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 1629 October 13, 2012
Multiplying positive integers – easy 143 kB 1615 October 13, 2012
Multiplying positive integers – medium 166.3 kB 1637 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 1522 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1107 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1194 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1057 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1032 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 997 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 895 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 936 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 916 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 916 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1316 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1028 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 963 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 893 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 886 October 13, 2012
Multiplying positive fractions – very hard 581 kB 916 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 896 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 924 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 890 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 881 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 829 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 870 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 888 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 920 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 862 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 833 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 840 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 845 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1275 October 13, 2012
Multiplying integers – easy 143.6 kB 1139 October 13, 2012
Multiplying integers – medium 173.3 kB 1165 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1155 October 13, 2012
Multiplying integers – hard 565.9 kB 958 October 13, 2012
Multiplying integers – very hard 568 kB 895 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1095 October 13, 2012
Multiplying decimals – easy 187 kB 1223 October 13, 2012
Multiplying decimals – medium 578.8 kB 902 October 13, 2012
Multiplying decimals – medium-hard 577 kB 823 October 13, 2012
Multiplying decimals – hard 564.9 kB 872 October 13, 2012
Multiplying decimals – very hard 567.9 kB 859 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 858 October 13, 2012
Multiplying fractions – easy 186.7 kB 985 October 13, 2012
Multiplying fractions – medium 583.8 kB 825 October 13, 2012
Multiplying fractions – medium-hard 589 kB 842 October 13, 2012
Multiplying fractions – hard 588 kB 804 October 13, 2012
Multiplying fractions – very hard 594.9 kB 846 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 838 October 13, 2012
Multiplying mixed numbers – easy 209 kB 942 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 862 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 785 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 793 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 797 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 773 October 13, 2012
Multiplying improper fractions – easy 174 kB 805 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 796 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 733 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 796 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 780 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1239 October 14, 2012
Multiplying positive decimals 51.8 kB 1041 October 14, 2012
Multiplying positive fractions 632.1 kB 835 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 921 October 14, 2012
Multiplying positive improper fractions 594.6 kB 775 October 14, 2012
Non positive
Multiplying integers 166.8 kB 975 October 14, 2012
Multiplying decimals 246.3 kB 916 October 14, 2012
Multiplying fractions 393.1 kB 854 October 14, 2012
Multiplying mixed numbers 412.4 kB 828 October 14, 2012
Multiplying improper fractions 334.1 kB 847 October 14, 2012


Multiplying knowledge test