Varukorgen är tom
Mixed exercises
{{exercise_number}}. Simplify, and then perform the following operations.
- \latex{(+19) + (-27) + (+42)}
- \latex{(-15) + (52) + (-81)}
- \latex{(-47)-(-53)-(+28)}
- \latex{(+25)-(-69)-(+71)-(-24)}
{{exercise_number}}. Combine the terms.
- \latex{81-(-13)-(+9)-(-19)}
- \latex{-22 + 47-53 + 23}
- \latex{448-256 + 189}
- \latex{-3-(+27)-93-37}
{{exercise_number}}. Perform the following operations. Pay attention to the order of operations.
- \latex{(-17)-(-2)\times(-25) + (+40)\div(-8)}
- \latex{-91\div(-21 + 8) + (-17)}
- \latex{(-10)\times(+23) + (-30)\div(+6)}
- \latex{(+42)\div(-7)\times[+9-(-5)\times(-2)]}
{{exercise_number}}. Perform the following operations.
- \latex{(+4)-(-6) + (-2)\times(+13)}
- \latex{(-3)\times(-2 + 5) + (-4)\times(-3)}
- \latex{-2.5-(-2)\times(-2) + (-3)\times(-3)}
- \latex{41.6-0.8\times1.25}
- \latex{1.6\div0.25-(-4)\times0.4}
- \latex{2.4\div3-3.6\div0.04}
{{exercise_number}}. Fill in the missing numbers.
a)
b)
c)
d)
\latex{-10.8}
\latex{\div0.2}
\latex{\div(-1.8)}
\latex{\times(-0.5)}
\latex{\div(-0.09)}
\latex{+7.9}
\latex{-15.8}
\latex{-9.6}
\latex{+1.25}
\latex{-0.75}
\latex{+2.5}
\latex{\times(\qquad)}
\latex{\times(\qquad)}
\latex{-(\qquad)}
\latex{-(\qquad)}
{{exercise_number}}. Perform the following operations in the simplest way possible.
- \latex{4.5\times6 + 4.5\times4}
- \latex{9.5\times11.2-9.5\times9.2}
- \latex{7.9\times3.2 + 7.9\times16.8}
- \latex{8.7\times24.5-24.5\times3.7}
{{exercise_number}}. Decide whether the following statements are true or false.
- When adding a number to another, the sum will be greater than either of the original numbers.
- When subtracting a number from another, the difference will be smaller than the minuend.
- When a number other than zero is multiplied by a negative number, the sign of the product will be different than that of the original number.
{{exercise_number}}. Determine which digits can replace the letters if identical letters stand for the same digit, and different letters should be replaced by other digits.
B
\latex{1.}
A
\latex{\times}
\latex{3.}
C
\latex{2}
\latex{7}
F
G
\latex{\times}
\latex{7.}
G
C
\latex{3}
D
D
\latex{2}
E
\latex{3}
\latex{2}
\latex{1}
B
\latex{5}
\latex{1}
A
\latex{8.}
A
\latex{3}
\latex{0}
\latex{3}
\latex{6}
F
G
G
G
G
G
\latex{7}
\latex{0}
\latex{4.}
\latex{3}
\latex{7}
{{exercise_number}}. Which integer is
- equal to \latex{ –2 } times one-tenth of the sum of \latex{ –185 } and \latex{ +105 };
- \latex{ 1 } smaller than half of the sum of \latex{ –75 } and \latex{ –25 ?}
{{exercise_number}}. Edith made a diagram of the morning temperatures she measured over the course of one \latex{ week }.
- On which \latex{ days } was the morning temperature the highest and the lowest?
- Was the difference between the morning temperatures greater on Monday and Thursday or on Tuesday and Friday
- What was the average morning temperature during the \latex{ week? }
\latex{\degree \text{C}}
\latex{3}
\latex{2}
\latex{1}
\latex{0}
\latex{-1}
\latex{-2}
\latex{-3}
\latex{-4}
\latex{ Temperature }
Mon.
Tue.
Wed.
Thu.
Fri.
Sat.
Sun.
{{exercise_number}}. Olivia completed one lap in \latex{ 1.45 \;minutes }. How many \latex{ minutes } does it take her to complete \latex{ 3 } and a half laps if she runs at a uniform speed?
{{exercise_number}}. Who is faster: someone who ran \latex{ 100 \,metres } in \latex{ 10 \,seconds } or someone who ran \latex{ 100 \,yards } in \latex{ 9.1 \,seconds ?} \latex{ (1 \,yard \,≈ \,0.914 \,m) }
{{exercise_number}}. The sum of two numbers is \latex{ 12.7 }. One of the numbers is \latex{ 2.6 } larger than the other. What are the two numbers?
{{exercise_number}}. The sum of two decimals is \latex{ 84.15 }. The larger decimal is ten times greater than the smaller one. What are the two decimals?
{{exercise_number}}. One of the sides of a rectangle is \latex{ 0.27\, m } long, which is \latex{ 0.9} times the other side's length. How many \latex{ centimetres } is the perimeter of the rectangle? How many \latex{ square} \latex{centimetres} is its area?
{{exercise_number}}. Is \latex{ 1 } \latex{ litre } of paint enough to cover a wall that is \latex{ 4.5 } \latex{ m } long and \latex{ 2.4 } \latex{ m } high if \latex{ 1 } \latex{ litre } of paint can cover \latex{10.2 {\,m}^{2}?}
{{exercise_number}}. A kiddie pool is \latex{ 6.4 \;m } long, \latex{ 1.15 \;m } longer than its width. How many \latex{ cubic} \latex{ metres } of water are needed to fill it if its depth is \latex{ 50 \;cm?}
{{exercise_number}}. The largest popcorn box was made in Florida in \latex{ 1988 }. How high was the box if its base was a square with \latex{ 7.7 \;m } long sides, and its volume was \latex{110.2794{ \,m}^{3}?}
{{exercise_number}}.
The winners of an owner-dog running event completed the distance of \latex{ 2.5 \;km } in \latex{ 7.3 \;minutes }. On average, how many \latex{ minutes } does it take the winners to run \latex{ 1 \;km?} How many \latex{ seconds } is that?
{{exercise_number}}. The average of three numbers is \latex{ 6.1 }. The average of the two larger numbers is \latex{ 10.4 }, and their difference is \latex{ 2.8 }. What are the three numbers?
{{exercise_number}}. Make a coordinate system.
- Mark the following points in a coordinate system and plot them in this order.
\latex{A(0; 2)\quad B(1; 3)\quad C(2; 3)\quad D(3; 2)\quad E(2; 0)\quad F(0; -2)}
- Take the additive inverses of the first coordinates and leave the second coordinates unchanged. Mark these points as well. Connect the new points to the previous figure.
- Multiply every coordinate of the points in exercises a) and b) by \latex{ +2 }. Mark the resulting points in the same coordinate system.
- Subtract \latex{ –4 } from the first coordinates of points in exercises a) and b). Mark the resulting points using the same coordinate system. What do you notice?
Point hunter game in a coordinate system
The game is for \latex{2–4} players.
Equipment:
- two different dice, one for the \latex{ x }-coordinates and the other for the \latex{ y }-coordinates;
- different coloured pencils for each player;
- a coordinate system drawn on a sheet of paper as shown in the image;
- one table for each player, as shown below.
\latex{y}
\latex{x}
\latex{6}
\latex{-6}
\latex{-1}
\latex{1}
\latex{-1}
\latex{1}
\latex{6}
\latex{-6}
Rules:
- The first player throws the dice, then decides what sign the numbers will have. For example, in the case of a \latex{ 3 } and a \latex{ 4 }, the player can decide to move to point \latex{ (–3; +4) }. The player marks this point in the coordinate system using his/her own colour. Now, the player has occupied the marked point.
- The other players should determine their starting point in the same way.
\latex{-3}
\latex{+5}
\latex{+4}
\latex{-3}
\latex{-3}
\latex{+2}
\latex{+1}
\latex{+4}
the numbers thrown
with signs
with signs
the coordinates
of the occupied point
of the occupied point
- The players can again decide what signs to put in front of the next two numbers they throw. They should add the new numbers to the coordinates of their previous point. Players are not allowed to move out of the coordinate system or to a point that another player has already occupied. When moving to a new point, they should cross out the previous point.
(For example, if Player \latex{ 1 } throws a \latex{ 5 } and a \latex{ 3 }, they can be used only as \latex{ +5 } and \latex{ -3 } because otherwise Player \latex{ 1 } would move outside the coordinate system. This way, Player \latex{ 1 } moves from point \latex{ (–3; +4) } to point \latex{ (+2; +1) }.) - The player who cannot move is eliminated. The player who makes the last move wins.
