Abacus (1958)

[Music] every second of the day and night use machines to help them solve number problems quickly and easily these modern machines speed through tiresome jobs here is a machine that can add subtract multiply divide and do many other things man has come far from the days of long ago when the things he used for figuring were the built-in type man found his ready-made Computing system very useful but very limited man being very clever looked for better ways to tell how many he began to use use markers to keep track of things counters notches and sticks knots in a rope or Pebbles to stand for each animal in his flock helped him tell how many that worked well for a while but gradually his flocks grew larger and larger and he began to own so many other things that using one counter for each object was too clumsy something quicker and easier was needed to show how many what do you think man did to solve this problem well he thought and he thought and he developed the idea of taking 10 counters out of the original line of counters and then placing one counter in a line at the left to stand for 10 ones this idea led him to make one of the first counting machines which we call an abacus the Abacus was invented thousands of years ago but it's still used today in many parts of the world here is a Chinese Swan pon a Japanese soroban and a Russian shti although the idea of the Abacus is very old its use for us is as modern as satellites space travel and guided [Music] missiles by understanding and using the Abacus we can discover the meaning of our number system let's watch these children as they discuss some of the things they discovered about the number system these are openend abachi they are boards on which we have fitted sticks to show groupings of ones groupings of tens groupings of hundreds and groupings of thousands we put counters on the sticks to show how many of each grouping we have we really carry in addition when we add eight and four on our Abacus we put eight counters on the one stick and then we put on four more and we have 12 counters but on our Abacus just as when we write numbers the largest value we show in one position is nine when we have 10 or more counters on any stick we take 10 counters off and use one counter to stand for a group of 10 so we take 10 counters off the one stick and use one of the 10 counters to place on the 10 stick the one counter on the 10 stick stands for one group of 10 we have 11 10 and two 1es or 12 can you add 26 and 16 on your Abacus we' show 26 on the advocus as 2 10 and 6 1es now we add six ones to the ones position this makes 12 ones so we take 10 counters off the one stick the 10 counters are used as one group of 10 then we add 1 10 we have four 10 and two 1es we can read the answer on the Abacus 42 if we add 43 and 72 it works like this three ones and two ones make five ones four tens and seven tens make 11 t What do we do if we have 10 or more counters on the 10 stick we take 10 of the counters off the 10 stick and group them as 100 on the 100 stick the abaca shows 115 as our answer let's see how we show zeros on our Abacus we add five ones and five ones and we have 10 ones when we take the 10 counters off the one stick and put one counter on the 10 stick to show a group of 110 there aren't any counters on the one stick when we write 5 + 5 = 10 we use a zero to show not any ones do we need a zero on the Abacus well let's see on the Abacus we don't need a special counter or marker for a zero the stick that hasn't any counters is kind of zero the stick holds the player not any do you see why we talk about carrying in addition when we group 10 ones to 110 we say we carry one we mean that we group the 10 ones to 110 when we group 101 to 100 we carry 100 the one we carry always stands for a group of 10 of the value to its right subtraction works in the opposite direction from addition when we add we increase when we subtract we decrease there are two directions for counting increase and decrease let's work this example to work the example we can show 35 on the Abacus 3 10 and 5 1es then we can subtract the ones 5 1es - 2 1's leaves 3 1es next we subtract the 10 3 10 - 1 10 leaves 2 10 the answer 23 but what about 42 - 16 we'd show 42 on the Abus we want to take away 6 1es but since 6 ones are more than two 1es we must use one of the four tens leaving three tens we regrouped the 1 10 to 10 1es adding them to the two 1es making 12 1es we subtract 6 1es from the 12 1es leaving 6 1es 31 - 11 10 leaves 2 10 our answer is 26 grouping 10 1's to 110 and regrouping 110 to 10 ones is like trading one dime for 10 pennies or 10 pennies for one dime 10 pennies and one dime are equal in money value grouping 10 tens to 100 and regrouping 100 to 10 10 is like trading 10 dimes for $1 or like trading $1 for 10 dimes and on our Abacus one counter on the 10 stick stands for 10 10 counters on the one stick one counter on the 100 stick stands for 10 counters on the 10 stick do you see what is true each time we move a counter one place to the left it stands for a value that is 10 times as large as it was before if we move a counter two places to the left it stands for a number value that is 100 times as large as it was before look do you see this idea three counters on the 10 stick stand for a value that is 10 times as much as three counters on the one stick the three counters on the one stick have a value t as small as the three counters on the 10 stick as man needed to show larger and larger numbers he could keep adding more sticks to his is Abacus as in writing numbers we can keep on and on and there is no last number the ideas that work with ones tens hundreds and thousands can go to tens of thousands hundreds of thousands millions tens of millions hundreds of millions billions and on and on and on use you receive with the film to illustrate the things that we have disc used now you'll want to include these ideas positions on the Abacus are like positions that we use when we write numbers ones tens hundreds and so on the largest number value we write in a position is nine on the Abacus we show only nine counters on any one stick when we add numbers such as8 and 8 we have 16 counters on the stick but we group group them as 11 10 and 6 1es when we subtract we can regroup 110 to 10 1es 100 to 10 10 and so on the stick that doesn't have any counters on it acts as a placeholder it serves like the zero we use when we write numbers the ideas of grouping and regrouping are great ideas show how they work on your advocus or by telling about them in your class the number system is one of the greatest things that man ever invented the advocus can help you understand the number system if you understand the how and why of mathematics mathematics will be one of your favorite subjects oh