Operations with integers
A diver is at $-15$ metres and descends $12$ more. Your bank account goes from $+450$ € to having several movements, both positive and negative. To solve this without getting muddled, you need to master operations with integers.
Adding and subtracting integers
Calculate the following simple additions and subtractions of integers: a) $(+7) + (+5) =$ b) $(-8) + (-3) =$ c) $(+9) + (-4) =$ d) $(-6) + (+10) =$
Calculate the following simple additions and subtractions of integers:
- a) $(+7) + (+5) =$
- b) $(-8) + (-3) =$
- c) $(+9) + (-4) =$
- d) $(-6) + (+10) =$
Solve the following operations by removing the brackets first: a) $12 + (-5) =$ b) $8 - (+10) =$ c) $(-3) - (-7) =$ d) $(-5) + (+5) =$
Solve the following operations by removing the brackets first:
- a) $12 + (-5) =$
- b) $8 - (+10) =$
- c) $(-3) - (-7) =$
- d) $(-5) + (+5) =$
A weather station in the Pyrenees recorded the following temperature changes over the course of a winter's day: 1. At 8:00 h, the temperature was $-5\ ^\circ C$. 2. At…
A weather station in the Pyrenees recorded the following temperature changes over the course of a winter's day:
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At 8:00 h, the temperature was $-5\ ^\circ C$.
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At 12:00 h, it had risen by $8\ ^\circ C$.
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At 18:00 h, it dropped by $4\ ^\circ C$ compared to the previous reading.
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At 22:00 h, it dropped again by another $6\ ^\circ C$.
Write a single mathematical expression using integers that reflects all these changes, and calculate the final temperature at the end of the day.
Multiplying and dividing: the rule of signs
Use the rule of signs to solve these multiplications and divisions: a) $(+4) \cdot (-3) =$ b) $(-5) \cdot (-2) =$ c) $(-20) : (+5) =$ d) $(-18) : (-3) =$
Use the rule of signs to solve these multiplications and divisions:
- a) $(+4) \cdot (-3) =$
- b) $(-5) \cdot (-2) =$
- c) $(-20) : (+5) =$
- d) $(-18) : (-3) =$
Apply the distributive property to calculate these expressions in the simplest way possible (factorise out a common factor when necessary): a)…
Apply the distributive property to calculate these expressions in the simplest way possible (factorise out a common factor when necessary):
- a) $(-7) \cdot (+12) + (-7) \cdot (-2)$
- b) $15 \cdot (-4) - 15 \cdot (+6)$
- c) $(-10) \cdot (-3) + (-10) \cdot (+13)$
Combined operations
When additions, subtractions, multiplications, divisions and brackets are mixed together, there is a fixed order that must always be followed.
Calculate the result of these simple combined operations, respecting the order of operations (remember: multiplication and division first, then addition and…
Calculate the result of these simple combined operations, respecting the order of operations (remember: multiplication and division first, then addition and subtraction):
- a) $5 + 2 \cdot (-3) =$
- b) $(-10) : 2 + 8 =$
- c) $4 \cdot 3 - 15 =$
Calculate the result of the following combined operations, paying special attention to the order of operations and the rule of signs: a) $15 - (8 - 12) + (-5) \cdot 2$…
Calculate the result of the following combined operations, paying special attention to the order of operations and the rule of signs:
- a) $15 - (8 - 12) + (-5) \cdot 2$
- b) $(-3) \cdot [(-2) + (-4) \cdot (-3)]$
- c) $24 : (-4) - (-6) : (+3)$
- d) $(-10) + (-2) \cdot (-5) + (-20) : 5$
Solve the following combined operations with square brackets. Remember to perform the operations inside the brackets first: a) $18 - [ 2 + (-5) - (4 - 7) ]$ b)…
Solve the following combined operations with square brackets. Remember to perform the operations inside the brackets first:
- a) $18 - [ 2 + (-5) - (4 - 7) ]$
- b) $[ (-6) \cdot 2 - (-10) ] : (-2)$
- c) $30 : [ (-4) + (-2) \cdot (-3) ]$
- d) $(-5) \cdot [ 8 - (12 : (-3)) ]$
Back to the start: The diver starts at $-15\text{ m}$ and descends a further $12\text{ m}$, so reaches a depth of $-15 - 12 = -27\text{ m}$.