximately) separates the years BC (which are treated as negative, and the higher the number the older the date) from the years AD (positive).
A historian is studying the life of an Ancient Greek sculptor. According to records, the sculptor was born in $495$ BC and died in $429$ BC. How many years did this…
A historian is studying the life of an Ancient Greek sculptor. According to records, the sculptor was born in $495$ BC and died in $429$ BC. How many years did this sculptor live?
Pythagoras, the famous Greek mathematician and philosopher, was born in $570$ BC and died in $495$ BC. At what age did Pythagoras die? Use integers (associating years BC…
Pythagoras, the famous Greek mathematician and philosopher, was born in $570$ BC and died in $495$ BC. At what age did Pythagoras die? Use integers (associating years BC with negative numbers) to carry out the calculation.
Multi-step problems
Longer problems chain several movements together: it helps to write down the intermediate result after each step.
At a ski resort in the Aragonese Pyrenees, the thermometer showed a temperature of $-6\,^\circ\mathrm{C}$ at 8:00 in the morning. At 12:00 noon, the temperature had…
At a ski resort in the Aragonese Pyrenees, the thermometer showed a temperature of $-6\,^\circ\mathrm{C}$ at 8:00 in the morning. At 12:00 noon, the temperature had risen $9\,^\circ\mathrm{C}$, and at 20:00 in the evening it had dropped $7\,^\circ\mathrm{C}$ compared with the noon temperature. What temperature did the thermometer show at the end of the day?
An Amazon delivery driver starts their working day on floor $3$ of a large logistics centre. First, they go down $5$ floors to pick up a parcel in the basement, then go…
An Amazon delivery driver starts their working day on floor $3$ of a large logistics centre. First, they go down $5$ floors to pick up a parcel in the basement, then go up $7$ floors to deliver it to an office and, finally, go down another $3$ floors to rest in the cafeteria. Which floor is the cafeteria on? Express the result as an integer.
A scientist is carrying out a chemical experiment. They place a compound in a special freezer that lowers the temperature of the sample by $4^\circ C$ every hour. If the…
A scientist is carrying out a chemical experiment. They place a compound in a special freezer that lowers the temperature of the sample by $4^\circ C$ every hour. If the sample was initially at a room temperature of $18^\circ C$, what temperature will the sample be after $6$ hours? Express the result using a single calculation combining integers.