# 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 3391 September 3, 2019 Multiplying positive integers – easy 143 kB 3391 September 3, 2019 Multiplying positive integers – medium 166.3 kB 3768 September 3, 2019 Multiplying positive integers – medium-hard 173.1 kB 3087 September 3, 2019 Multiplying positive integers – hard 561.5 kB 2469 September 3, 2019 Multiplying positive integers – very hard 571.8 kB 2705 September 3, 2019 Positive decimals Multiplying positive decimals – very easy 554.5 kB 2329 September 3, 2019 Multiplying positive decimals – easy 555.5 kB 2290 September 3, 2019 Multiplying positive decimals – medium 579.2 kB 2151 September 3, 2019 Multiplying positive decimals – medium-hard 580.2 kB 1943 September 3, 2019 Multiplying positive decimals – hard 569.5 kB 2120 September 3, 2019 Multiplying positive decimals – very hard 567.2 kB 1919 September 3, 2019 Positive fractions Multiplying positive fractions – very hard 567.2 kB 1919 September 3, 2019 Multiplying positive fractions – very easy 172.7 kB 2942 September 3, 2019 Multiplying positive fractions – easy 188.9 kB 2737 September 3, 2019 Multiplying positive fractions – medium 577.2 kB 2172 September 3, 2019 Multiplying positive fractions – medium-hard 591.9 kB 1937 September 3, 2019 Multiplying positive fractions – hard 575.7 kB 1953 September 3, 2019 Multiplying positive fractions – very hard 581 kB 1904 September 3, 2019 Positive mixed numbers Multiplying positive mixed numbers – very easy 176.8 kB 2139 September 3, 2019 Multiplying positive mixed numbers – easy 209.8 kB 2123 September 3, 2019 Multiplying positive mixed numbers – medium 585.6 kB 1978 September 3, 2019 Multiplying positive mixed numbers – medium-hard 592.9 kB 1870 September 3, 2019 Multiplying positive mixed numbers – hard 589.3 kB 1910 September 3, 2019 Multiplying positive mixed numbers – very hard 596.6 kB 1841 September 3, 2019 Positive improper fractions Multiplying positive improper fractions – very easy 166 kB 1892 September 3, 2019 Multiplying positive improper fractions – easy 169.9 kB 1998 September 3, 2019 Multiplying positive improper fractions – medium 571.6 kB 1905 September 3, 2019 Multiplying positive improper fractions – medium-hard 569.5 kB 1785 September 3, 2019 Multiplying positive improper fractions – hard 560.5 kB 1755 September 3, 2019 Multiplying positive improper fractions – very hard 571.8 kB 1808 September 3, 2019 Non positive integers Multiplying integers – very easy 137.9 kB 2515 September 3, 2019 Multiplying integers – easy 143.6 kB 2597 September 3, 2019 Multiplying integers – medium 173.3 kB 2545 September 3, 2019 Multiplying integers – medium-hard 173.5 kB 2354 September 3, 2019 Multiplying integers – hard 565.9 kB 2118 September 3, 2019 Multiplying integers – very hard 568 kB 2011 September 3, 2019 Non positive decimals Multiplying decimals – very easy 186.6 kB 2345 September 3, 2019 Multiplying decimals – easy 187 kB 2492 September 3, 2019 Multiplying decimals – medium 578.8 kB 2008 September 3, 2019 Multiplying decimals – medium-hard 577 kB 1843 September 3, 2019 Multiplying decimals – hard 564.9 kB 1955 September 3, 2019 Multiplying decimals – very hard 567.9 kB 1845 September 3, 2019 Non positive fractions Multiplying fractions – very easy 179.6 kB 2079 September 3, 2019 Multiplying fractions – easy 186.7 kB 2321 September 3, 2019 Multiplying fractions – medium 583.8 kB 1979 September 3, 2019 Multiplying fractions – medium-hard 589 kB 1820 September 3, 2019 Multiplying fractions – hard 588 kB 1723 September 3, 2019 Multiplying fractions – very hard 594.9 kB 1789 September 3, 2019 Non positive mixed numbers Multiplying mixed numbers – very easy 192.9 kB 1836 September 3, 2019 Multiplying mixed numbers – easy 209 kB 1953 September 3, 2019 Multiplying mixed numbers – medium 594.7 kB 1811 September 3, 2019 Multiplying mixed numbers – medium-hard 602.2 kB 1664 September 3, 2019 Multiplying mixed numbers – hard 586.3 kB 1673 September 3, 2019 Multiplying mixed numbers – very hard 591.3 kB 1666 September 3, 2019 Non positive improper fractions Multiplying improper fractions – very easy 171.2 kB 1714 September 3, 2019 Multiplying improper fractions – easy 174 kB 1752 September 3, 2019 Multiplying improper fractions – medium 574.7 kB 1711 September 3, 2019 Multiplying improper fractions – medium-hard 573.9 kB 1664 September 3, 2019 Multiplying improper fractions – hard 570.7 kB 1634 September 3, 2019 Multiplying improper fractions – very hard 577.4 kB 1677 September 3, 2019

## Multiplying worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Multiplying positive integers 496.1 kB 2844 September 3, 2019 Multiplying positive decimals 51.8 kB 2140 September 3, 2019 Multiplying positive fractions 632.1 kB 1929 September 3, 2019 Multiplying positive mixed numbers 637.8 kB 2120 September 3, 2019 Multiplying positive improper fractions 594.6 kB 1699 September 3, 2019 Non positive Multiplying integers 166.8 kB 2200 September 3, 2019 Multiplying decimals 246.3 kB 1976 September 3, 2019 Multiplying fractions 393.1 kB 2010 September 3, 2019 Multiplying mixed numbers 412.4 kB 1834 September 3, 2019 Multiplying improper fractions 334.1 kB 1712 September 3, 2019