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 2164 October 13, 2012
Multiplying positive integers – easy 143 kB 2220 October 13, 2012
Multiplying positive integers – medium 166.3 kB 2366 October 13, 2012
Multiplying positive integers – medium-hard 173.1 kB 2010 October 13, 2012
Multiplying positive integers – hard 561.5 kB 1554 October 13, 2012
Multiplying positive integers – very hard 571.8 kB 1713 October 13, 2012
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1467 October 13, 2012
Multiplying positive decimals – easy 555.5 kB 1407 October 13, 2012
Multiplying positive decimals – medium 579.2 kB 1302 October 13, 2012
Multiplying positive decimals – medium-hard 580.2 kB 1189 October 13, 2012
Multiplying positive decimals – hard 569.5 kB 1332 October 13, 2012
Multiplying positive decimals – very hard 567.2 kB 1208 October 13, 2012
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1208 October 13, 2012
Multiplying positive fractions – very easy 172.7 kB 1710 October 13, 2012
Multiplying positive fractions – easy 188.9 kB 1447 October 13, 2012
Multiplying positive fractions – medium 577.2 kB 1289 October 13, 2012
Multiplying positive fractions – medium-hard 591.9 kB 1193 October 13, 2012
Multiplying positive fractions – hard 575.7 kB 1197 October 13, 2012
Multiplying positive fractions – very hard 581 kB 1184 October 13, 2012
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1295 October 13, 2012
Multiplying positive mixed numbers – easy 209.8 kB 1246 October 13, 2012
Multiplying positive mixed numbers – medium 585.6 kB 1184 October 13, 2012
Multiplying positive mixed numbers – medium-hard 592.9 kB 1156 October 13, 2012
Multiplying positive mixed numbers – hard 589.3 kB 1177 October 13, 2012
Multiplying positive mixed numbers – very hard 596.6 kB 1117 October 13, 2012
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1179 October 13, 2012
Multiplying positive improper fractions – easy 169.9 kB 1284 October 13, 2012
Multiplying positive improper fractions – medium 571.6 kB 1147 October 13, 2012
Multiplying positive improper fractions – medium-hard 569.5 kB 1172 October 13, 2012
Multiplying positive improper fractions – hard 560.5 kB 1091 October 13, 2012
Multiplying positive improper fractions – very hard 571.8 kB 1120 October 13, 2012
Non positive integers
Multiplying integers – very easy 137.9 kB 1701 October 13, 2012
Multiplying integers – easy 143.6 kB 1591 October 13, 2012
Multiplying integers – medium 173.3 kB 1591 October 13, 2012
Multiplying integers – medium-hard 173.5 kB 1489 October 13, 2012
Multiplying integers – hard 565.9 kB 1353 October 13, 2012
Multiplying integers – very hard 568 kB 1239 October 13, 2012
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1438 October 13, 2012
Multiplying decimals – easy 187 kB 1631 October 13, 2012
Multiplying decimals – medium 578.8 kB 1172 October 13, 2012
Multiplying decimals – medium-hard 577 kB 1099 October 13, 2012
Multiplying decimals – hard 564.9 kB 1159 October 13, 2012
Multiplying decimals – very hard 567.9 kB 1131 October 13, 2012
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1210 October 13, 2012
Multiplying fractions – easy 186.7 kB 1410 October 13, 2012
Multiplying fractions – medium 583.8 kB 1175 October 13, 2012
Multiplying fractions – medium-hard 589 kB 1119 October 13, 2012
Multiplying fractions – hard 588 kB 1088 October 13, 2012
Multiplying fractions – very hard 594.9 kB 1102 October 13, 2012
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1128 October 13, 2012
Multiplying mixed numbers – easy 209 kB 1257 October 13, 2012
Multiplying mixed numbers – medium 594.7 kB 1144 October 13, 2012
Multiplying mixed numbers – medium-hard 602.2 kB 1014 October 13, 2012
Multiplying mixed numbers – hard 586.3 kB 1084 October 13, 2012
Multiplying mixed numbers – very hard 591.3 kB 1037 October 13, 2012
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1060 October 13, 2012
Multiplying improper fractions – easy 174 kB 1073 October 13, 2012
Multiplying improper fractions – medium 574.7 kB 1106 October 13, 2012
Multiplying improper fractions – medium-hard 573.9 kB 1014 October 13, 2012
Multiplying improper fractions – hard 570.7 kB 1052 October 13, 2012
Multiplying improper fractions – very hard 577.4 kB 1047 October 13, 2012

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 1824 October 14, 2012
Multiplying positive decimals 51.8 kB 1352 October 14, 2012
Multiplying positive fractions 632.1 kB 1195 October 14, 2012
Multiplying positive mixed numbers 637.8 kB 1314 October 14, 2012
Multiplying positive improper fractions 594.6 kB 1099 October 14, 2012
Non positive
Multiplying integers 166.8 kB 1391 October 14, 2012
Multiplying decimals 246.3 kB 1264 October 14, 2012
Multiplying fractions 393.1 kB 1224 October 14, 2012
Multiplying mixed numbers 412.4 kB 1182 October 14, 2012
Multiplying improper fractions 334.1 kB 1128 October 14, 2012

Multiplying knowledge test