JP2017091074A - Multiplying and dividing abacus - Google Patents
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本発明は、掛け算、割り算を行う際に九九を覚えずとも相当の速さで計算のでき、正確に計算するのに好適な乗除算そろばんに関する。 The present invention relates to a multiplication and division abacus that can be calculated at a considerable speed without having to remember multiplication when performing multiplication and division, and is suitable for accurate calculation.
数の概念と加減乗除の計算力は、現代の社会生活を営む上で基本となるものであり、小さいうち（小学校低学年のうち）にしっかりと身につけておく必要がある。しかし、数は、非常に抽象的なものであるため、それ自体の把握はもとより、数の足し算や引き算を習得することは子供にとって難しい。このためそろばん教育が見直され復活している。しかし乗除算においては掛け算九九を覚える必要がある。掛け算九九は理屈抜きで覚えるため、乗除算の意味がとかくおろそかになり、ある具体的な文章問題を解くのに乗算でやるのか除算でやるのかが判定できない生徒が相当数発生するという問題がある。 The concept of numbers and the ability to add, subtract, multiply, and divide are fundamental to running a modern social life, and it is necessary to acquire them well while they are small (in the lower grades of elementary school). However, because numbers are very abstract, it is difficult for children to learn how to add and subtract numbers, as well as knowing the numbers themselves. For this reason, abacus education has been reviewed and revived. However, in multiplication and division, it is necessary to remember multiplication table. Multiplication tables are memorized without reason, so the meaning of multiplication and division is neglected, and there is a problem that there are a considerable number of students who can not determine whether to do multiplication or division to solve a specific sentence problem is there.
なし None
新版 そろばん入門、相楽茂一著、金園社、東京、
２００２年８月１０日
New edition abacus introduction, Souichi Soraku, Kinensha, Tokyo,
August 10, 2002
しかし掛け算、割り算をかなりの速さで計算するためには掛け算九九を覚えなければならない。 However, in order to calculate multiplication and division very quickly, you must remember multiplication tables.
また九九を覚えたからといって、ともすると掛け算の意味、被乗数をゼロに乗数回足したものが積であること、また割り算の意味、被除数から除数がゼロになるまでに何回引けるかが商であるということが理解できていないため、文章題を掛け算でやるのか割り算でやるのかが判断できない子供が大勢できる。 Also, because I learned the multiplication table, the meaning of multiplication, the product of the multiplicand plus zero times the product, the meaning of division, how many times can I subtract from the dividend until the divisor becomes zero? Since it is not understood that it is a quotient, there can be many children who cannot determine whether to write or divide text problems.
従来のそろばんを用いても、掛け算の積は被乗数をゼロに乗数回足せば計算でき、また割り算の商も被除数から除数をゼロになるまで何回も引いて求めることは可能であり、従来のそろばんを用いて九九を覚えずとも掛け算、割り算を実行する事ができ、掛け算、割り算の意味も理解できる。 Even with the conventional abacus, the product of multiplication can be calculated by multiplying the multiplicand by zero and the division quotient can be obtained by subtracting the divisor from the dividend many times until it reaches zero. You can execute multiplication and division using the abacus without having to remember the table, and understand the meaning of multiplication and division.
しかし、上記した従来のそろばんで何回も足し算、引き算を行うという方法は九九を覚えて計算する場合に比べて非常に長い時間がかかり、特に数字の桁数が大きくなると時間がかかりすぎるという欠点を有している。 However, the method of adding and subtracting many times with the above-mentioned conventional abacus takes a very long time compared with the case of memorizing the multiplication tables, especially when the number of digits increases, it takes too much time. Has drawbacks.
本発明の目的は、上記事情に鑑み、繰り返し足し算・引き算を行う為の時間を短縮することにあり、本発明は以下の手段をとり乗除算そろばんと称する。 In view of the above circumstances, an object of the present invention is to shorten the time required for repeated addition / subtraction, and the present invention takes the following means and calls it a multiplication / division abacus.
足し算・引き算５回分を１回で済ますため五珠５個分を１個で表す五五珠（７）を追加し、また通常１個か２個の五珠（６）の数を４個ないし五個に増やす。また場合によって五五珠（７）２個分を１個で表す五十珠（８）を追加する。 In order to complete 5 additions and subtractions in 1 time, add 5 pearls (7) that represent 5 pearls as 1 and usually add 4 or 5 pearls (6). Increase to five. In some cases, fifty pearls (8) representing two fifty pearls (7) are added.
掛け算を何回も足し算を行って実行する際、５回分の足し算を五五珠（７）および五珠（６）を用いて１回で済ます事ができるようになるため、計算が速くなる。また掛け算九九を覚える必要が無くなる。 When the multiplication is performed by adding many times, the addition of five times can be performed once using Gogoro (7) and Goro (6), so the calculation becomes faster. Also, there is no need to learn multiplication tables.
また割り算についても、何回も引き算を行って実行する際、５回分の引き算を五五珠（７）および五珠（６）を用いて１回で済ます事ができるようになるため、計算が速くなる。また掛け算九九を覚える必要が無くなる。 In addition, when dividing and executing a number of times, the subtraction for 5 times can be done once with Gogoro (7) and Goro (6). Get faster. Also, there is no need to learn multiplication tables.
以下発明を実施する為の形態を実施例１と実施例２につき説明する。 A mode for carrying out the invention will be described below with respect to Example 1 and Example 2.
五回分の足し算、引き算を一回で済ます為に五珠（６）の数を４個乃
至５個とし梁（３）の下に一珠（５）と並べて配置する。
In order to add and subtract five times in one time, the number of five pearls (6) is four to five, and the pearls (5) are arranged side by side under the beam (3).
また五珠（６）５個分を１個で表すために五五珠（７）。読み方は「ごごだま」、
５＋５は１０なので五珠（６）２個で一桁上の一珠１個（５）と同じ値です
[５＋５=１０]。また五五珠（７）１個は同じ桁の五珠（６）１個と
一桁上の一珠（５）２個と同じ値です[５＋５＋５＋５＋５＝２５]。
In addition, in order to express five pearls (6) by one, five pearls (7). How to read "Sago"
Since 5 + 5 is 10, 2 pearls (6) are the same value as 1 pearl (5) one digit higher
[5 + 5 = 10]. In addition, one Gogo (7) is the same value as one Gogo (6) of the same digit and two single Gojo (5) [5 + 5 + 5 + 5 + 5 = 25].
五五珠（７）は３個以上とし、梁（３）の上に配置する。 There are three or more gogo beads (7), and they are placed on the beam (3).
または五五珠（７）を１個として五珠（６）の梁（３）の上に配置し、五
五珠（７）２個分を五十珠（８）として一珠（５）の梁（３）の上に配置
する。図１−１及び図４−１に示す。
Or, place one of the five five pearls (7) on the beam (3) of the five pearls (6), and two five five pearls (7) as one fifty pearls (8) of one pearl (5). Place on the beam (3). It is shown in FIGS. 1-1 and 4-1.
乗除算そろばんの１番目の実施例を図１−１および図１−２に示す。 A first embodiment of the multiplication and division abacus is shown in FIGS. 1-1 and 1-2.
図１−１は実施例１の平面図、図１−２は実施例１の断面図である。図１−１の乗除算そろばんの下の数字は珠の位置が表す数である。 1-1 is a plan view of the first embodiment, and FIG. 1-2 is a cross-sectional view of the first embodiment. The numbers under the multiplication / division abacus in FIG. 1-1 are the numbers represented by the positions of the beads.
この例では五十珠（８）を用いる代わりに五五珠（７）を４個用いている。
五五珠（７）は３個でも掛け算、割り算ができる。
なお一珠（５）、五珠（６）も五個ずつ用いているが、４個ずつでも良い。
In this example, instead of using fifty pearls (8), four fifty pearls (7) are used.
You can multiply and divide Gogoro (7) by three.
Note that one pearl (5) and five pearls (6) are also used, but four may be used.
色彩乃至材質乃至形状を変えて１珠（５）、五珠（６）五五珠（７）が一見して区別できるようにする。例えば一珠（５）は茶色とし１，１００，
１００００の位の五珠（６）及び五五珠（７）は例えば白色とし、１０，１０００、の位の五珠（６）及び五五珠（７）は例えば赤色とする。
By changing the color, material, or shape, one pearl (5), five pearls (6), five pearls (7) can be distinguished at a glance. For example, one pearl (5) is brown, 1,100,
For example, the five-thousand pearls (6) and five-five pearls (7) at the 10000th place are white, and the five-thousands (6) and the five-thousand pearls (7) at the 10,1000th order are, for example, red.
なおこの乗除算そろばんは五珠（６）を一珠（５）、五五珠（７）を五珠（６）と見なせば図１−３のように従来の中国式のそろばんとしても使用でき、より１０進法の桁数の大きい足し算、引き算、更に掛け算九九を覚えればより桁数の大きい掛け算、割り算に使用する事もできる。また１６進数の計算にも使用できる。 This multiplication / division abacus can also be used as a traditional Chinese abacus as shown in Fig. 1-3, assuming that five pearls (6) are one pearl (5) and five pearls (7) are five pearls (6). It can also be used for addition and subtraction with a larger number of decimal digits, and further multiplication and division with a greater number of digits by learning the multiplication table. It can also be used to calculate hexadecimal numbers.
掛け算の例として８x６を実施例１の乗除算そろばん図１−１で実行するやりかたを
図２−１、図２−２、図２−３、図２−４、図２−５、図２−６に示す。図２−１で問いの位置に６の形をつくる。
As an example of multiplication, FIG. 2-1, FIG. 2-2, FIG. 2-3, FIG. 2-4, FIG. 2-5, FIG. It is shown in FIG. In Fig. 2-1, form 6 at the question position.
図２−２で問いの位置の五珠（５）を下げ、また答えの位置の五五珠（７）１個と五
珠（６）３個をあげて８を５回足した結果を作る。
In Fig. 2-2, lowering the five pearls (5) at the question position, and raising one five (5) pearls (7) and three five pearls (6) in the answer position, the result of adding 8 five times is created. .
図２−３でさらに問いの位置の一珠を下げ、８を１回足すために答えの位置の五珠（
６）１個を上げ、一珠（５）３個を上げる。
In Fig. 2-3, the pearl of the question position is further lowered, and the pearl of the answer position (in order to add 8 once)
6) Raise 1 and raise 3 pearls (5).
図２−４で答えの位置の１の位の五五珠（７）１個を取り，一桁上の１０の位の一珠
（５）２個を上げ、また１の位の五珠を１個上げる。
In Fig. 2-4, take one gobet (7) at the 1st place in the answer position, raise 2 1st place bead (5) at the 10th digit, and raise the 1st place bead Raise one.
図２−５で答えの位置の１の位の五珠を２個下げ、１０の位の１珠を１個上げる。 In Fig. 2-5, lower the first five bead at the answer position by two and raise one tenth at the tenth position.
図２−６で答えの位置の１の位の五珠を２個下げ、１０の位の１珠を１個上げて、答
え４８を得る。
In FIG. 2-6, the first five bead at the answer position is lowered by two, and the first one at the tenth place is raised by one to obtain answer 48.
割り算の例として６７÷８を実施例１の乗除算そろばん図１−１で実行するやりか
たを図３−１、図３−２、図３−３、図３−４、図３−５、図３−６、図３−７に示す。図３−１で除数の位置に８の形をつくり、被除数の位置に６７の形をつくる。被除数の１０の位の６から除数８は引けない。そこで被除数の１０の位の６を１の位に下ろす。
As an example of division, how to execute 67 ÷ 8 in the multiplication and division abacus of FIG. 1-1 according to the first embodiment is shown in FIGS. 3-1, 3-2, 3-3, 3-4, 3-5, FIG. It is shown in 3-6 and FIGS. 3-7. In FIG. 3-1, a shape of 8 is created at the divisor position and a shape of 67 is created at the dividend position. The divisor 8 cannot be subtracted from 6 in the 10th place of the dividend. Therefore, the 6th digit of the dividend is lowered to the 1st digit.
図３−２被除数の１０の位の五珠（５）を１個下げ、１の位の五五珠（６）を２個下
げる。また答えの位置の１０の位の一珠（５）を１個下げ、１の位の五珠（６）を２個上げる。
Fig. 3-2 Decrease the tenth place bead (5) of the dividend by one and lower the first place five bead (6) by two. In addition, the tenth place bead (5) in the answer position is lowered by one and the first place bead (6) is raised by two.
図３−３で除数を引いた回数の１の桁の五珠（５）を１個上げ、被除数の１の桁の五
五珠（６）１個を上げる。また五珠を３個下げる。
In Fig. 3-3, raise the one-digit gobet (5), which is the number of times the divisor is subtracted, and raise the one-digit gobet (6) of the dividend. Also lower 3 pearls.
図３−４で被除数の１の桁の五五珠（７）１個を上げ、五珠（６）を５個上げる。 In Fig. 3-4, raise one gogo pearl (7) of the first digit of the dividend, and raise five pearls (6).
図３−５で除数を引いた回数の１の桁の一珠（５）１個を上げ、被除数の五珠（６）
を１個下げる。また被除数の五珠（６）を１個下げ、一珠（５）を２つ上げる。
Fig. 3-5 Raises one pearl (5), which is the number of times the divisor has been subtracted, to give the dividend five pearls (6)
1 down. Also, lower the dividend of 5 pearls (6) and raise 2 pearls (5).
図３−６で除数を引いた回数の１の桁の一珠（５）１個を上げ、被除数の五珠（６）
を１個下げる。また被除数の一珠（５）を３個下げる。
Fig. 3-6 Increase the number of one-digit pearl (5) that is the number of times the divisor has been subtracted, then increase the number of pearls (6)
1 down. Also, lower the divide 1 pearl (5) by three.
図３−７で除数を引いた回数の１の桁の一珠（５）１個を上げ、被除数の五珠（６）
を２個下げる。また被除数の一珠（５）を２個上げる。
このようにして６７割る８は商８、あまり３を得る。
Raise one pearl (5), one digit of the number obtained by subtracting the divisor in Fig. 3-7, and divide five pearls (6)
Lower two. Also, raise 2 pearls (5) of the dividend.
In this way, 67 divided by 8 gets quotient 8, too much 3.
図４−１に乗除算そろばんの２番目の例を示す。 Fig. 4-1 shows the second example of multiplication and division abacus.
図４−１の乗除算そろばんの下の数字は珠の位置が表す数である。
図４−２は断面図である。
一珠（５）４個と五珠（６）４個を並べて配置する。五五珠（７）１個を五珠（６）４個の梁の上に配置する。また五五珠２個を表す五十珠（８）（ごじゅうだま）１個を一珠（５）４個の梁の上に配置する。
The numbers below the multiplication / division abacus in Fig. 4-1 are the numbers that the positions of the beads represent.
FIG. 4B is a cross-sectional view.
Four pearls (5) and four pearls (6) are arranged side by side. One Gogo (7) is placed on four (6) four beams. Also, one fifty pearl (8) representing two fifty pearls is placed on four beams of one pearl (5).
なお図４−３に示すように、この乗除算そろばんは五珠（６）を一珠、五五珠（７）
及び五十珠（８）を５珠と見なせば従来のそろばんとしても使用でき、桁数の大きな乗除算そろばんを用いずともより桁数の大きい足し算、引き算、更に九九を覚えればより桁数の大きい掛け算、割り算に使用する事もできる。
As shown in Fig. 4-3, this multiplication and division abacus has five pearls (6), one pearl (5)
And if fifty-five pearls (8) are regarded as five pearls, it can be used as a conventional abacus, and without using a multiplication / division abacus with a large number of digits, more digits can be added and subtracted. It can also be used for multiplication and division with large numbers.
一珠（５）と五珠（６）を区別するために一珠（５）と五珠（６）の色彩乃至材質乃至形状を変え、一見して一珠と五珠（６）が判別できるようにする。五五珠（７）と五十珠（８）も色彩乃至材質乃至形状を変えて五五珠（７）と五十珠（８）が一見して区別できるようにする。 In order to distinguish one pearl (5) from five pearls (6), the color or material or shape of one pearl (5) and five pearls (6) can be changed, and one pearl and five pearls (6) can be distinguished at a glance. Like that. The five-five pearls (7) and fifty-five pearls (8) are also changed in color, material or shape so that the five-five pearls (7) and fifty-five pearls (8) can be distinguished at a glance.
例えば一珠（５）は茶色とし１，１００，１００００の位の五珠（６）及び五五珠（７）は例えば白色とし、１０，１０００、の位の五珠（６）及び五五珠（７）は例えば赤色とする。また五十珠（８）は例えば青色とする。 For example, one pearl (5) is brown and five pearls (6) and five five pearls (1) in the order of 1,100,10000 are white, for example, five pearls (6) and five (5) pearls in the order of 10,1000. (7) is, for example, red. The fifty pearls (8) are blue, for example.
掛け算の例として９x７を実施例２の乗除算そろばん図４−１およ
び図４−２で実行するやりかたを図５−１、図５−２、図５−３
、図５−４、図５−５、図５−６に示す。
As an example of multiplication, FIG. 5-1, FIG. 5-2, FIG. 5-3 show how to execute 9 × 7 in the multiplication and division abacus of FIG. 4-1 and FIG. 4-2.
5-4, FIG. 5-5, and FIG. 5-6.
被乗数９と乗数７を図５−１のようにつくる。 Multiplicand 9 and multiplier 7 are created as shown in FIG.
まず９を五回積の位置の０に足す為に図５−２のように乗数の位置の五珠（６）を
上げて２とし、積の位置の五五珠（７）を下げ、また五珠（６）４個を上げて９を５回足した数の形を作る。
First, in order to add 9 to 0 at the position of the 5th product, as shown in Fig. 5-2, the goblet (6) at the multiplier position is raised to 2 and the gobet (7) at the product position is lowered. Raise four pearls (6) to make a shape that adds 9 to 5 times.
さらに９をもう１回足す為に図５−３のように乗数の位置の一珠を下げて１とし、
積の位置に９を足すために五五珠（７）を上げ、五珠（６）４個を下げる。そして五十珠（８）を下げて積の位置に５を足す。さらに一珠（５）４個を上げて積の位置に追加の４を足す。
In order to add 9 again, the multiplier position is lowered to 1 as shown in Fig. 5-3.
Raise Gogo (7) to add 9 to the position of the product, and lower 4 Goju (6). Then lower fifty pearls (8) and add 5 to the product position. Raise 4 pearls (5) and add an additional 4 to the product position.
９をもう１回足す為に図５−４のように乗数の位置の一珠（５）を下げて０とし、
積の位置に９を足すために五珠（６）２個を上げ、一珠（５）１個を下げる。
In order to add 9 again, as shown in Fig. 5-4, the multiplier pearl (5) is lowered to 0,
In order to add 9 to the position of the product, raise 5 pearls (6) and lower 1 pearl (5).
結果を整理するため図５−５のように積の位置の五十珠（８）を上げ、１０の位の
五珠を１個あげる。
In order to organize the results, as shown in Fig. 5-5, raise the fifty pearls (8) at the product position and raise one pearl at the tenth place.
更に１の位の五珠（６）２個を下げ、１０の位の一珠（５）を１個あげる。 Further, lower the two 1st place bead (6) and raise one 10th place bead (5).
結果を整理する為に図５−６のように１の位の五珠（６）２個を下げ、１０の位の
一珠（５）を１個あげる。この結果９x７＝６３を得る。
In order to organize the results, as shown in Fig. 5-6, two 1-digit pearls (6) are lowered and one 10-digit pearl (5) is raised. As a result, 9 × 7 = 63 is obtained.
割り算の例として７２÷９を実施例２の乗除算そろばん、図４−１および図４−
２で実行するやりかたを図６−１、図６−２、図６−３、図６−４、
図６−５、図６−６、図６−７に示す。
As an example of division, 72 ÷ 9 is the multiplication / division abacus of the second embodiment, FIG.
6, FIG. 6-2, FIG. 6-3, FIG. 6-4,
It is shown in FIGS. 6-5, 6-6, and 6-7.
まず図６−１のように除数の位置に９、被除数の位置に７２の形をつくる。また除
数を引いた回数は０である。
First, as shown in FIG. 6A, 9 is formed at the divisor position and 72 is formed at the dividend position. The number of times the divisor is subtracted is 0.
被除数の１０の位の被除数７から除数９は引けないので、図６−２の
ように被除数の１０の位の五珠（６）を１個下げ、被除数の１の位の五十珠（８）を下げる。
Since the divisor 9 cannot be subtracted from the dividend of the tenth place of the dividend, as shown in FIG. 6-2, the tenth place of the tenth place of the dividend (6) is lowered by one, and the first place of the dividend is the 50th place (8 ).
図６−３のように被除数の１０の位の一珠（５）を２個下げ、被除数の１の位の五珠
（６）を４個上げる。
As shown in FIG. 6-3, the tenth pearl (5) of the dividend is lowered by two, and the five first pearls (6) of the dividend is raised by four.
図６−４のように除数を引いた回数１の位の五珠（６）を１個上げ、被除数の１の位
の五十珠（８）を上げる。さらに被除数の１の位の五珠（６）
４個を下げ、被除数の１の位の五五珠（７）を下げる。
As shown in FIG. 6-4, the number of the 1st place bead (6) subtracted from the divisor is raised by one, and the number of the 1st place of the dividend is raised by 50 (8). Furthermore, the five-digit pearl of the dividend (6)
Lower 4 and lower the five-digit pearl (7) of the dividend.
図６−５のように除数を引いた回数１の位の一珠（５）を１個上げ、被除数の１の位
の五五珠（７）を上げ、さらに被除数の１の位の五珠（６）
３個を上げ、被除数の１の位の一珠（５）１個を上げる。
As shown in Fig. 6-5, the number of the 1st place pearl (5) minus the divisor is raised by 1, the number of the 5th place of the dividend (5) is raised, and the place of the 1st place of the dividend is further increased. (6)
Raise 3 and raise 1 pearl (5) of the dividend.
図６−６のように除数を引いた回数１の位の一珠（５）を１個上げ、被除数の１の位
の五珠（６）を２個下げ、さらに被除数の１の位の一珠（５）
１個を上げる。
As shown in Fig. 6-6, the number of the 1st place pearl (5) minus the divisor is increased by 1, the number of the 1st place bead (6) is lowered by 2, and the number of the 1st place of the dividend is further reduced. Pearl (5)
Raise one.
図６−７のように除数を引いた回数１の位の一珠（５）を１個上げ、被除数の１の位
の五珠（６）を１個下げ、さらに被除数の１の位の一珠（５）
４個を下げる。こうして７２割る９の商は８であまりは０であることがわかる。
As shown in Fig. 6-7, the number of the 1st place pearl (5) minus the divisor is increased by 1, the number of the 1st place bead (6) is lowered by 1, and the number of the 1st place of the dividend is further decreased. Pearl (5)
Lower 4 pieces. Thus, it can be seen that the quotient of 9 divided by 72 is 8 and is too much.
１ 乗除算そろばん
２ 枠
３ 梁
４ 桁
５ 一珠
６ 五珠
７ 五五珠
８ 五十珠
1 Multiplication abacus 2 Frame 3 Beam 4 Digit 5 One pearl 6 Five pearls 7 Five five pearls 8 Fifty pearls
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