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Mixed exercises
{{exercise_number}}. Which of the following statements is true?
- Zero is an even number.
- There is at least one negative integer that is less than zero.
- There is at least one negative integer that is greater than zero.
- The sum of a number and its additive inverse is always zero.
- All negative integers are less than zero.
{{exercise_number}}. Draw a number line and mark the integers that are at the following distances from \latex{ –2 }
- less than \latex{ 3 } units;
- at most \latex{ 4 } units;
- at least \latex{ 2 } units;
- more than \latex{ 5 } units;
- more than \latex{ 1 } but less than \latex{ 5 } units;
- at least \latex{ 4 } but at most \latex{ 8 } units.
{{exercise_number}}. Draw a number line and mark the integers that are at the following distances from \latex{ 3 }
- no less than \latex{ 2 } units;
- no more than \latex{ 4 } units;
- at least \latex{ 2 } but at most \latex{ 6 } units;
- at most \latex{ 2 } and more than \latex{ 1 } units;
- at least \latex{ 5 } and no less than \latex{ 3 } units;
- no more than \latex{ 5 } but no less than \latex{ 3 } units.
{{exercise_number}}. What is common in the numbers marked on the number lines?
a)
c)
d)
b)
\latex{-6}
\latex{-5}
\latex{-4}
\latex{-3}
\latex{-2}
\latex{-1}
\latex{0}
\latex{1}
\latex{2}
\latex{3}
\latex{4}
\latex{5}
\latex{6}
\latex{-6}
\latex{-5}
\latex{-4}
\latex{-3}
\latex{-2}
\latex{-1}
\latex{0}
\latex{1}
\latex{2}
\latex{3}
\latex{4}
\latex{5}
\latex{6}
\latex{-6}
\latex{-5}
\latex{-4}
\latex{-3}
\latex{-2}
\latex{-1}
\latex{0}
\latex{1}
\latex{2}
\latex{3}
\latex{4}
\latex{5}
\latex{6}
\latex{-6}
\latex{-5}
\latex{-4}
\latex{-3}
\latex{-2}
\latex{-1}
\latex{0}
\latex{1}
\latex{2}
\latex{3}
\latex{4}
\latex{5}
\latex{6}
{{exercise_number}}. Complete the table.
\latex{a}
\latex{b}
\latex{+4}
\latex{-3}
\latex{-8}
\latex{-3}
\latex{+8}
\latex{+5}
\latex{-5}
\latex{+2}
\latex{|a|}
\latex{|b|}
\latex{a+b}
\latex{|a+b|}
\latex{|a|+|b|}
\latex{|a|+b}
\latex{a+|b|}
{{exercise_number}}. The absolute values of how many integers are smaller than \latex{ 202 }?
{{exercise_number}}. Which of the following statements is true?
- The sum of two natural numbers is always a natural number.
- The difference of two natural numbers is always a natural number.
{{exercise_number}}. Perform the subtractions.
a) \latex{(+200)-(-400)}
b) \latex{(-800)-(-500)}
c) \latex{(+65)-(+450)}
d) \latex{(+370)-(-540)}
e) \latex{(-930)-(+230)}
f) \latex{(+240)-(-540)}
g) \latex{(+714)-(-825)}
h) \latex{(-756)-(-394)}
i) \latex{(-324)-(-793)}
{{exercise_number}}. What number should be subtracted from
- \latex{+18} to get \latex{+25};
- \latex{-15} to get \latex{+13};
- \latex{-32} to get \latex{-27};
- \latex{+29} to get \latex{-14};
- \latex{-37} to get \latex{0};
- \latex{-42} to get \latex{-42}?
{{exercise_number}}. The sum of three consecutive odd numbers is \latex{ −2,001 }. Which numbers are these?
{{exercise_number}}. Adding a two-digit and a three-digit integer, the result is \latex{ −1,098 }. Which are these numbers?
{{exercise_number}}. What is the sum of the numbers larger than \latex{ −20 } but smaller than \latex{ 20 }?
{{exercise_number}}. Write down
- two different negative numbers whose difference is negative;
- two different negative numbers whose difference is positive;
- two different positive numbers whose difference is negative;
- two different integers whose difference is zero;
- a negative and a positive number whose difference is zero.
{{exercise_number}}. In the calculation \latex{(\fcolorbox{black}{eaf1f9}{\phantom{a}}8) + (\fcolorbox{black}{eaf1f9}{\phantom{a}}5) - (\fcolorbox{black}{eaf1f9}{\phantom{a}}3) + (\fcolorbox{black}{eaf1f9}{\phantom{a}}6)} \latex{\fcolorbox{black}{eaf1f9}{\phantom{a}}}-s should be replaced by signs.
- How many combinations are possible?
- Calculate the result of each combination.
- Which combination gives the smallest and which the largest result?
{{exercise_number}}. Complete the table.
\latex{a}
\latex{b}
\latex{+2}
\latex{+7}
\latex{-8}
\latex{+8}
\latex{+5}
\latex{+3}
\latex{-2}
\latex{+2}
\latex{|a|}
\latex{|b|}
\latex{a-b}
\latex{|a-b|}
\latex{|a|-|b|}
\latex{|a|-b}
\latex{a-|b|}
\latex{-2}
\latex{-7}
\latex{-6}
\latex{-4}
{{exercise_number}}. Perform the calculations.
a) \latex{(+12)+(-23)-(+13)}
b) \latex{(-43)+(-23)+(+78)}
c) \latex{(-84)-(-23)+(-35)}
d) \latex{(-135)+(-43)-(+26)}
e) \latex{(+256)-(-142)+(-329)}
f) \latex{(+451)-(-253)+(-186)}
{{exercise_number}}. The results of which calculations are zero?
a) \latex{(+10)-(-10)}
b) \latex{(-15)-(-15)}
c) \latex{(+8)+(-8)}
d) \latex{(-16)-(+16)}
e) \latex{|+29|+|-29|}
f) \latex{|(+7)+(-7)|}
{{exercise_number}}. Draw a number line and mark the integers that make the following open formulas true.
a) \latex{a-(+5)=(+9)}
b) \latex{b+3=(-2)}
c) \latex{|c|=5}
d) \latex{|d|\gt4}
e) \latex{|e|\leq0}
f) \latex{|f|\lt3}
g) \latex{1\lt|g|\lt5}
*h) \latex{-h\lt(-6)}
{{exercise_number}}. All four faces of the solid in the image (tetrahedron) are regular triangles. One of the vertices is marked with \latex{ +1 }, while the other three are marked with \latex{ –1 }. On each edge of the solid, write the sum of the numbers found at its endpoints. Then, on each face, write the sum of the numbers found on the three edges serving as the sides of the face.
Calculate the sum of the numbers on each face of the solid.
\latex{-1}
\latex{-1}
\latex{-1}
\latex{+1}
{{exercise_number}}. Two adjacent vertices of a cube are marked with \latex{ +1 }, while the rest of the vertices are marked with \latex{ –1 }. On each edge of the cube, write the sum of the numbers found at its endpoints. Then, on each face, write the sum of the numbers found on the four edges serving as the sides of the face. Calculate the sum of the numbers on each face of the solid. What is the result?
\latex{+1}
\latex{+1}
\latex{-1}
\latex{-1}
\latex{-1}
\latex{-1}
\latex{-1}
\latex{-1}
\latex{\color{00918f}{-3}}
\latex{\color{00918f}{-1}}
\latex{\color{de175b}{+2}}
{{exercise_number}}. The edges of a rectangular cuboid are \latex{ 3 } \latex{ cm }, \latex{ 4 } \latex{ cm } and \latex{ 5 } \latex{ cm } long. The shortest edge is marked with \latex{ −3 }, the longest edge is marked with \latex{ −1 }, while the third edge is marked with \latex{ +2 }. On each vertex, write the sum of the numbers found on the edges meeting in that vertex. Calculate the sum of the numbers on each vertex of the solid.
{{exercise_number}}. Let’s play. The game involves throwing a blue and a red dice at the same time. The number on the blue dice will be positive (\latex{ + }), while that on the red dice will be negative (\latex{ - }). Each player starts from the space marked with \latex{ 0 } and advances on the board according to the sum or the difference of the numbers they have thrown. The players can decide whether they want to add or subtract the numbers on the dice. The winner is the first player who gets back to \latex{ 0 }.
{{exercise_number}}. While playing the previous game, Erica’s first throw was (\latex{ 3 }; \latex{ 6 }), while the second was (\latex{ 2 }; \latex{ 5 }). Andy threw (\latex{ 4 }; \latex{ 2 }) first, then (\latex{ 1 }; \latex{ 1 }). Is it possible that one of them has won the game after the second round? If the answer is yes, how?
