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 78 kB 2210 October 13, 2012
Multiplying positive integers – easy 143 kB 2269 October 13, 2012
Multiplying positive integers – medium 166.3 kB 2440 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 2073 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1591 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1769 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1506 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1444 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 1335 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 1217 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 1372 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 1244 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1244 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1756 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1486 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 1330 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 1219 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 1235 October 13, 2012
Multiplying positive fractions – very hard 581 kB 1213 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1338 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 1289 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 1214 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 1184 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 1206 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 1146 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1206 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 1320 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 1177 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 1203 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 1116 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 1148 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1740 October 13, 2012
Multiplying integers – easy 143.6 kB 1628 October 13, 2012
Multiplying integers – medium 173.3 kB 1631 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1517 October 13, 2012
Multiplying integers – hard 565.9 kB 1387 October 13, 2012
Multiplying integers – very hard 568 kB 1273 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1494 October 13, 2012
Multiplying decimals – easy 187 kB 1665 October 13, 2012
Multiplying decimals – medium 578.8 kB 1206 October 13, 2012
Multiplying decimals – medium-hard 577 kB 1134 October 13, 2012
Multiplying decimals – hard 564.9 kB 1193 October 13, 2012
Multiplying decimals – very hard 567.9 kB 1167 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1239 October 13, 2012
Multiplying fractions – easy 186.7 kB 1455 October 13, 2012
Multiplying fractions – medium 583.8 kB 1210 October 13, 2012
Multiplying fractions – medium-hard 589 kB 1145 October 13, 2012
Multiplying fractions – hard 588 kB 1114 October 13, 2012
Multiplying fractions – very hard 594.9 kB 1135 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1161 October 13, 2012
Multiplying mixed numbers – easy 209 kB 1290 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 1173 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 1045 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 1115 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 1070 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1093 October 13, 2012
Multiplying improper fractions – easy 174 kB 1104 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 1142 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 1043 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 1083 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 1073 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1892 October 14, 2012
Multiplying positive decimals 51.8 kB 1386 October 14, 2012
Multiplying positive fractions 632.1 kB 1232 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 1345 October 14, 2012
Multiplying positive improper fractions 594.6 kB 1126 October 14, 2012
Non positive
Multiplying integers 166.8 kB 1435 October 14, 2012
Multiplying decimals 246.3 kB 1297 October 14, 2012
Multiplying fractions 393.1 kB 1258 October 14, 2012
Multiplying mixed numbers 412.4 kB 1217 October 14, 2012
Multiplying improper fractions 334.1 kB 1159 October 14, 2012

Multiplying knowledge test