Informal Methods of Multiplication   Children are taught formal procedures of multiplication at school. However, they frequently develop their own informal methods which are quicker and easier to do than these formal algorithms. Those with a good understanding of place value and number principles will devise their own methods of multiplication or various methods to suit specific questions. It is important that such alternative and logically correct methods be accepted and encouraged so that children are not 'put off ' mathematics as a whole. This section shows some of the informal methods used by children to carry out multiplication, loosely classified according to the mathematical principles used. Some of these methods are mental methods and there might be more than one possible way of representing them in the written form. Some procedures used by children may have characteristics of more than one category.   Classifications Front end multiplication (left to right) Multiplication in stages (using factors) Multiplication by rounding (using distributive law) Multiplication by halving and doubling (moving factors) Miscellaneous methods to suit specific questions   Back to Main Menu Front end multiplication When multiplying, people generally like to do the bigger or important quantities first. This gives an estimate of the value expected. Such an approach is front end or left to right multiplication. Students using this method multiply the tens before the ones and hundreds before the tens and so on. They then add up these partial products to get the final result. This method is based on the distributive law of multiplication over addition. Given below are some examples of front end multiplication. Note that there will be more than one possible way of presenting the written form as this is mainly used for mental computations.   Mike Question: 23 x 8   Sam Question: 535 x 3   Chris Question: 24 x 15   Back to top Multiplication in stages Some students simplify multiplication by multiplying by the factors one by one instead of the number itself. This method could help children learn multiplication tables. For instance, the 4xtables would be much easier if thought of as double the 2xtable, or that x6 is double of x3. Here are some examples to illustrate some of the procedures using this principle. Here are some examples to illustrate some of the procedures using this principle. Sarah Question: 25 x 6 The same question was done by Nick as follows.   Nick   This method is often used when multiplication involves multiples of 10 as illustrated by David's method. David Question: 12 x 40   Back to top Multiplication by rounding Children usually use this method in multiplications where one of the numbers is close to a multiple of 10. Sometimes they use it for numbers nearby a known fact. Such a number is then rounded to the nearest ten or the known fact and then compensated by addition or subtraction. Thus this method again uses the distributive law.   Jason Question: 99 x 5 Jason thinks of 99 as 100 -1   Question: 26 x 7   Indira Question: 198 x 3 This method gives an easy way to multiply by 9 by multiplying by 10 and then subtracting the number.   Back to top Multiplication by halving and doubling Another method adopted by students is to double one factor and halve the other which leaves the product unaltered. This may be extended to four times one factor and quarter the other, or eight times one factor and eighth the other depending on the question.   Andrew Question: 8 x 15   Luke Question: 16 x 25 This gives quick method for multiplying by 25. Divide by 4 and add two zeroes. Similarly to multiply by 50, divide by 2 and add two zeroes, to multiply by 125, divide by 8 and add three zeroes.   Alan Question: 51 x 16   Back to top Miscellaneous methods to suit specific questions Apart from the methods classified above, children device short cuts to suit the question at hand. Such methods often combine more than one of the above methods.   Brendan Question: 35 x 3 Brendan used repeated addition for multiplication . However for the following question he uses halving and doubling followed by front end multiplication.   Question: 32 x 45   Anna Anna uses a number pattern with compatible numbers which she can express as follows. Question: 8 x 12 By this method, 7 x 13 = 10 x 10 - 9 = 91 24 x 16 = 20 x 20 - 16 = 400 - 16 = 384   Monica Question: 26 x 84 Monica has combined halving and doubling and front end multiplication. It is clear that she knows her number principles and multiplication well but goes to great lengths to avoid the actual written algorithm.   Back to top Back to Main Menu