Multiplying

Multiplication is a mathematical operation that scales one number by another (multiplying – sign: x). It replaces addition of a large quantity of numbers in a row. Multiplying is a math operation that is opposite of division. For example: you can substitute the mathematical expression 5+5+5+5 with 5×4 (the number 5 multiplied with the number of times it has appeared in a row).

Multiplication has several properties. When a number is multiplied with the number 1, the product (the result of multiplication) is the same as that number. When a number is multiplied with zero, the product is always zero. When a number is multiplied with negative one, the result is the negative version of that number.  It also has properties of commutativity, associativity and distributivity.

The commutative and associative properties are similar to those properties in addition. Distributivity applies when addition and multiplication are combined, as they are in this example:

a * (b + c) = a * b + a * c

A very important thing to remember is that the order of importance of multiplication is always greater than the order of importace of addition or subtraction. You first multiply the numbers (where there is need for that) and them add or subtract them. Here is an example:

5 * 4 + 3 = 20 + 3 = 23

The single exception to the rule is that addition or subtraction has priority over multiplication when  the numbers that need to be added and the operator are in brackets, and the operator of multiplication is not.

multiplication

Multiplying exams for teachers

Exam Name File Size Downloads Upload date
Positive integers
Multiplying positive integers – very easy 78 kB 1783 October 13, 2012
Multiplying positive integers – easy 143 kB 1806 October 13, 2012
Multiplying positive integers – medium 166.3 kB 1846 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 1648 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1232 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1339 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1147 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1117 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 1077 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 967 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 1041 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 1002 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1002 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1431 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1128 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 1052 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 989 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 978 October 13, 2012
Multiplying positive fractions – very hard 581 kB 996 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 990 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 1041 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 969 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 972 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 904 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 938 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 985 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 1019 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 955 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 927 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 907 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 939 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1410 October 13, 2012
Multiplying integers – easy 143.6 kB 1264 October 13, 2012
Multiplying integers – medium 173.3 kB 1280 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1257 October 13, 2012
Multiplying integers – hard 565.9 kB 1074 October 13, 2012
Multiplying integers – very hard 568 kB 991 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1184 October 13, 2012
Multiplying decimals – easy 187 kB 1335 October 13, 2012
Multiplying decimals – medium 578.8 kB 979 October 13, 2012
Multiplying decimals – medium-hard 577 kB 894 October 13, 2012
Multiplying decimals – hard 564.9 kB 959 October 13, 2012
Multiplying decimals – very hard 567.9 kB 938 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 963 October 13, 2012
Multiplying fractions – easy 186.7 kB 1087 October 13, 2012
Multiplying fractions – medium 583.8 kB 908 October 13, 2012
Multiplying fractions – medium-hard 589 kB 928 October 13, 2012
Multiplying fractions – hard 588 kB 897 October 13, 2012
Multiplying fractions – very hard 594.9 kB 925 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 918 October 13, 2012
Multiplying mixed numbers – easy 209 kB 1020 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 944 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 849 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 878 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 857 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 864 October 13, 2012
Multiplying improper fractions – easy 174 kB 877 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 874 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 821 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 865 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 867 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1405 October 14, 2012
Multiplying positive decimals 51.8 kB 1147 October 14, 2012
Multiplying positive fractions 632.1 kB 920 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 1040 October 14, 2012
Multiplying positive improper fractions 594.6 kB 852 October 14, 2012
Non positive
Multiplying integers 166.8 kB 1087 October 14, 2012
Multiplying decimals 246.3 kB 997 October 14, 2012
Multiplying fractions 393.1 kB 953 October 14, 2012
Multiplying mixed numbers 412.4 kB 918 October 14, 2012
Multiplying improper fractions 334.1 kB 926 October 14, 2012


Multiplying knowledge test