# 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 2478 January 1, 1970 Multiplying positive integers – easy 0 B 2483 January 1, 1970 Multiplying positive integers – medium 0 B 2751 January 1, 1970 Multiplying positive integers – medium-hard 0 B 2316 January 1, 1970 Multiplying positive integers – hard 0 B 1759 January 1, 1970 Multiplying positive integers – very hard 0 B 1975 January 1, 1970 Positive decimals Multiplying positive decimals – very easy 0 B 1613 January 1, 1970 Multiplying positive decimals – easy 0 B 1613 January 1, 1970 Multiplying positive decimals – medium 0 B 1446 January 1, 1970 Multiplying positive decimals – medium-hard 0 B 1308 January 1, 1970 Multiplying positive decimals – hard 0 B 1436 January 1, 1970 Multiplying positive decimals – very hard 0 B 1309 January 1, 1970 Positive fractions Multiplying positive fractions – very hard 0 B 1309 January 1, 1970 Multiplying positive fractions – very easy 0 B 1939 January 1, 1970 Multiplying positive fractions – easy 0 B 1632 January 1, 1970 Multiplying positive fractions – medium 0 B 1457 January 1, 1970 Multiplying positive fractions – medium-hard 0 B 1313 January 1, 1970 Multiplying positive fractions – hard 0 B 1308 January 1, 1970 Multiplying positive fractions – very hard 0 B 1306 January 1, 1970 Positive mixed numbers Multiplying positive mixed numbers – very easy 0 B 1481 January 1, 1970 Multiplying positive mixed numbers – easy 0 B 1485 January 1, 1970 Multiplying positive mixed numbers – medium 0 B 1309 January 1, 1970 Multiplying positive mixed numbers – medium-hard 0 B 1255 January 1, 1970 Multiplying positive mixed numbers – hard 0 B 1261 January 1, 1970 Multiplying positive mixed numbers – very hard 0 B 1247 January 1, 1970 Positive improper fractions Multiplying positive improper fractions – very easy 0 B 1291 January 1, 1970 Multiplying positive improper fractions – easy 0 B 1385 January 1, 1970 Multiplying positive improper fractions – medium 0 B 1264 January 1, 1970 Multiplying positive improper fractions – medium-hard 0 B 1251 January 1, 1970 Multiplying positive improper fractions – hard 0 B 1177 January 1, 1970 Multiplying positive improper fractions – very hard 0 B 1248 January 1, 1970 Non positive integers Multiplying integers – very easy 0 B 1846 January 1, 1970 Multiplying integers – easy 0 B 1816 January 1, 1970 Multiplying integers – medium 0 B 1767 January 1, 1970 Multiplying integers – medium-hard 0 B 1656 January 1, 1970 Multiplying integers – hard 0 B 1470 January 1, 1970 Multiplying integers – very hard 0 B 1363 January 1, 1970 Non positive decimals Multiplying decimals – very easy 0 B 1704 January 1, 1970 Multiplying decimals – easy 0 B 1821 January 1, 1970 Multiplying decimals – medium 0 B 1324 January 1, 1970 Multiplying decimals – medium-hard 0 B 1252 January 1, 1970 Multiplying decimals – hard 0 B 1301 January 1, 1970 Multiplying decimals – very hard 0 B 1243 January 1, 1970 Non positive fractions Multiplying fractions – very easy 0 B 1336 January 1, 1970 Multiplying fractions – easy 0 B 1571 January 1, 1970 Multiplying fractions – medium 0 B 1293 January 1, 1970 Multiplying fractions – medium-hard 0 B 1251 January 1, 1970 Multiplying fractions – hard 0 B 1183 January 1, 1970 Multiplying fractions – very hard 0 B 1192 January 1, 1970 Non positive mixed numbers Multiplying mixed numbers – very easy 0 B 1233 January 1, 1970 Multiplying mixed numbers – easy 0 B 1395 January 1, 1970 Multiplying mixed numbers – medium 0 B 1262 January 1, 1970 Multiplying mixed numbers – medium-hard 0 B 1146 January 1, 1970 Multiplying mixed numbers – hard 0 B 1163 January 1, 1970 Multiplying mixed numbers – very hard 0 B 1150 January 1, 1970 Non positive improper fractions Multiplying improper fractions – very easy 0 B 1193 January 1, 1970 Multiplying improper fractions – easy 0 B 1231 January 1, 1970 Multiplying improper fractions – medium 0 B 1183 January 1, 1970 Multiplying improper fractions – medium-hard 0 B 1116 January 1, 1970 Multiplying improper fractions – hard 0 B 1143 January 1, 1970 Multiplying improper fractions – very hard 0 B 1137 January 1, 1970

## Multiplying worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Multiplying positive integers 0 B 2105 January 1, 1970 Multiplying positive decimals 0 B 1498 January 1, 1970 Multiplying positive fractions 0 B 1326 January 1, 1970 Multiplying positive mixed numbers 0 B 1563 January 1, 1970 Multiplying positive improper fractions 0 B 1162 January 1, 1970 Non positive Multiplying integers 0 B 1533 January 1, 1970 Multiplying decimals 0 B 1394 January 1, 1970 Multiplying fractions 0 B 1365 January 1, 1970 Multiplying mixed numbers 0 B 1289 January 1, 1970 Multiplying improper fractions 0 B 1215 January 1, 1970