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 1703 October 13, 2012
Multiplying positive integers – easy 143 kB 1734 October 13, 2012
Multiplying positive integers – medium 166.3 kB 1749 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 1601 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1168 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1264 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1094 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1072 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 1036 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 934 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 1000 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 968 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 968 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1365 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1076 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 1004 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 944 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 939 October 13, 2012
Multiplying positive fractions – very hard 581 kB 960 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 942 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 997 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 929 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 938 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 864 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 910 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 948 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 978 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 918 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 887 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 873 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 903 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1357 October 13, 2012
Multiplying integers – easy 143.6 kB 1217 October 13, 2012
Multiplying integers – medium 173.3 kB 1237 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1213 October 13, 2012
Multiplying integers – hard 565.9 kB 1027 October 13, 2012
Multiplying integers – very hard 568 kB 951 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1143 October 13, 2012
Multiplying decimals – easy 187 kB 1290 October 13, 2012
Multiplying decimals – medium 578.8 kB 941 October 13, 2012
Multiplying decimals – medium-hard 577 kB 857 October 13, 2012
Multiplying decimals – hard 564.9 kB 924 October 13, 2012
Multiplying decimals – very hard 567.9 kB 904 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 919 October 13, 2012
Multiplying fractions – easy 186.7 kB 1045 October 13, 2012
Multiplying fractions – medium 583.8 kB 863 October 13, 2012
Multiplying fractions – medium-hard 589 kB 886 October 13, 2012
Multiplying fractions – hard 588 kB 856 October 13, 2012
Multiplying fractions – very hard 594.9 kB 893 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 876 October 13, 2012
Multiplying mixed numbers – easy 209 kB 992 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 904 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 815 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 849 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 827 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 836 October 13, 2012
Multiplying improper fractions – easy 174 kB 848 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 840 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 778 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 833 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 834 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1321 October 14, 2012
Multiplying positive decimals 51.8 kB 1100 October 14, 2012
Multiplying positive fractions 632.1 kB 880 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 982 October 14, 2012
Multiplying positive improper fractions 594.6 kB 817 October 14, 2012
Non positive
Multiplying integers 166.8 kB 1039 October 14, 2012
Multiplying decimals 246.3 kB 961 October 14, 2012
Multiplying fractions 393.1 kB 902 October 14, 2012
Multiplying mixed numbers 412.4 kB 882 October 14, 2012
Multiplying improper fractions 334.1 kB 891 October 14, 2012


Multiplying knowledge test