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 2282 January 1, 1970
Multiplying positive integers – easy 0 B 2301 January 1, 1970
Multiplying positive integers – medium 0 B 2517 January 1, 1970
Multiplying positive integers – medium-hard 0 B 2134 January 1, 1970
Multiplying positive integers – hard 0 B 1626 January 1, 1970
Multiplying positive integers – very hard 0 B 1833 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1481 January 1, 1970
Multiplying positive decimals – easy 0 B 1497 January 1, 1970
Multiplying positive decimals – medium 0 B 1341 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1207 January 1, 1970
Multiplying positive decimals – hard 0 B 1344 January 1, 1970
Multiplying positive decimals – very hard 0 B 1223 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1223 January 1, 1970
Multiplying positive fractions – very easy 0 B 1819 January 1, 1970
Multiplying positive fractions – easy 0 B 1520 January 1, 1970
Multiplying positive fractions – medium 0 B 1344 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1220 January 1, 1970
Multiplying positive fractions – hard 0 B 1226 January 1, 1970
Multiplying positive fractions – very hard 0 B 1224 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1365 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1374 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1210 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1172 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1174 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1159 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1198 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1304 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1173 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1167 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1098 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1156 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1738 January 1, 1970
Multiplying integers – easy 0 B 1668 January 1, 1970
Multiplying integers – medium 0 B 1644 January 1, 1970
Multiplying integers – medium-hard 0 B 1540 January 1, 1970
Multiplying integers – hard 0 B 1374 January 1, 1970
Multiplying integers – very hard 0 B 1268 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1573 January 1, 1970
Multiplying decimals – easy 0 B 1710 January 1, 1970
Multiplying decimals – medium 0 B 1209 January 1, 1970
Multiplying decimals – medium-hard 0 B 1152 January 1, 1970
Multiplying decimals – hard 0 B 1213 January 1, 1970
Multiplying decimals – very hard 0 B 1159 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1246 January 1, 1970
Multiplying fractions – easy 0 B 1454 January 1, 1970
Multiplying fractions – medium 0 B 1190 January 1, 1970
Multiplying fractions – medium-hard 0 B 1158 January 1, 1970
Multiplying fractions – hard 0 B 1111 January 1, 1970
Multiplying fractions – very hard 0 B 1125 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1147 January 1, 1970
Multiplying mixed numbers – easy 0 B 1307 January 1, 1970
Multiplying mixed numbers – medium 0 B 1175 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1072 January 1, 1970
Multiplying mixed numbers – hard 0 B 1086 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1073 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1126 January 1, 1970
Multiplying improper fractions – easy 0 B 1155 January 1, 1970
Multiplying improper fractions – medium 0 B 1107 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 1037 January 1, 1970
Multiplying improper fractions – hard 0 B 1071 January 1, 1970
Multiplying improper fractions – very hard 0 B 1068 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 1945 January 1, 1970
Multiplying positive decimals 0 B 1398 January 1, 1970
Multiplying positive fractions 0 B 1240 January 1, 1970
Multiplying positive mixed numbers 0 B 1477 January 1, 1970
Multiplying positive improper fractions 0 B 1095 January 1, 1970
Non positive
Multiplying integers 0 B 1432 January 1, 1970
Multiplying decimals 0 B 1304 January 1, 1970
Multiplying fractions 0 B 1276 January 1, 1970
Multiplying mixed numbers 0 B 1200 January 1, 1970
Multiplying improper fractions 0 B 1145 January 1, 1970


Multiplying knowledge test