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 2398 January 1, 1970
Multiplying positive integers – easy 0 B 2394 January 1, 1970
Multiplying positive integers – medium 0 B 2654 January 1, 1970
Multiplying positive integers – medium-hard 0 B 2235 January 1, 1970
Multiplying positive integers – hard 0 B 1702 January 1, 1970
Multiplying positive integers – very hard 0 B 1911 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1550 January 1, 1970
Multiplying positive decimals – easy 0 B 1559 January 1, 1970
Multiplying positive decimals – medium 0 B 1397 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1264 January 1, 1970
Multiplying positive decimals – hard 0 B 1392 January 1, 1970
Multiplying positive decimals – very hard 0 B 1271 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1271 January 1, 1970
Multiplying positive fractions – very easy 0 B 1886 January 1, 1970
Multiplying positive fractions – easy 0 B 1573 January 1, 1970
Multiplying positive fractions – medium 0 B 1401 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1265 January 1, 1970
Multiplying positive fractions – hard 0 B 1271 January 1, 1970
Multiplying positive fractions – very hard 0 B 1270 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1434 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1434 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1261 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1212 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1223 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1208 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1243 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1345 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1218 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1212 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1137 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1200 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1800 January 1, 1970
Multiplying integers – easy 0 B 1753 January 1, 1970
Multiplying integers – medium 0 B 1718 January 1, 1970
Multiplying integers – medium-hard 0 B 1604 January 1, 1970
Multiplying integers – hard 0 B 1427 January 1, 1970
Multiplying integers – very hard 0 B 1316 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1646 January 1, 1970
Multiplying decimals – easy 0 B 1773 January 1, 1970
Multiplying decimals – medium 0 B 1275 January 1, 1970
Multiplying decimals – medium-hard 0 B 1206 January 1, 1970
Multiplying decimals – hard 0 B 1258 January 1, 1970
Multiplying decimals – very hard 0 B 1206 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1293 January 1, 1970
Multiplying fractions – easy 0 B 1520 January 1, 1970
Multiplying fractions – medium 0 B 1253 January 1, 1970
Multiplying fractions – medium-hard 0 B 1209 January 1, 1970
Multiplying fractions – hard 0 B 1149 January 1, 1970
Multiplying fractions – very hard 0 B 1160 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1198 January 1, 1970
Multiplying mixed numbers – easy 0 B 1360 January 1, 1970
Multiplying mixed numbers – medium 0 B 1225 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1116 January 1, 1970
Multiplying mixed numbers – hard 0 B 1129 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1117 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1163 January 1, 1970
Multiplying improper fractions – easy 0 B 1198 January 1, 1970
Multiplying improper fractions – medium 0 B 1147 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 1074 January 1, 1970
Multiplying improper fractions – hard 0 B 1111 January 1, 1970
Multiplying improper fractions – very hard 0 B 1107 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 2044 January 1, 1970
Multiplying positive decimals 0 B 1449 January 1, 1970
Multiplying positive fractions 0 B 1286 January 1, 1970
Multiplying positive mixed numbers 0 B 1524 January 1, 1970
Multiplying positive improper fractions 0 B 1131 January 1, 1970
Non positive
Multiplying integers 0 B 1492 January 1, 1970
Multiplying decimals 0 B 1353 January 1, 1970
Multiplying fractions 0 B 1327 January 1, 1970
Multiplying mixed numbers 0 B 1252 January 1, 1970
Multiplying improper fractions 0 B 1184 January 1, 1970

Multiplying knowledge test