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 2326 January 1, 1970
Multiplying positive integers – easy 0 B 2332 January 1, 1970
Multiplying positive integers – medium 0 B 2567 January 1, 1970
Multiplying positive integers – medium-hard 0 B 2174 January 1, 1970
Multiplying positive integers – hard 0 B 1655 January 1, 1970
Multiplying positive integers – very hard 0 B 1869 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1511 January 1, 1970
Multiplying positive decimals – easy 0 B 1527 January 1, 1970
Multiplying positive decimals – medium 0 B 1368 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1233 January 1, 1970
Multiplying positive decimals – hard 0 B 1365 January 1, 1970
Multiplying positive decimals – very hard 0 B 1245 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1245 January 1, 1970
Multiplying positive fractions – very easy 0 B 1839 January 1, 1970
Multiplying positive fractions – easy 0 B 1545 January 1, 1970
Multiplying positive fractions – medium 0 B 1368 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1237 January 1, 1970
Multiplying positive fractions – hard 0 B 1242 January 1, 1970
Multiplying positive fractions – very hard 0 B 1243 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1392 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1400 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1238 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1191 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1197 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1182 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1216 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1319 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1194 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1186 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1116 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1174 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1762 January 1, 1970
Multiplying integers – easy 0 B 1700 January 1, 1970
Multiplying integers – medium 0 B 1674 January 1, 1970
Multiplying integers – medium-hard 0 B 1563 January 1, 1970
Multiplying integers – hard 0 B 1396 January 1, 1970
Multiplying integers – very hard 0 B 1289 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1607 January 1, 1970
Multiplying decimals – easy 0 B 1738 January 1, 1970
Multiplying decimals – medium 0 B 1235 January 1, 1970
Multiplying decimals – medium-hard 0 B 1173 January 1, 1970
Multiplying decimals – hard 0 B 1230 January 1, 1970
Multiplying decimals – very hard 0 B 1180 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1263 January 1, 1970
Multiplying fractions – easy 0 B 1476 January 1, 1970
Multiplying fractions – medium 0 B 1215 January 1, 1970
Multiplying fractions – medium-hard 0 B 1182 January 1, 1970
Multiplying fractions – hard 0 B 1125 January 1, 1970
Multiplying fractions – very hard 0 B 1138 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1168 January 1, 1970
Multiplying mixed numbers – easy 0 B 1326 January 1, 1970
Multiplying mixed numbers – medium 0 B 1192 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1093 January 1, 1970
Multiplying mixed numbers – hard 0 B 1103 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1089 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1139 January 1, 1970
Multiplying improper fractions – easy 0 B 1169 January 1, 1970
Multiplying improper fractions – medium 0 B 1120 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 1052 January 1, 1970
Multiplying improper fractions – hard 0 B 1084 January 1, 1970
Multiplying improper fractions – very hard 0 B 1084 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 1992 January 1, 1970
Multiplying positive decimals 0 B 1415 January 1, 1970
Multiplying positive fractions 0 B 1254 January 1, 1970
Multiplying positive mixed numbers 0 B 1491 January 1, 1970
Multiplying positive improper fractions 0 B 1110 January 1, 1970
Non positive
Multiplying integers 0 B 1454 January 1, 1970
Multiplying decimals 0 B 1321 January 1, 1970
Multiplying fractions 0 B 1296 January 1, 1970
Multiplying mixed numbers 0 B 1221 January 1, 1970
Multiplying improper fractions 0 B 1161 January 1, 1970

Multiplying knowledge test