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 2255 January 1, 1970
Multiplying positive integers – easy 0 B 2262 January 1, 1970
Multiplying positive integers – medium 0 B 2460 January 1, 1970
Multiplying positive integers – medium-hard 0 B 2077 January 1, 1970
Multiplying positive integers – hard 0 B 1602 January 1, 1970
Multiplying positive integers – very hard 0 B 1790 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1459 January 1, 1970
Multiplying positive decimals – easy 0 B 1475 January 1, 1970
Multiplying positive decimals – medium 0 B 1323 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1185 January 1, 1970
Multiplying positive decimals – hard 0 B 1327 January 1, 1970
Multiplying positive decimals – very hard 0 B 1204 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1204 January 1, 1970
Multiplying positive fractions – very easy 0 B 1791 January 1, 1970
Multiplying positive fractions – easy 0 B 1495 January 1, 1970
Multiplying positive fractions – medium 0 B 1321 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1202 January 1, 1970
Multiplying positive fractions – hard 0 B 1206 January 1, 1970
Multiplying positive fractions – very hard 0 B 1211 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1344 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1355 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1188 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1154 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1157 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1140 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1179 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1284 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1160 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1154 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1085 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1138 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1719 January 1, 1970
Multiplying integers – easy 0 B 1640 January 1, 1970
Multiplying integers – medium 0 B 1615 January 1, 1970
Multiplying integers – medium-hard 0 B 1511 January 1, 1970
Multiplying integers – hard 0 B 1355 January 1, 1970
Multiplying integers – very hard 0 B 1247 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1523 January 1, 1970
Multiplying decimals – easy 0 B 1686 January 1, 1970
Multiplying decimals – medium 0 B 1190 January 1, 1970
Multiplying decimals – medium-hard 0 B 1124 January 1, 1970
Multiplying decimals – hard 0 B 1182 January 1, 1970
Multiplying decimals – very hard 0 B 1141 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1221 January 1, 1970
Multiplying fractions – easy 0 B 1423 January 1, 1970
Multiplying fractions – medium 0 B 1168 January 1, 1970
Multiplying fractions – medium-hard 0 B 1144 January 1, 1970
Multiplying fractions – hard 0 B 1093 January 1, 1970
Multiplying fractions – very hard 0 B 1107 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1130 January 1, 1970
Multiplying mixed numbers – easy 0 B 1287 January 1, 1970
Multiplying mixed numbers – medium 0 B 1160 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1054 January 1, 1970
Multiplying mixed numbers – hard 0 B 1069 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1055 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1103 January 1, 1970
Multiplying improper fractions – easy 0 B 1126 January 1, 1970
Multiplying improper fractions – medium 0 B 1092 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 1020 January 1, 1970
Multiplying improper fractions – hard 0 B 1056 January 1, 1970
Multiplying improper fractions – very hard 0 B 1050 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 1895 January 1, 1970
Multiplying positive decimals 0 B 1383 January 1, 1970
Multiplying positive fractions 0 B 1222 January 1, 1970
Multiplying positive mixed numbers 0 B 1456 January 1, 1970
Multiplying positive improper fractions 0 B 1082 January 1, 1970
Non positive
Multiplying integers 0 B 1406 January 1, 1970
Multiplying decimals 0 B 1284 January 1, 1970
Multiplying fractions 0 B 1260 January 1, 1970
Multiplying mixed numbers 0 B 1181 January 1, 1970
Multiplying improper fractions 0 B 1133 January 1, 1970


Multiplying knowledge test