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 2571 January 1, 1970
Multiplying positive integers – easy 0 B 2573 January 1, 1970
Multiplying positive integers – medium 0 B 2842 January 1, 1970
Multiplying positive integers – medium-hard 0 B 2389 January 1, 1970
Multiplying positive integers – hard 0 B 1829 January 1, 1970
Multiplying positive integers – very hard 0 B 2040 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1680 January 1, 1970
Multiplying positive decimals – easy 0 B 1680 January 1, 1970
Multiplying positive decimals – medium 0 B 1506 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1369 January 1, 1970
Multiplying positive decimals – hard 0 B 1503 January 1, 1970
Multiplying positive decimals – very hard 0 B 1357 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1357 January 1, 1970
Multiplying positive fractions – very easy 0 B 1998 January 1, 1970
Multiplying positive fractions – easy 0 B 1681 January 1, 1970
Multiplying positive fractions – medium 0 B 1522 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1357 January 1, 1970
Multiplying positive fractions – hard 0 B 1359 January 1, 1970
Multiplying positive fractions – very hard 0 B 1347 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1530 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1540 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1371 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1307 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1300 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1290 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1338 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1432 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1314 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1295 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1225 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1289 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1892 January 1, 1970
Multiplying integers – easy 0 B 1879 January 1, 1970
Multiplying integers – medium 0 B 1820 January 1, 1970
Multiplying integers – medium-hard 0 B 1721 January 1, 1970
Multiplying integers – hard 0 B 1522 January 1, 1970
Multiplying integers – very hard 0 B 1419 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1756 January 1, 1970
Multiplying decimals – easy 0 B 1875 January 1, 1970
Multiplying decimals – medium 0 B 1385 January 1, 1970
Multiplying decimals – medium-hard 0 B 1309 January 1, 1970
Multiplying decimals – hard 0 B 1357 January 1, 1970
Multiplying decimals – very hard 0 B 1294 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1377 January 1, 1970
Multiplying fractions – easy 0 B 1628 January 1, 1970
Multiplying fractions – medium 0 B 1347 January 1, 1970
Multiplying fractions – medium-hard 0 B 1302 January 1, 1970
Multiplying fractions – hard 0 B 1229 January 1, 1970
Multiplying fractions – very hard 0 B 1235 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1275 January 1, 1970
Multiplying mixed numbers – easy 0 B 1444 January 1, 1970
Multiplying mixed numbers – medium 0 B 1311 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1187 January 1, 1970
Multiplying mixed numbers – hard 0 B 1198 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1187 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1233 January 1, 1970
Multiplying improper fractions – easy 0 B 1267 January 1, 1970
Multiplying improper fractions – medium 0 B 1226 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 1156 January 1, 1970
Multiplying improper fractions – hard 0 B 1178 January 1, 1970
Multiplying improper fractions – very hard 0 B 1175 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 2155 January 1, 1970
Multiplying positive decimals 0 B 1550 January 1, 1970
Multiplying positive fractions 0 B 1365 January 1, 1970
Multiplying positive mixed numbers 0 B 1604 January 1, 1970
Multiplying positive improper fractions 0 B 1203 January 1, 1970
Non positive
Multiplying integers 0 B 1578 January 1, 1970
Multiplying decimals 0 B 1437 January 1, 1970
Multiplying fractions 0 B 1406 January 1, 1970
Multiplying mixed numbers 0 B 1333 January 1, 1970
Multiplying improper fractions 0 B 1254 January 1, 1970

Multiplying knowledge test