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 2576 January 1, 1970
Multiplying positive integers – easy 0 B 2579 January 1, 1970
Multiplying positive integers – medium 0 B 2850 January 1, 1970
Multiplying positive integers – medium-hard 0 B 2393 January 1, 1970
Multiplying positive integers – hard 0 B 1833 January 1, 1970
Multiplying positive integers – very hard 0 B 2045 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1683 January 1, 1970
Multiplying positive decimals – easy 0 B 1681 January 1, 1970
Multiplying positive decimals – medium 0 B 1509 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1370 January 1, 1970
Multiplying positive decimals – hard 0 B 1508 January 1, 1970
Multiplying positive decimals – very hard 0 B 1360 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1360 January 1, 1970
Multiplying positive fractions – very easy 0 B 2001 January 1, 1970
Multiplying positive fractions – easy 0 B 1684 January 1, 1970
Multiplying positive fractions – medium 0 B 1524 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1358 January 1, 1970
Multiplying positive fractions – hard 0 B 1360 January 1, 1970
Multiplying positive fractions – very hard 0 B 1349 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1532 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1545 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1375 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1310 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1302 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1291 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1342 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1435 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1316 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1297 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1229 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1292 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1895 January 1, 1970
Multiplying integers – easy 0 B 1882 January 1, 1970
Multiplying integers – medium 0 B 1823 January 1, 1970
Multiplying integers – medium-hard 0 B 1723 January 1, 1970
Multiplying integers – hard 0 B 1525 January 1, 1970
Multiplying integers – very hard 0 B 1424 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1760 January 1, 1970
Multiplying decimals – easy 0 B 1878 January 1, 1970
Multiplying decimals – medium 0 B 1389 January 1, 1970
Multiplying decimals – medium-hard 0 B 1313 January 1, 1970
Multiplying decimals – hard 0 B 1358 January 1, 1970
Multiplying decimals – very hard 0 B 1295 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1378 January 1, 1970
Multiplying fractions – easy 0 B 1633 January 1, 1970
Multiplying fractions – medium 0 B 1348 January 1, 1970
Multiplying fractions – medium-hard 0 B 1305 January 1, 1970
Multiplying fractions – hard 0 B 1233 January 1, 1970
Multiplying fractions – very hard 0 B 1237 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1278 January 1, 1970
Multiplying mixed numbers – easy 0 B 1446 January 1, 1970
Multiplying mixed numbers – medium 0 B 1312 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1188 January 1, 1970
Multiplying mixed numbers – hard 0 B 1200 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1189 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1235 January 1, 1970
Multiplying improper fractions – easy 0 B 1269 January 1, 1970
Multiplying improper fractions – medium 0 B 1230 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 1159 January 1, 1970
Multiplying improper fractions – hard 0 B 1179 January 1, 1970
Multiplying improper fractions – very hard 0 B 1177 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 2160 January 1, 1970
Multiplying positive decimals 0 B 1552 January 1, 1970
Multiplying positive fractions 0 B 1367 January 1, 1970
Multiplying positive mixed numbers 0 B 1606 January 1, 1970
Multiplying positive improper fractions 0 B 1205 January 1, 1970
Non positive
Multiplying integers 0 B 1580 January 1, 1970
Multiplying decimals 0 B 1439 January 1, 1970
Multiplying fractions 0 B 1409 January 1, 1970
Multiplying mixed numbers 0 B 1336 January 1, 1970
Multiplying improper fractions 0 B 1256 January 1, 1970

Multiplying knowledge test