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 1680 October 13, 2012
Multiplying positive integers – easy 143 kB 1688 October 13, 2012
Multiplying positive integers – medium 166.3 kB 1706 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 1575 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1145 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1240 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1081 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1058 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 1025 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 925 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 981 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 957 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 957 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1349 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1063 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 992 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 932 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 923 October 13, 2012
Multiplying positive fractions – very hard 581 kB 952 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 929 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 969 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 917 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 926 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 854 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 898 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 935 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 966 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 906 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 874 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 867 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 889 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1333 October 13, 2012
Multiplying integers – easy 143.6 kB 1187 October 13, 2012
Multiplying integers – medium 173.3 kB 1218 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1202 October 13, 2012
Multiplying integers – hard 565.9 kB 1012 October 13, 2012
Multiplying integers – very hard 568 kB 939 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1134 October 13, 2012
Multiplying decimals – easy 187 kB 1267 October 13, 2012
Multiplying decimals – medium 578.8 kB 931 October 13, 2012
Multiplying decimals – medium-hard 577 kB 846 October 13, 2012
Multiplying decimals – hard 564.9 kB 909 October 13, 2012
Multiplying decimals – very hard 567.9 kB 895 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 906 October 13, 2012
Multiplying fractions – easy 186.7 kB 1033 October 13, 2012
Multiplying fractions – medium 583.8 kB 850 October 13, 2012
Multiplying fractions – medium-hard 589 kB 875 October 13, 2012
Multiplying fractions – hard 588 kB 843 October 13, 2012
Multiplying fractions – very hard 594.9 kB 884 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 868 October 13, 2012
Multiplying mixed numbers – easy 209 kB 982 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 892 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 808 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 837 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 820 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 822 October 13, 2012
Multiplying improper fractions – easy 174 kB 838 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 828 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 768 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 826 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 821 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1300 October 14, 2012
Multiplying positive decimals 51.8 kB 1085 October 14, 2012
Multiplying positive fractions 632.1 kB 868 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 957 October 14, 2012
Multiplying positive improper fractions 594.6 kB 808 October 14, 2012
Non positive
Multiplying integers 166.8 kB 1017 October 14, 2012
Multiplying decimals 246.3 kB 950 October 14, 2012
Multiplying fractions 393.1 kB 890 October 14, 2012
Multiplying mixed numbers 412.4 kB 864 October 14, 2012
Multiplying improper fractions 334.1 kB 877 October 14, 2012


Multiplying knowledge test