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 1831 October 13, 2012
Multiplying positive integers – easy 143 kB 1859 October 13, 2012
Multiplying positive integers – medium 166.3 kB 1908 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 1679 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1278 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1384 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1199 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1153 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 1103 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 992 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 1079 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 1026 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1026 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1467 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1178 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 1082 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 1017 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 1007 October 13, 2012
Multiplying positive fractions – very hard 581 kB 1018 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1034 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 1065 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 992 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 990 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 940 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 958 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1005 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 1050 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 979 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 958 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 926 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 965 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1448 October 13, 2012
Multiplying integers – easy 143.6 kB 1304 October 13, 2012
Multiplying integers – medium 173.3 kB 1308 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1283 October 13, 2012
Multiplying integers – hard 565.9 kB 1108 October 13, 2012
Multiplying integers – very hard 568 kB 1011 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1209 October 13, 2012
Multiplying decimals – easy 187 kB 1369 October 13, 2012
Multiplying decimals – medium 578.8 kB 1000 October 13, 2012
Multiplying decimals – medium-hard 577 kB 913 October 13, 2012
Multiplying decimals – hard 564.9 kB 980 October 13, 2012
Multiplying decimals – very hard 567.9 kB 961 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 985 October 13, 2012
Multiplying fractions – easy 186.7 kB 1118 October 13, 2012
Multiplying fractions – medium 583.8 kB 936 October 13, 2012
Multiplying fractions – medium-hard 589 kB 950 October 13, 2012
Multiplying fractions – hard 588 kB 918 October 13, 2012
Multiplying fractions – very hard 594.9 kB 947 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 946 October 13, 2012
Multiplying mixed numbers – easy 209 kB 1048 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 969 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 868 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 900 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 880 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 884 October 13, 2012
Multiplying improper fractions – easy 174 kB 898 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 895 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 849 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 886 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 891 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1452 October 14, 2012
Multiplying positive decimals 51.8 kB 1177 October 14, 2012
Multiplying positive fractions 632.1 kB 951 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 1074 October 14, 2012
Multiplying positive improper fractions 594.6 kB 880 October 14, 2012
Non positive
Multiplying integers 166.8 kB 1125 October 14, 2012
Multiplying decimals 246.3 kB 1033 October 14, 2012
Multiplying fractions 393.1 kB 989 October 14, 2012
Multiplying mixed numbers 412.4 kB 955 October 14, 2012
Multiplying improper fractions 334.1 kB 954 October 14, 2012


Multiplying knowledge test