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Adding integers
Frank, Bella, Gabrielle, Tina and Pete are playing a board game called The little banker.
The cards in the game represent:
The cards in the game represent:
€\latex{1} cash \latex{(+1)},
€\latex{1} debt \latex{(-1)}.
Adding two positive or two negative numbers
Example 1
- Frank won €\latex{4} in the first round and €\latex{2} in the second. How much money does he have?
- Bella finished the first round with \latex{ 3 } debt cards and collected \latex{ 2 } more in the second round. How much debt does she have?
Solution (a)
Cards:
Numbers:
\latex{+}
\latex{=}
\latex{(+4)}
\latex{(+2)}
\latex{(+6)}
\latex{=}
\latex{+}
Frank has €\latex{6}.
Solution (b)
Cards:
Numbers:
\latex{+}
\latex{=}
\latex{(-3)}
\latex{(-2)}
\latex{(-5)}
\latex{=}
\latex{+}
Bella has €\latex{-5}, so she has a debt of €\latex{5}.
Add the absolute values of the numbers in the example.
(a)
\latex{(+4)+(+2)=(+6)}
\latex{|+4| +|+2|=4+2=6}
\latex{|+4| +|+2|=4+2=6}
(b)
\latex{(-2)+(-3)=(-5)}
\latex{|-2| +|-3|=2+3=5}
\latex{|-2| +|-3|=2+3=5}
When adding two positive or two negative numbers, we add their absolute values. The sign of the sum will be the same as that of the addends.
Adding positive and negative numbers
Example 2
- Tina finished the first round with a debt of €\latex{2} and won €\latex{3} in the second. How much money does she have?
- Gabrielle finished the first round with a debt of €\latex{ 2 } and won €\latex{ 2 } in the second. How much money does she have?
- Pete won €\latex{1} in the first round and collected a debt of €\latex{3} in the second. How much money does he have?
Solution (a)
Cards:
Numbers:
\latex{+}
\latex{=}
\latex{(-2)}
\latex{0}
\latex{(+1)}
Tina has €\latex{1}.
\latex{=}
\latex{+}
\latex{+}
\latex{+}
\latex{(+3)}
\latex{=}
\latex{0}
\latex{+}
\latex{+}
\latex{=}
\latex{(+1)}
\latex{ = }€\latex{0}
\latex{=}€\latex{0}
\latex{\begin{rcases} \\\\\end{rcases}}
.
.
.
Solution (b)
Cards:
Numbers:
\latex{+}
\latex{(-2)}
\latex{0}
Gabrielle has the same amount of money as she had at the start.
\latex{=}
\latex{+}
\latex{+}
\latex{(+2)}
\latex{=}
\latex{0}
\latex{+}
\latex{=}
\latex{0}
Solution (c)
Cards:
Numbers:
\latex{+}
\latex{(+1)}
\latex{0}
\latex{(-2)}
Pete finished the game with €\latex{-2}, that is, with a debt of €\latex{2}.
\latex{=}
\latex{+}
\latex{=}
\latex{+}
\latex{(-3)}
\latex{=}
\latex{(-2)}
\latex{+}
\latex{=}
Determine the absolute values of the addends in the previous example and subtract the smaller absolute value from the larger one.
(a)
\latex{(-2)+(+3)=+1}
\latex{|-2|=2} and \latex{|+3|=3}
\latex{3\gt2}
\latex{3-2=1}
\latex{|-2|=2} and \latex{|+3|=3}
\latex{3\gt2}
\latex{3-2=1}
\latex{(-2)+(+2)=0}
\latex{|-2|=2} and \latex{|+2|=2}
\latex{2=2}
\latex{2-2=0}
\latex{|-2|=2} and \latex{|+2|=2}
\latex{2=2}
\latex{2-2=0}
\latex{(+1)+(-3)=-2}
\latex{|+1|=1} and \latex{|-3|=3}
\latex{3\gt1}
\latex{3-1=2}
\latex{|+1|=1} and \latex{|-3|=3}
\latex{3\gt1}
\latex{3-1=2}
(b)
(c)
When adding a positive and a negative number, we determine their absolute values and subtract the smaller absolute value from the larger one. The sign of the sum will be the same as that of the number with the larger absolute value. If the absolute values of a positive and a negative number are equal, their sum is zero.
Exercises
{{exercise_number}}. At the end of a round of The little banker, the players have the following cards in front of them. Which child has the least and which one the most money?
a) Kate
b) Joe
c) Paul
d) Erica
{{exercise_number}}. After paying his debts, how much money will Ben have, if now he has:
a) €\latex{5} in cash and a debt of €\latex{3};
b) €\latex{5} in cash and a debt of €\latex{5};
c) €\latex{3} in cash and a debt of €\latex{7};
d) €\latex{2} in cash and a debt of €\latex{8};
e) €\latex{6} in cash and a debt of €\latex{2};
f) €\latex{3} in cash and a debt of €\latex{4?}
{{exercise_number}}. In the second round of The little banker, Zoe collected \latex{ 15 } debt cards, Norbert gained \latex{ 8 } money cards and Britney received \latex{ 6 } debt cards. Whose wealth has increased/decreased and by how much?
{{exercise_number}}. Write down the corresponding operations and calculate how much money you have if
- you have a debt of €\latex{20} and another debt of €\latex{50};
- you have €\latex{300} in cash and a debt of €\latex{450};
- you have a debt of €\latex{200} and another debt of €\latex{300}.
{{exercise_number}}. Joe has some money, but he also has debts. His bank account shows a) €\latex{ 3 }; b) €\latex{ –10 }; c) €\latex{ 0 }. Write \latex{ 3 } examples for each case and draw them as well.
{{exercise_number}}. The thermometer shows \latex{ −8 } °C. What value will it show if the temperature increases by
a) \latex{2}\latex{ °C };
b) \latex{5}\latex{ °C };
c) \latex{8}\latex{ °C };
d) \latex{10}\latex{ °C };
e) \latex{15}\latex{ °C };
f) \latex{20}\latex{ °C };
g) \latex{17}\latex{ °C };
h) \latex{14}\latex{ °C? }
{{exercise_number}}. What value did the thermometer originally show if, after a decrease of \latex{ 8 } °C, it now shows
a) \latex{2}\latex{ °C };
b) \latex{0}\latex{ °C };
c) \latex{-5}\latex{ °C };
d) \latex{-8}\latex{ °C };
e) \latex{-10}\latex{ °C };
f) \latex{-15}\latex{ °C? }
{{exercise_number}}. Write down the next five members of each sequence.
a) \latex{-15};\latex{-12};\latex{-9};\latex{-6}; ...;
b) \latex{-10};\latex{-8};\latex{-6};\latex{-4}; ...
c) \latex{-59};\latex{-47};\latex{-35};\latex{-23}; ...
d) \latex{-10};\latex{-9};\latex{-7};\latex{-6};\latex{-4}; ...
{{exercise_number}}. Perform the additions.
a) \latex{(+3)+(+7)}
b) \latex{(-3)+(-7)}
c) \latex{(+3)+(-7)}
d) \latex{(-3)+(+7)}
e) \latex{(+5)+(+8)}
f) \latex{(-5)+(-8)}
g) \latex{(+5)+(-8)}
h) \latex{(-5)+(+8)}
i) \latex{(+9)+(+4)}
j) \latex{(-9)+(-4)}
k) \latex{(+9)+(-4)}
l) \latex{(-9)+(+4)}
{{exercise_number}}. Perform the additions.
a) \latex{(-2)+(+6)}
b) \latex{(-4)+(-3)}
c) \latex{(-2)+(+1)}
d) \latex{(-8)+(-2)}
e) \latex{(+6)+(-1)}
f) \latex{(-7)+(+7)}
g) \latex{(-1)+(+5)}
h) \latex{(-4)+(+2)}
i) \latex{(-8)+(+3)}
j) \latex{(+8)+(-5)}
k) \latex{(-6)+(-6)}
l) \latex{0+(-9)}
{{exercise_number}}. Perform the additions.
a) \latex{(+30)+(+40)}
b) \latex{(+80)+(-30)}
c) \latex{(+20)+(-40)}
d) \latex{(-10)+(+10)}
e) \latex{(-60)+(+80)}
f) \latex{(+70)+(-10)}
g) \latex{(-40)+(-70)}
h) \latex{(-20)+(-80)}
{{exercise_number}}. To what numbers should you add \latex{ +6 } to get the following results?
a) \latex{+15}
b) \latex{+3}
c) \latex{-10}
d) \latex{+6}
e) \latex{-12}
f) \latex{-2,000}
{{exercise_number}}. Perform the additions.
a) \latex{(-45)+(-34)}
b) \latex{(-58)+(+37)}
c) \latex{(-52)+(+49)}
d) \latex{(-92)+(+49)}
e) \latex{(+64)+(+78)}
f) \latex{(+77)+(-72)}
g) \latex{(+65)+(-39)}
h) \latex{(-94)+(-18)}
i) \latex{(-74)+(+74)}
j) \latex{(-74)+(+84)}
k) \latex{(-74)+(+64)}
l) \latex{(+74)+(-74)}
{{exercise_number}}. To what numbers should you add \latex{ -8 } to get the following results?
a) \latex{-4}
b) \latex{+5}
c) \latex{-12}
d) \latex{+8}
e) \latex{0}
f) \latex{+1,000}
{{exercise_number}}. Fill in the table if \latex{ a + b = -4 }.
\latex{a}
\latex{b}
\latex{-5}
\latex{10}
\latex{0}
\latex{4}
\latex{5}
\latex{-10}
\latex{-21}
\latex{7}
{{exercise_number}}. If you add the number represented by letters on the arrows to the number in the rectangle on the left, you will get the number shown in the rectangle to the right. Calculate the values represented by the letters.
a)
\latex{-8}
\latex{-5}
\latex{+2}
\latex{+8}
a
b
c
b)
\latex{+9}
\latex{+5}
\latex{+3}
\latex{0}
d
e
f
c)
\latex{-7}
\latex{-3}
\latex{+2}
\latex{-2}
g
h
i
d)
\latex{+3}
\latex{-1}
\latex{-2}
\latex{+4}
j
k
l
{{exercise_number}}. Which one is greater? By how much?
- \latex{A=(+3)+(+8)\quad} or \latex{\quad B=(+3)+(+2)}?
- \latex{C=(+5)+(-4)\quad} or \latex{\quad D=(+5)+(-9)}?
- \latex{E=(-3)+(-5)\quad} or \latex{\quad F=(-3)+(-2)}?
- \latex{G=(-8)+(+2)\quad} or \latex{\quad H=(-8)+(+7)}?
{{exercise_number}}. Which one is greater? By how much?
- \latex{A=(+7)+(-5)}; \latex{\qquad{}B=(+3)+(+2)};\latex{\\}\latex{\qquad C=(+7)+(0)}; \latex{\qquad D=(+7)+(-9)}.
- \latex{E=(-8)+(+8)}; \latex{\qquad{}F=(-8)+(+5)};\latex{\\}\latex{\qquad G=(-8)+(-2)};\latex{\qquad H=(-8)+(+6)}.
- \latex{J=(-8)+(-5)}; \latex{\qquad{}K=(-8)+(+5)};\latex{\\}\latex{\qquad L=(+8)+(-5)}; \latex{\qquad M=(+8)+(+5)}.
{{exercise_number}}. Write word problems for the following additions.
a) \latex{(+5)+(-3)}
b) \latex{(+3)+(-8)}
c) \latex{(-4)+(-5)}
{{exercise_number}}. Complete the number pyramids. The number in each brick shows the sum of the two numbers written in the bricks below. Which numbers should be written in the bricks on top?
\latex{-1}
\latex{-2}
\latex{-3}
\latex{-4}
\latex{-2}
\latex{+4}
\latex{-5}
\latex{+2}
\latex{-5}
\latex{+8}
\latex{-4}
\latex{-2}
{{exercise_number}}. What numbers should replace the symbols to make the equalities true?
a) \latex{\bigcirc+(+8)=(+12)}
b) \latex{\bigtriangleup + (-5)=(-9)}
c) \latex{\bigcirc+(-3)=(+2)}
d) \latex{\bigtriangleup+(+2)=(-8)}
e) \latex{\square+(-8)=(-3)}
f) \latex{(-7)+\bigtriangleup=(-2)}
g) \latex{(+9)+\square=(-5)}
h) \latex{(-5)+\bigcirc=(-10)}
i) \latex{(+8)+\square=(-12)}
{{exercise_number}}. What is the sum of the numbers written on each fish?
a)
c)
d)
c)
\latex{-27}
\latex{+46}
\latex{+27}
\latex{-26}
\latex{+72}
\latex{+29}
\latex{-57}
\latex{-19}
\latex{-72}
\latex{-59}
\latex{-44}
\latex{+39}
\latex{-56}
\latex{+81}
\latex{-24}
\latex{+53}
\latex{-28}
\latex{+25}
{{exercise_number}}. In the following magic squares, the sums of the numbers in each row, column and the two diagonals are the same. What number is substituted by each letter?
a)
b)
c)
d)
\latex{-2}
\latex{-4}
\latex{+6}
\latex{-8}
\latex{-15}
\latex{-7}
\latex{+1}
\latex{-11}
\latex{+42}
\latex{-56}
\latex{-14}
\latex{+28}
\latex{-50}
\latex{+70}
\latex{+10}
\latex{-20}
B
C
E
D
F
G
H
I
J
K
L
N
M
O
P
Q
R
S
T
A
Quiz
What result do you get if you multiply the positive one-digit integers by nine and add the sum of the negative two-digit integers to it?
