# 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. ## Multiplying exams for teachers

 Exam Name File Size Downloads Upload date Positive integers Multiplying positive integers – very easy 0 B 2474 January 1, 1970 Multiplying positive integers – easy 0 B 2481 January 1, 1970 Multiplying positive integers – medium 0 B 2746 January 1, 1970 Multiplying positive integers – medium-hard 0 B 2314 January 1, 1970 Multiplying positive integers – hard 0 B 1757 January 1, 1970 Multiplying positive integers – very hard 0 B 1972 January 1, 1970 Positive decimals Multiplying positive decimals – very easy 0 B 1609 January 1, 1970 Multiplying positive decimals – easy 0 B 1609 January 1, 1970 Multiplying positive decimals – medium 0 B 1441 January 1, 1970 Multiplying positive decimals – medium-hard 0 B 1303 January 1, 1970 Multiplying positive decimals – hard 0 B 1432 January 1, 1970 Multiplying positive decimals – very hard 0 B 1306 January 1, 1970 Positive fractions Multiplying positive fractions – very hard 0 B 1306 January 1, 1970 Multiplying positive fractions – very easy 0 B 1937 January 1, 1970 Multiplying positive fractions – easy 0 B 1631 January 1, 1970 Multiplying positive fractions – medium 0 B 1453 January 1, 1970 Multiplying positive fractions – medium-hard 0 B 1306 January 1, 1970 Multiplying positive fractions – hard 0 B 1305 January 1, 1970 Multiplying positive fractions – very hard 0 B 1304 January 1, 1970 Positive mixed numbers Multiplying positive mixed numbers – very easy 0 B 1478 January 1, 1970 Multiplying positive mixed numbers – easy 0 B 1483 January 1, 1970 Multiplying positive mixed numbers – medium 0 B 1306 January 1, 1970 Multiplying positive mixed numbers – medium-hard 0 B 1252 January 1, 1970 Multiplying positive mixed numbers – hard 0 B 1259 January 1, 1970 Multiplying positive mixed numbers – very hard 0 B 1245 January 1, 1970 Positive improper fractions Multiplying positive improper fractions – very easy 0 B 1288 January 1, 1970 Multiplying positive improper fractions – easy 0 B 1382 January 1, 1970 Multiplying positive improper fractions – medium 0 B 1261 January 1, 1970 Multiplying positive improper fractions – medium-hard 0 B 1248 January 1, 1970 Multiplying positive improper fractions – hard 0 B 1175 January 1, 1970 Multiplying positive improper fractions – very hard 0 B 1245 January 1, 1970 Non positive integers Multiplying integers – very easy 0 B 1841 January 1, 1970 Multiplying integers – easy 0 B 1813 January 1, 1970 Multiplying integers – medium 0 B 1762 January 1, 1970 Multiplying integers – medium-hard 0 B 1653 January 1, 1970 Multiplying integers – hard 0 B 1467 January 1, 1970 Multiplying integers – very hard 0 B 1359 January 1, 1970 Non positive decimals Multiplying decimals – very easy 0 B 1698 January 1, 1970 Multiplying decimals – easy 0 B 1818 January 1, 1970 Multiplying decimals – medium 0 B 1321 January 1, 1970 Multiplying decimals – medium-hard 0 B 1249 January 1, 1970 Multiplying decimals – hard 0 B 1298 January 1, 1970 Multiplying decimals – very hard 0 B 1241 January 1, 1970 Non positive fractions Multiplying fractions – very easy 0 B 1331 January 1, 1970 Multiplying fractions – easy 0 B 1569 January 1, 1970 Multiplying fractions – medium 0 B 1291 January 1, 1970 Multiplying fractions – medium-hard 0 B 1247 January 1, 1970 Multiplying fractions – hard 0 B 1181 January 1, 1970 Multiplying fractions – very hard 0 B 1190 January 1, 1970 Non positive mixed numbers Multiplying mixed numbers – very easy 0 B 1230 January 1, 1970 Multiplying mixed numbers – easy 0 B 1391 January 1, 1970 Multiplying mixed numbers – medium 0 B 1260 January 1, 1970 Multiplying mixed numbers – medium-hard 0 B 1144 January 1, 1970 Multiplying mixed numbers – hard 0 B 1161 January 1, 1970 Multiplying mixed numbers – very hard 0 B 1149 January 1, 1970 Non positive improper fractions Multiplying improper fractions – very easy 0 B 1189 January 1, 1970 Multiplying improper fractions – easy 0 B 1230 January 1, 1970 Multiplying improper fractions – medium 0 B 1181 January 1, 1970 Multiplying improper fractions – medium-hard 0 B 1111 January 1, 1970 Multiplying improper fractions – hard 0 B 1142 January 1, 1970 Multiplying improper fractions – very hard 0 B 1136 January 1, 1970

## Multiplying worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Multiplying positive integers 0 B 2103 January 1, 1970 Multiplying positive decimals 0 B 1496 January 1, 1970 Multiplying positive fractions 0 B 1323 January 1, 1970 Multiplying positive mixed numbers 0 B 1559 January 1, 1970 Multiplying positive improper fractions 0 B 1160 January 1, 1970 Non positive Multiplying integers 0 B 1530 January 1, 1970 Multiplying decimals 0 B 1391 January 1, 1970 Multiplying fractions 0 B 1362 January 1, 1970 Multiplying mixed numbers 0 B 1288 January 1, 1970 Multiplying improper fractions 0 B 1214 January 1, 1970