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.
Showing posts with label New Drill. Show all posts
Showing posts with label New Drill. Show all posts
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 New Drill (Level 1) : Velocity Running around a pond
It takes 12 minutes for Taro and 8 minutes for Jiro to run the surroundings of a pond 1 round.
When they started from the same point to the same direction, every how many minutes is Taro passed by Jiro ?
Math New Drill (Level 1) : Sum and difference Buy two articles in a store
There are two articles A and B in a certain store and if you buy four pieces of A and three pieces of B, it is 1000 yen.
Moreover, the price of three A is 70 yen higher than the price of two B.
Find a price of one piece of A.
Math New Drill (Level 1) : Velocity Distance between two points
I walked from A point to B point at 4 km/h and returned running at 8 km/h.
The time of a round trip was 45 minutes.
Find the distance between A and B.
Math New Drill (Level 1) : Ratios and proportions 10% discounted list price
I set the list price with 15 % profit on the cost price of a certain article.
But it did not be sold.
Then I decided to sell at 2070 yen which is 10 % discount of the list price.
Find the cost price.
Math New Drill (Level 2) Geometry (Solid figure) Cut a big cube with 125 pieces of small cubes
There are white and black cubes whose one side is 1 cm.
63 white cubes and 62 black cubes are arranged in by turns as shown in lower Fig. 1 and a large cube is made.
Furthermore, this large cube is cut so that it may pass along three point A, B, and C.
Answer the following questions.
Noted that the volume of a triangular pyramid is calculated by the formula of (the area of the bottom) × (height) / 3.
(1) Draw the situation of the cut face in the lower Fig. 2.
(2) Find the ratio of the volume of a solid including the point D to the volume of the original large cube.
(3) Find the number of white cube in a solid including the point D which is not cut.
Math New Drill (Level 2) : Number of cases Ways of route for moving
Answer the following questions.
(1) How many ways of route from A to B is there in lower Fig. 1?
Noted that there are right or down directions of moving.
(2) How many ways of route from A to B is there in lower Fig. 2?
Noted that there are right or down or lower right directions of moving.
(3) How many ways of route from A to B with passing along neither P nor Q is there in lower Fig. 3?
Noted that there are right or down or lower right directions of moving.
Math New Drill (level 2) : Patterns and Regularity Line arrangement of fractions
Numbers are arranged in a line as follows.
1/1, 1/2, 2/2, 1/3, 2/3, 3/3, 1/4, 2/4, 3/4, 4/4, 1/5, 2/5, -----
Answer the following questions.
(1) Find the 26th number.
(2) Find the sum total of the numbers from the 37th to the 55th.
(3) The sum total was 76 when I added numbers sequentially from the beginning.
Which number did I add by ?
Math New Drill (Level 1) : Geometry(Plane figure) Right hexagon in an equilateral triangle
As shown in a lower figure, the right hexagon DEFGHI is in equilateral triangle ABC.
Three points D, F, and H are on the side of the equilateral triangle and AD : DB = BF : FC = CH : HA = 2 : 3.
Answer the following questions.
(1) Find the ratio of the area of equilateral triangle ABC to the area of the triangle ADH.
(2) Find the ratio of the area of equilateral triangle ABC to the area of the right hexagon DEFGHI.
Math New Drill (level 1) : Velocity Two persons run in the round running course
There is a running course of 3.2 km one round.
Taro and Jiro run to the same direction three round from the same position.
Taro began to run at 200 m/m and Jiro began to run at 240 m/m 3 minutes afterward.
When Taro finished running one round, he stopped and drank water.
While he was drinking water, he was passed by Jiro.
Then, Taro began to run at 260 m/m, he caught up with Jiro 3 minutes afterward.
Then, although Taro ran with the same speed as Jiro, when they finished running two round, Taro walked at 80 m/m.
Furthermore, after that, Taro began to run at 200 m/m and finished running three round later than Jiro for 7 minutes and 10 seconds.
Answer the following questions.
(1) Find the time while Taro was drinking water.
(2) Find the distance where two persons ran with the same speed.
(3) Find the distance where Taro walked.
Math New Drill (level 1) : Geometry(Plane figure) Shadow area in a right hexagon
As shown in a lower figure, a right hexagon is in a circle 3 cm in radius.
The point A is the middle point of the side.
Find the area of a shadow area.
Pi is assumed to be 3.14.
Math New Drill (Level 1) : Ratios and proportions Pocket money savings
Taro gets a same amount of pocket money every month and also has some savings.
If he spends 2000 yen every month, the balance of savings come to be zero in six months.
Moreover, if he spends 1600 yen every month, the balance of savings come to be zero in nine months.
Answer the following questions.
(1) Find the amount of the pocket money every month.
(2) Find the amount of savings at the beginning.
(3) In order for Taro to have the amount of savings 12000 yen in one year, find the amount of the pocket money which can be spent every month.
Math New Drill (level 1) : Patterns and Regularity Repeated sequence of characters
The sequence of characters of "rikkyoniiza" is repeatedly arranged as rikkyoniizarikkyonizari --------.
Answer the following questions.
(1) Answer the 50th character.
(2) When counting only i, which number from the 1st character is the 2008th i ?
Math New Drill (Level 1) : Number sense and theory Find a fraction
Find such a fraction when 5 is subtracted from a denominator, it will be 1/9 and when 5 is added to a numerator, it will be 1/4.
Math New Drill (Level 2) : Patterns and Regularity Problem 9 TOYOEIWA-2008
As shown in a lower figure, the integer was clockwise arranged in order from 1.
The located integer will be expressed with which direction of what round it is.
For example, 30 is the number of the northeast of the 3rd round.
Answer the following questions.
(1) With which direction of what round is 64 located ?
(2) Find the number of the northwest of the 10th round.
(3) It was 4160 when numbers of the northwest, northeast, southeast, and southwest of a certain round was added.
Find the number of the southeast of this round.
Math New Drill (Level 2) : Geometry (Solid figure) Problem 8 TOYOEIWA-2008
The vessel below is 10 cm in height and the bottom is the form which combined a rectangle and semicircles as shown in Fig. 1.
Putting water into this vessel full and with attaching the portions of A and B to a floor, 45 degrees was leaned and water was spilt.
Fig. 2 is a figure showing that it was seen from the side.
Find the amount of the remaining water.
Pi is assumed to be 3.14.
Math New Drill (Level 2) : Velocity Problem 7 TOYOEIWA-2008
One day when Taro left home toward the school, 7 minutes after his leaving his mother noticed the thing left behind of Taro.
Although she pursued at the speed of 80 m/m immediately, she thought that she could not catch up Taro.
Then she borrowed a bicycle at the house of Taro's friend which is on the way and kept pursuing.
Although she took 3 minutes to borrow, she caught up with Taro just in front of the school gate.
The way from the house to a school is straight and the distance is 1500 m.
The graph below expresses the relation between the time after Taro leaves home and the distance of two persons.
Answer the following questions.
Noted that the speed which Taro walks, the speed which his mother walks, and the speed of the bicycle are constant respectively.
(1) Find the speed which Taro walks at the speed per minute.
(2) Find the distance from the house of Taro to his friend's house.
(3) Find the speed of the bicycle at the speed per minute.
Math New Drill (Level 1) : Number sense and theory Problem 6 TOYOEIWA-2008
There are ten cards.
One of odd numbers from 1 to 19 is written on each card.
When taking out two cards in order four times, each sum was 16, 18, 24, and 34 in order.
Find the numbers of the 2nd set and the 3rd set, respectively.
Math New Drill (Level 1) : Ratios and proportions Problem 5 TOYOEIWA-2008
There are in total 400 balls of 4 colors of red, yellow, blue and green.
We threw balls to a box.
We threw balls to a box.
The number of balls which were not in the box was 100 or less pieces.
Among the balls in a box, 1/4 was red, 1/6 was yellow and 3/7 was green.
Find the number of green balls in the box.
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