# 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 3132 September 3, 2019 Multiplying positive integers – easy 143 kB 3156 September 3, 2019 Multiplying positive integers – medium 166.3 kB 3439 September 3, 2019 Multiplying positive integers – medium-hard 173.1 kB 2871 September 3, 2019 Multiplying positive integers – hard 561.5 kB 2274 September 3, 2019 Multiplying positive integers – very hard 571.8 kB 2486 September 3, 2019 Positive decimals Multiplying positive decimals – very easy 554.5 kB 2114 September 3, 2019 Multiplying positive decimals – easy 555.5 kB 2100 September 3, 2019 Multiplying positive decimals – medium 579.2 kB 1938 September 3, 2019 Multiplying positive decimals – medium-hard 580.2 kB 1740 September 3, 2019 Multiplying positive decimals – hard 569.5 kB 1908 September 3, 2019 Multiplying positive decimals – very hard 567.2 kB 1740 September 3, 2019 Positive fractions Multiplying positive fractions – very hard 567.2 kB 1740 September 3, 2019 Multiplying positive fractions – very easy 172.7 kB 2596 September 3, 2019 Multiplying positive fractions – easy 188.9 kB 2446 September 3, 2019 Multiplying positive fractions – medium 577.2 kB 1964 September 3, 2019 Multiplying positive fractions – medium-hard 591.9 kB 1741 September 3, 2019 Multiplying positive fractions – hard 575.7 kB 1746 September 3, 2019 Multiplying positive fractions – very hard 581 kB 1699 September 3, 2019 Positive mixed numbers Multiplying positive mixed numbers – very easy 176.8 kB 1913 September 3, 2019 Multiplying positive mixed numbers – easy 209.8 kB 1938 September 3, 2019 Multiplying positive mixed numbers – medium 585.6 kB 1764 September 3, 2019 Multiplying positive mixed numbers – medium-hard 592.9 kB 1677 September 3, 2019 Multiplying positive mixed numbers – hard 589.3 kB 1702 September 3, 2019 Multiplying positive mixed numbers – very hard 596.6 kB 1667 September 3, 2019 Positive improper fractions Multiplying positive improper fractions – very easy 166 kB 1695 September 3, 2019 Multiplying positive improper fractions – easy 169.9 kB 1809 September 3, 2019 Multiplying positive improper fractions – medium 571.6 kB 1706 September 3, 2019 Multiplying positive improper fractions – medium-hard 569.5 kB 1628 September 3, 2019 Multiplying positive improper fractions – hard 560.5 kB 1593 September 3, 2019 Multiplying positive improper fractions – very hard 571.8 kB 1648 September 3, 2019 Non positive integers Multiplying integers – very easy 137.9 kB 2287 September 3, 2019 Multiplying integers – easy 143.6 kB 2348 September 3, 2019 Multiplying integers – medium 173.3 kB 2304 September 3, 2019 Multiplying integers – medium-hard 173.5 kB 2131 September 3, 2019 Multiplying integers – hard 565.9 kB 1911 September 3, 2019 Multiplying integers – very hard 568 kB 1799 September 3, 2019 Non positive decimals Multiplying decimals – very easy 186.6 kB 2161 September 3, 2019 Multiplying decimals – easy 187 kB 2283 September 3, 2019 Multiplying decimals – medium 578.8 kB 1794 September 3, 2019 Multiplying decimals – medium-hard 577 kB 1678 September 3, 2019 Multiplying decimals – hard 564.9 kB 1748 September 3, 2019 Multiplying decimals – very hard 567.9 kB 1662 September 3, 2019 Non positive fractions Multiplying fractions – very easy 179.6 kB 1853 September 3, 2019 Multiplying fractions – easy 186.7 kB 2063 September 3, 2019 Multiplying fractions – medium 583.8 kB 1805 September 3, 2019 Multiplying fractions – medium-hard 589 kB 1663 September 3, 2019 Multiplying fractions – hard 588 kB 1575 September 3, 2019 Multiplying fractions – very hard 594.9 kB 1589 September 3, 2019 Non positive mixed numbers Multiplying mixed numbers – very easy 192.9 kB 1639 September 3, 2019 Multiplying mixed numbers – easy 209 kB 1795 September 3, 2019 Multiplying mixed numbers – medium 594.7 kB 1659 September 3, 2019 Multiplying mixed numbers – medium-hard 602.2 kB 1490 September 3, 2019 Multiplying mixed numbers – hard 586.3 kB 1519 September 3, 2019 Multiplying mixed numbers – very hard 591.3 kB 1508 September 3, 2019 Non positive improper fractions Multiplying improper fractions – very easy 171.2 kB 1560 September 3, 2019 Multiplying improper fractions – easy 174 kB 1596 September 3, 2019 Multiplying improper fractions – medium 574.7 kB 1560 September 3, 2019 Multiplying improper fractions – medium-hard 573.9 kB 1480 September 3, 2019 Multiplying improper fractions – hard 570.7 kB 1490 September 3, 2019 Multiplying improper fractions – very hard 577.4 kB 1490 September 3, 2019

## Multiplying worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Multiplying positive integers 496.1 kB 2638 September 3, 2019 Multiplying positive decimals 51.8 kB 1948 September 3, 2019 Multiplying positive fractions 632.1 kB 1734 September 3, 2019 Multiplying positive mixed numbers 637.8 kB 1937 September 3, 2019 Multiplying positive improper fractions 594.6 kB 1541 September 3, 2019 Non positive Multiplying integers 166.8 kB 1990 September 3, 2019 Multiplying decimals 246.3 kB 1807 September 3, 2019 Multiplying fractions 393.1 kB 1832 September 3, 2019 Multiplying mixed numbers 412.4 kB 1687 September 3, 2019 Multiplying improper fractions 334.1 kB 1574 September 3, 2019