The ability to multiply large numbers is required daily. Sometimes it is necessary to consider the cost of several commodity units in shop. And sometimes the child asks to help with doing homework. There are several ways to learn the work of two large numbers without use of the calculator. Let's consider them on the example of multiplication 42 and 21.
It is required to you
- - sheet of paper;
- - handle.
Instruction
1. One of the easiest ways to learn the work of two numbers - to multiply them in a column. Teach it at elementary school, but if you forgot partially how to do it, it is worth refreshing the knowledge. Write two numbers the friend under the friend and draw from below a horizontal line. Execute multiplication of the first by units of the second and write down result. Increase the first by the dozen second (the result of multiplication in this case should be written, having a little displaced it to the left). Draw one more horizontal line and calculate the sum of the received numbers. It will also be work 42 and 21. The same way it is possible to multiply both three-digit, and five-digit numbers.
2. If near at hand there is no sheet of paper, then it is possible to multiply numbers in mind. For this purpose it is necessary to present one of multipliers in the form of dozens and units. Thus, 42kh21=42kh (20+1). Multiplication by round number is carried out by multiplication of the first multiplier by 10 with the subsequent multiplication of the received work by quantity of the dozen second multiplier. To increase by 10, it is optional to make difficult mathematical calculations, it is enough to attribute to number zero on the right. So, at multiplication 42 on 20 it is necessary at first 42 to increase by 10, and then to double the received work. 42х20=42х10х2=420х2=840. This number should be held in memory. The second stage of multiplication in mind is multiplication of the first by units of the second, in this case 42х1=42. Then it is necessary to put the numbers which turned out as a result of the first and second action. Their sum will also be work 42 and 21. 840+42=882danny the way helps to multiply two-place numbers. Someone can find the work of three-digit thus. To multiply numbers with a large number of categories hardly it will turn out.
3. There is one more unusual way of multiplication of numbers. Draw the graphic scheme of the first multiplier on the sheet of paper. Present it in the form of the parallel horizontal lines designating number of dozens and units. Between the first and second category of schematically presented number leave distance in five centimeters. In the same way draw the graphic scheme of the second multiplier, only its parallel lines have to be located vertically and cross lines of the first. Now count quantity of points in which lines are crossed. The number of points in the left top crossing will designate the number of hundreds. Points in the right lower crossing - the number of units. The sum of the points located on diagonal (in the left lower and right top crossing) - the number of dozens. Write down the received result, it also is work 42 and 21. In such a way it is possible to multiply any multidigit numbers. Only it will be necessary to pay much attention to calculation of points of intersection in various diagonals.