Operations with integers
A player has $150$ energy points, loses $25$ per hour in a cave and gains $40$ for each crystal. To work out their final energy you need to add and subtract integers without making mistakes, and then combine several operations at once in the right order. Let's go through it step by step.
Adding and subtracting integers
At a ski resort in Sierra Nevada, the thermometer read $-5^{\circ}C$ at seven in the morning. At noon, the temperature rose by $12^{\circ}C$ and, by nightfall, it…
At a ski resort in Sierra Nevada, the thermometer read $-5^{\circ}C$ at seven in the morning. At noon, the temperature rose by $12^{\circ}C$ and, by nightfall, it dropped again by $9^{\circ}C$. What temperature did the thermometer read at the end of the day? Write the complete calculation using integers.
In your savings account for the end-of-year trip, you have an initial balance of $45 €$. During the week, you make the following transactions: You deposit $20 €$ given…
In your savings account for the end-of-year trip, you have an initial balance of $45 €$. During the week, you make the following transactions:
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You deposit $20 €$ given to you by your grandmother.
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You pay for a cinema ticket costing $9 €$.
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You buy a second-hand book for $6 €$.
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You are paid back $3 €$ that you had lent to a friend.
Calculate the final balance using an expression with positive and negative numbers.
Multiplying and dividing: the rule of signs
Solve the following multiplications and divisions, correctly applying the rule of signs: a) $(+6) \cdot (-3) =$ b) $(-20) : (-5) =$ c) $(-8) \cdot (-4) =$ d)…
Solve the following multiplications and divisions, correctly applying the rule of signs:
- a) $(+6) \cdot (-3) =$
- b) $(-20) : (-5) =$
- c) $(-8) \cdot (-4) =$
- d) $(+35) : (-7) =$
Solve the following multiplication number pyramid. The value in each box is the product of the two integers located directly below it.
Solve the following multiplication number pyramid. The value in each box is the product of the two integers located directly below it.
Removing brackets with a sign in front
When a bracket is preceded by $+$, the signs inside stay the same; if it is preceded by $-$, all the signs inside change.
Expand the brackets and calculate the final result of the following expressions: a) $+(+7) + (-3) - (+5) =$ b) $-(-4) - (+8) + (-2) =$ c) $+(-10) - (-6) - (-1) =$
Expand the brackets and calculate the final result of the following expressions:
- a) $+(+7) + (-3) - (+5) =$
- b) $-(-4) - (+8) + (-2) =$
- c) $+(-10) - (-6) - (-1) =$
Combined operations: round brackets, square brackets and braces
When there are round brackets inside square brackets inside braces, you always work from the inside outwards.
Calculate the result of these combined operations, respecting the order of operations: a) $10 + 2 \cdot (-3) =$ b) $(-15) : 3 - 4 =$ c) $8 - (-10) : 2 =$ d)…
Calculate the result of these combined operations, respecting the order of operations:
- a) $10 + 2 \cdot (-3) =$
- b) $(-15) : 3 - 4 =$
- c) $8 - (-10) : 2 =$
- d) $(-5) \cdot (-2) + (-6) =$
In a survival video game, a player starts with $150$ energy points. For every hour spent exploring dark caves, they lose $25$ points, but for every "light crystal" they…
In a survival video game, a player starts with $150$ energy points. For every hour spent exploring dark caves, they lose $25$ points, but for every "light crystal" they collect, they gain $40$ points.
If the player spends $4$ hours in the caves and manages to collect $3$ crystals, write an expression with integers that represents their final energy and calculate it.
The distributive property and the unknown term
Apply the distributive property to solve the following expressions in two different ways (first calculating inside the brackets and then distributing the factor): a)…
Apply the distributive property to solve the following expressions in two different ways (first calculating inside the brackets and then distributing the factor):
- a) $-3 \cdot ( 8 - 12 )$
- b) $5 \cdot [ -4 + ( -6 ) ]$
- c) $( -10 + 2 ) \cdot ( -4 )$
Fill in the blanks with the corresponding integer to make the equations true: a) $-15 + ( \square ) = -32$ b) $4 \cdot ( \square ) = -36$ c) $( \square ) : (-3) = +12$…
Fill in the blanks with the corresponding integer to make the equations true:
- a) $-15 + ( \square ) = -32$
- b) $4 \cdot ( \square ) = -36$
- c) $( \square ) : (-3) = +12$
- d) $-10 - ( \square ) = -4$
Back to the beginning: If the player spends $3$ hours in the cave and collects $2$ crystals, their final energy is $150 - 3 \cdot 25 + 2 \cdot 40 = 150 - 75 + 80 = 155$ points.