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 0 B 2138 January 1, 1970
Multiplying positive integers – easy 0 B 2153 January 1, 1970
Multiplying positive integers – medium 0 B 2306 January 1, 1970
Multiplying positive integers – medium-hard 0 B 1959 January 1, 1970
Multiplying positive integers – hard 0 B 1534 January 1, 1970
Multiplying positive integers – very hard 0 B 1692 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1397 January 1, 1970
Multiplying positive decimals – easy 0 B 1411 January 1, 1970
Multiplying positive decimals – medium 0 B 1258 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1133 January 1, 1970
Multiplying positive decimals – hard 0 B 1273 January 1, 1970
Multiplying positive decimals – very hard 0 B 1154 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1154 January 1, 1970
Multiplying positive fractions – very easy 0 B 1690 January 1, 1970
Multiplying positive fractions – easy 0 B 1408 January 1, 1970
Multiplying positive fractions – medium 0 B 1258 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1150 January 1, 1970
Multiplying positive fractions – hard 0 B 1150 January 1, 1970
Multiplying positive fractions – very hard 0 B 1156 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1266 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1291 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1135 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1106 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1105 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1087 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1123 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1231 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1106 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1110 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1035 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1088 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1652 January 1, 1970
Multiplying integers – easy 0 B 1556 January 1, 1970
Multiplying integers – medium 0 B 1529 January 1, 1970
Multiplying integers – medium-hard 0 B 1447 January 1, 1970
Multiplying integers – hard 0 B 1300 January 1, 1970
Multiplying integers – very hard 0 B 1180 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1405 January 1, 1970
Multiplying decimals – easy 0 B 1620 January 1, 1970
Multiplying decimals – medium 0 B 1130 January 1, 1970
Multiplying decimals – medium-hard 0 B 1066 January 1, 1970
Multiplying decimals – hard 0 B 1120 January 1, 1970
Multiplying decimals – very hard 0 B 1093 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1170 January 1, 1970
Multiplying fractions – easy 0 B 1352 January 1, 1970
Multiplying fractions – medium 0 B 1122 January 1, 1970
Multiplying fractions – medium-hard 0 B 1089 January 1, 1970
Multiplying fractions – hard 0 B 1049 January 1, 1970
Multiplying fractions – very hard 0 B 1060 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1073 January 1, 1970
Multiplying mixed numbers – easy 0 B 1225 January 1, 1970
Multiplying mixed numbers – medium 0 B 1113 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1008 January 1, 1970
Multiplying mixed numbers – hard 0 B 1020 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1000 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1023 January 1, 1970
Multiplying improper fractions – easy 0 B 1041 January 1, 1970
Multiplying improper fractions – medium 0 B 1045 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 975 January 1, 1970
Multiplying improper fractions – hard 0 B 1013 January 1, 1970
Multiplying improper fractions – very hard 0 B 1007 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 1785 January 1, 1970
Multiplying positive decimals 0 B 1320 January 1, 1970
Multiplying positive fractions 0 B 1157 January 1, 1970
Multiplying positive mixed numbers 0 B 1396 January 1, 1970
Multiplying positive improper fractions 0 B 1044 January 1, 1970
Non positive
Multiplying integers 0 B 1326 January 1, 1970
Multiplying decimals 0 B 1211 January 1, 1970
Multiplying fractions 0 B 1183 January 1, 1970
Multiplying mixed numbers 0 B 1130 January 1, 1970
Multiplying improper fractions 0 B 1084 January 1, 1970


Multiplying knowledge test