# 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 2520 January 1, 1970 Multiplying positive integers – easy 0 B 2525 January 1, 1970 Multiplying positive integers – medium 0 B 2792 January 1, 1970 Multiplying positive integers – medium-hard 0 B 2350 January 1, 1970 Multiplying positive integers – hard 0 B 1791 January 1, 1970 Multiplying positive integers – very hard 0 B 2004 January 1, 1970 Positive decimals Multiplying positive decimals – very easy 0 B 1643 January 1, 1970 Multiplying positive decimals – easy 0 B 1639 January 1, 1970 Multiplying positive decimals – medium 0 B 1474 January 1, 1970 Multiplying positive decimals – medium-hard 0 B 1335 January 1, 1970 Multiplying positive decimals – hard 0 B 1460 January 1, 1970 Multiplying positive decimals – very hard 0 B 1328 January 1, 1970 Positive fractions Multiplying positive fractions – very hard 0 B 1328 January 1, 1970 Multiplying positive fractions – very easy 0 B 1965 January 1, 1970 Multiplying positive fractions – easy 0 B 1656 January 1, 1970 Multiplying positive fractions – medium 0 B 1487 January 1, 1970 Multiplying positive fractions – medium-hard 0 B 1337 January 1, 1970 Multiplying positive fractions – hard 0 B 1335 January 1, 1970 Multiplying positive fractions – very hard 0 B 1328 January 1, 1970 Positive mixed numbers Multiplying positive mixed numbers – very easy 0 B 1504 January 1, 1970 Multiplying positive mixed numbers – easy 0 B 1510 January 1, 1970 Multiplying positive mixed numbers – medium 0 B 1334 January 1, 1970 Multiplying positive mixed numbers – medium-hard 0 B 1281 January 1, 1970 Multiplying positive mixed numbers – hard 0 B 1279 January 1, 1970 Multiplying positive mixed numbers – very hard 0 B 1268 January 1, 1970 Positive improper fractions Multiplying positive improper fractions – very easy 0 B 1311 January 1, 1970 Multiplying positive improper fractions – easy 0 B 1411 January 1, 1970 Multiplying positive improper fractions – medium 0 B 1289 January 1, 1970 Multiplying positive improper fractions – medium-hard 0 B 1275 January 1, 1970 Multiplying positive improper fractions – hard 0 B 1200 January 1, 1970 Multiplying positive improper fractions – very hard 0 B 1268 January 1, 1970 Non positive integers Multiplying integers – very easy 0 B 1871 January 1, 1970 Multiplying integers – easy 0 B 1842 January 1, 1970 Multiplying integers – medium 0 B 1793 January 1, 1970 Multiplying integers – medium-hard 0 B 1684 January 1, 1970 Multiplying integers – hard 0 B 1495 January 1, 1970 Multiplying integers – very hard 0 B 1390 January 1, 1970 Non positive decimals Multiplying decimals – very easy 0 B 1723 January 1, 1970 Multiplying decimals – easy 0 B 1842 January 1, 1970 Multiplying decimals – medium 0 B 1350 January 1, 1970 Multiplying decimals – medium-hard 0 B 1276 January 1, 1970 Multiplying decimals – hard 0 B 1322 January 1, 1970 Multiplying decimals – very hard 0 B 1265 January 1, 1970 Non positive fractions Multiplying fractions – very easy 0 B 1352 January 1, 1970 Multiplying fractions – easy 0 B 1592 January 1, 1970 Multiplying fractions – medium 0 B 1313 January 1, 1970 Multiplying fractions – medium-hard 0 B 1273 January 1, 1970 Multiplying fractions – hard 0 B 1205 January 1, 1970 Multiplying fractions – very hard 0 B 1214 January 1, 1970 Non positive mixed numbers Multiplying mixed numbers – very easy 0 B 1255 January 1, 1970 Multiplying mixed numbers – easy 0 B 1415 January 1, 1970 Multiplying mixed numbers – medium 0 B 1282 January 1, 1970 Multiplying mixed numbers – medium-hard 0 B 1166 January 1, 1970 Multiplying mixed numbers – hard 0 B 1183 January 1, 1970 Multiplying mixed numbers – very hard 0 B 1170 January 1, 1970 Non positive improper fractions Multiplying improper fractions – very easy 0 B 1215 January 1, 1970 Multiplying improper fractions – easy 0 B 1254 January 1, 1970 Multiplying improper fractions – medium 0 B 1208 January 1, 1970 Multiplying improper fractions – medium-hard 0 B 1140 January 1, 1970 Multiplying improper fractions – hard 0 B 1161 January 1, 1970 Multiplying improper fractions – very hard 0 B 1161 January 1, 1970

## Multiplying worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Multiplying positive integers 0 B 2133 January 1, 1970 Multiplying positive decimals 0 B 1519 January 1, 1970 Multiplying positive fractions 0 B 1347 January 1, 1970 Multiplying positive mixed numbers 0 B 1585 January 1, 1970 Multiplying positive improper fractions 0 B 1182 January 1, 1970 Non positive Multiplying integers 0 B 1555 January 1, 1970 Multiplying decimals 0 B 1416 January 1, 1970 Multiplying fractions 0 B 1387 January 1, 1970 Multiplying mixed numbers 0 B 1313 January 1, 1970 Multiplying improper fractions 0 B 1238 January 1, 1970