# 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 78 kB 2022 October 13, 2012 Multiplying positive integers – easy 143 kB 2082 October 13, 2012 Multiplying positive integers – medium 166.3 kB 2190 October 13, 2012 Multiplying positive integers – medium-hard 173.1 kB 1843 October 13, 2012 Multiplying positive integers – hard 561.5 kB 1435 October 13, 2012 Multiplying positive integers – very hard 571.8 kB 1581 October 13, 2012 Positive decimals Multiplying positive decimals – very easy 554.5 kB 1357 October 13, 2012 Multiplying positive decimals – easy 555.5 kB 1298 October 13, 2012 Multiplying positive decimals – medium 579.2 kB 1197 October 13, 2012 Multiplying positive decimals – medium-hard 580.2 kB 1081 October 13, 2012 Multiplying positive decimals – hard 569.5 kB 1225 October 13, 2012 Multiplying positive decimals – very hard 567.2 kB 1095 October 13, 2012 Positive fractions Multiplying positive fractions – very hard 567.2 kB 1095 October 13, 2012 Multiplying positive fractions – very easy 172.7 kB 1597 October 13, 2012 Multiplying positive fractions – easy 188.9 kB 1331 October 13, 2012 Multiplying positive fractions – medium 577.2 kB 1176 October 13, 2012 Multiplying positive fractions – medium-hard 591.9 kB 1093 October 13, 2012 Multiplying positive fractions – hard 575.7 kB 1090 October 13, 2012 Multiplying positive fractions – very hard 581 kB 1089 October 13, 2012 Positive mixed numbers Multiplying positive mixed numbers – very easy 176.8 kB 1187 October 13, 2012 Multiplying positive mixed numbers – easy 209.8 kB 1144 October 13, 2012 Multiplying positive mixed numbers – medium 585.6 kB 1081 October 13, 2012 Multiplying positive mixed numbers – medium-hard 592.9 kB 1057 October 13, 2012 Multiplying positive mixed numbers – hard 589.3 kB 1067 October 13, 2012 Multiplying positive mixed numbers – very hard 596.6 kB 1020 October 13, 2012 Positive improper fractions Multiplying positive improper fractions – very easy 166 kB 1073 October 13, 2012 Multiplying positive improper fractions – easy 169.9 kB 1178 October 13, 2012 Multiplying positive improper fractions – medium 571.6 kB 1050 October 13, 2012 Multiplying positive improper fractions – medium-hard 569.5 kB 1074 October 13, 2012 Multiplying positive improper fractions – hard 560.5 kB 998 October 13, 2012 Multiplying positive improper fractions – very hard 571.8 kB 1031 October 13, 2012 Non positive integers Multiplying integers – very easy 137.9 kB 1597 October 13, 2012 Multiplying integers – easy 143.6 kB 1481 October 13, 2012 Multiplying integers – medium 173.3 kB 1482 October 13, 2012 Multiplying integers – medium-hard 173.5 kB 1379 October 13, 2012 Multiplying integers – hard 565.9 kB 1246 October 13, 2012 Multiplying integers – very hard 568 kB 1137 October 13, 2012 Non positive decimals Multiplying decimals – very easy 186.6 kB 1299 October 13, 2012 Multiplying decimals – easy 187 kB 1528 October 13, 2012 Multiplying decimals – medium 578.8 kB 1072 October 13, 2012 Multiplying decimals – medium-hard 577 kB 996 October 13, 2012 Multiplying decimals – hard 564.9 kB 1058 October 13, 2012 Multiplying decimals – very hard 567.9 kB 1032 October 13, 2012 Non positive fractions Multiplying fractions – very easy 179.6 kB 1104 October 13, 2012 Multiplying fractions – easy 186.7 kB 1290 October 13, 2012 Multiplying fractions – medium 583.8 kB 1074 October 13, 2012 Multiplying fractions – medium-hard 589 kB 1019 October 13, 2012 Multiplying fractions – hard 588 kB 991 October 13, 2012 Multiplying fractions – very hard 594.9 kB 1007 October 13, 2012 Non positive mixed numbers Multiplying mixed numbers – very easy 192.9 kB 1023 October 13, 2012 Multiplying mixed numbers – easy 209 kB 1158 October 13, 2012 Multiplying mixed numbers – medium 594.7 kB 1047 October 13, 2012 Multiplying mixed numbers – medium-hard 602.2 kB 927 October 13, 2012 Multiplying mixed numbers – hard 586.3 kB 969 October 13, 2012 Multiplying mixed numbers – very hard 591.3 kB 945 October 13, 2012 Non positive improper fractions Multiplying improper fractions – very easy 171.2 kB 960 October 13, 2012 Multiplying improper fractions – easy 174 kB 970 October 13, 2012 Multiplying improper fractions – medium 574.7 kB 1010 October 13, 2012 Multiplying improper fractions – medium-hard 573.9 kB 920 October 13, 2012 Multiplying improper fractions – hard 570.7 kB 956 October 13, 2012 Multiplying improper fractions – very hard 577.4 kB 958 October 13, 2012

## Multiplying worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Multiplying positive integers 496.1 kB 1678 October 14, 2012 Multiplying positive decimals 51.8 kB 1249 October 14, 2012 Multiplying positive fractions 632.1 kB 1083 October 14, 2012 Multiplying positive mixed numbers 637.8 kB 1209 October 14, 2012 Multiplying positive improper fractions 594.6 kB 1001 October 14, 2012 Non positive Multiplying integers 166.8 kB 1281 October 14, 2012 Multiplying decimals 246.3 kB 1162 October 14, 2012 Multiplying fractions 393.1 kB 1115 October 14, 2012 Multiplying mixed numbers 412.4 kB 1089 October 14, 2012 Multiplying improper fractions 334.1 kB 1032 October 14, 2012