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 1958 October 13, 2012
Multiplying positive integers – easy 143 kB 2019 October 13, 2012
Multiplying positive integers – medium 166.3 kB 2105 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 1779 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1387 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1507 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1303 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1252 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 1165 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 1048 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 1175 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 1069 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1069 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1555 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1283 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 1146 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 1066 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 1057 October 13, 2012
Multiplying positive fractions – very hard 581 kB 1061 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1138 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 1116 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 1047 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 1031 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 1020 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 995 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1047 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 1133 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 1023 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 1031 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 969 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 1005 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1543 October 13, 2012
Multiplying integers – easy 143.6 kB 1415 October 13, 2012
Multiplying integers – medium 173.3 kB 1417 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1348 October 13, 2012
Multiplying integers – hard 565.9 kB 1196 October 13, 2012
Multiplying integers – very hard 568 kB 1087 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1257 October 13, 2012
Multiplying decimals – easy 187 kB 1477 October 13, 2012
Multiplying decimals – medium 578.8 kB 1048 October 13, 2012
Multiplying decimals – medium-hard 577 kB 961 October 13, 2012
Multiplying decimals – hard 564.9 kB 1031 October 13, 2012
Multiplying decimals – very hard 567.9 kB 1010 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1061 October 13, 2012
Multiplying fractions – easy 186.7 kB 1219 October 13, 2012
Multiplying fractions – medium 583.8 kB 1027 October 13, 2012
Multiplying fractions – medium-hard 589 kB 992 October 13, 2012
Multiplying fractions – hard 588 kB 963 October 13, 2012
Multiplying fractions – very hard 594.9 kB 983 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 983 October 13, 2012
Multiplying mixed numbers – easy 209 kB 1113 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 1017 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 906 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 937 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 919 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 935 October 13, 2012
Multiplying improper fractions – easy 174 kB 944 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 965 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 889 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 925 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 932 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1603 October 14, 2012
Multiplying positive decimals 51.8 kB 1220 October 14, 2012
Multiplying positive fractions 632.1 kB 1038 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 1158 October 14, 2012
Multiplying positive improper fractions 594.6 kB 961 October 14, 2012
Non positive
Multiplying integers 166.8 kB 1223 October 14, 2012
Multiplying decimals 246.3 kB 1113 October 14, 2012
Multiplying fractions 393.1 kB 1070 October 14, 2012
Multiplying mixed numbers 412.4 kB 1039 October 14, 2012
Multiplying improper fractions 334.1 kB 1001 October 14, 2012


Multiplying knowledge test