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 1728 October 13, 2012
Multiplying positive integers – easy 143 kB 1752 October 13, 2012
Multiplying positive integers – medium 166.3 kB 1784 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 1619 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1183 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1283 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1107 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1085 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 1049 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 942 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 1014 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 978 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 978 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1382 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1094 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 1018 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 958 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 949 October 13, 2012
Multiplying positive fractions – very hard 581 kB 973 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 956 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 1015 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 939 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 946 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 874 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 918 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 958 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 990 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 929 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 897 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 884 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 913 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1372 October 13, 2012
Multiplying integers – easy 143.6 kB 1231 October 13, 2012
Multiplying integers – medium 173.3 kB 1254 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1222 October 13, 2012
Multiplying integers – hard 565.9 kB 1041 October 13, 2012
Multiplying integers – very hard 568 kB 961 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1156 October 13, 2012
Multiplying decimals – easy 187 kB 1304 October 13, 2012
Multiplying decimals – medium 578.8 kB 953 October 13, 2012
Multiplying decimals – medium-hard 577 kB 869 October 13, 2012
Multiplying decimals – hard 564.9 kB 939 October 13, 2012
Multiplying decimals – very hard 567.9 kB 915 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 931 October 13, 2012
Multiplying fractions – easy 186.7 kB 1058 October 13, 2012
Multiplying fractions – medium 583.8 kB 877 October 13, 2012
Multiplying fractions – medium-hard 589 kB 899 October 13, 2012
Multiplying fractions – hard 588 kB 871 October 13, 2012
Multiplying fractions – very hard 594.9 kB 903 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 885 October 13, 2012
Multiplying mixed numbers – easy 209 kB 1003 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 916 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 822 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 857 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 835 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 846 October 13, 2012
Multiplying improper fractions – easy 174 kB 856 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 852 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 789 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 843 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 846 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1351 October 14, 2012
Multiplying positive decimals 51.8 kB 1109 October 14, 2012
Multiplying positive fractions 632.1 kB 888 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 1007 October 14, 2012
Multiplying positive improper fractions 594.6 kB 830 October 14, 2012
Non positive
Multiplying integers 166.8 kB 1054 October 14, 2012
Multiplying decimals 246.3 kB 974 October 14, 2012
Multiplying fractions 393.1 kB 917 October 14, 2012
Multiplying mixed numbers 412.4 kB 891 October 14, 2012
Multiplying improper fractions 334.1 kB 902 October 14, 2012


Multiplying knowledge test