Among the numbers of which remainder is 2 when it is divided by 4, and is 3 when it is divided by 5, what is the largest number of two-digit numbers?
Math New Drill (Level 1) : Number sense and theory Three fractions multiplied by a same fraction
Three fractions 28/3, 35/6, and 77/8 are multiplied by the same fraction and each product becomes to be integer.
Find the fraction more than 10 and the nearest to 10 among such fractions.
Math Problem (Level 3) : Tape winded around rectangular board (JJJ15)
As shown in a figure, there is a translucent red tape in which the end is cut at 45 degrees and there is a line drawn in the center of the tape.
Moreover, as shown in a figure, there is a rectangular transparent board and the point P is set on the side BC so as to BP = 3cm.
As shown in Fig. 1, the end of the central line of the tape is put on the point P and the tape is winded around a board on the surface.
The central line of the tape crosses each side of the rectangle at 45 degrees.
As for the sample in Fig.1, the tape is winded to the point S and cut with scissors along the side.
In this case, the length of the central line of the winded tape becomes PQ + QR + RS.
In addition, the shadow area of Fig. 1 is a portion where the surface and the back of the board are covered by the tape and look deep red.
Fig.2 shows that the tape is winded partially to the middle in case of the rectangle with AB=4cm and AD=12cm.
Then, the tape continues to be winded further and when the central line of the tape overlaps with the point P again, it is stopped winding and the tape is cut with scissors along the side.
Answer the following questions about the case of Fig. 2.
Consider if necessary that in case the length of two sides forming a right angle of a right-angled isosceles triangle is 1 cm, the length of the 3rd side of the triangle is assumed to be 1.414 cm.
Moreover, the thickness of the tape and the board is assumed to be 0 cm.
(1) Write the central line of the tape winded around in the figure.
Noted that write the central line of the tape on the back with a dotted line.
(2) Find the length of the central line of the winded tape.
(3) Find the area of the portion covered on the tape among the surfaces of a board.
(4) Find the area of the portion which is covered by the tape both of the surface and the back of the board and looks deep red.
Moreover, as shown in a figure, there is a rectangular transparent board and the point P is set on the side BC so as to BP = 3cm.
As shown in Fig. 1, the end of the central line of the tape is put on the point P and the tape is winded around a board on the surface.
The central line of the tape crosses each side of the rectangle at 45 degrees.
As for the sample in Fig.1, the tape is winded to the point S and cut with scissors along the side.
In this case, the length of the central line of the winded tape becomes PQ + QR + RS.
In addition, the shadow area of Fig. 1 is a portion where the surface and the back of the board are covered by the tape and look deep red.
Fig.2 shows that the tape is winded partially to the middle in case of the rectangle with AB=4cm and AD=12cm.
Then, the tape continues to be winded further and when the central line of the tape overlaps with the point P again, it is stopped winding and the tape is cut with scissors along the side.
Answer the following questions about the case of Fig. 2.
Consider if necessary that in case the length of two sides forming a right angle of a right-angled isosceles triangle is 1 cm, the length of the 3rd side of the triangle is assumed to be 1.414 cm.
Moreover, the thickness of the tape and the board is assumed to be 0 cm.
Noted that write the central line of the tape on the back with a dotted line.
(2) Find the length of the central line of the winded tape.
(3) Find the area of the portion covered on the tape among the surfaces of a board.
(4) Find the area of the portion which is covered by the tape both of the surface and the back of the board and looks deep red.
Math Problem (Level 1) : Fraction can not be reduced (G1)
How many fractions are there which cannot be reduced to its lowest numbers among 1/45, 2/45, 3/45 -- 44/45 ?
Math New Drill (Level 1) : Number of cases Point moving on the side of a square
There is a square ABCD whose length of one side of is 1.
First, the point P is in the position of A.
When I throw one coin and head comes out, the point P moves 1 and tail comes out, P moves 2 in the direction of an arrow on the side.
When I throw coin 5 times, the point P came to the position of A.
In this case, how many kinds of way of head and tail coming out are there?
<Example> When throwing twice and coming to the position of D, there are two kinds, (Head, Tail),(Tail, Head).
Math Problem (Level 3) : Right dodecagon (JJJ14)
Answer the following questions about a right dodecagon.
(1) Find the number of a diagonal line.
(2) Write in all the right dodecagons that have every side on the dotted line in the figure.
(1) Find the number of a diagonal line.
(2) Write in all the right dodecagons that have every side on the dotted line in the figure.
Math Problem (Level 1) : Questionnaire to 41 students (F7)
I took a questionnaire to 41 students.
There were eight students who drunk milk and 28 students who ate bread this morning.
Find the least number and the most number of the student who did not drink milk nor eat bread this morning.
There were eight students who drunk milk and 28 students who ate bread this morning.
Find the least number and the most number of the student who did not drink milk nor eat bread this morning.
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