# 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 3733 September 3, 2019 Multiplying positive integers – easy 143 kB 3737 September 3, 2019 Multiplying positive integers – medium 166.3 kB 4183 September 3, 2019 Multiplying positive integers – medium-hard 173.1 kB 3385 September 3, 2019 Multiplying positive integers – hard 561.5 kB 2713 September 3, 2019 Multiplying positive integers – very hard 571.8 kB 2997 September 3, 2019 Positive decimals Multiplying positive decimals – very easy 554.5 kB 2598 September 3, 2019 Multiplying positive decimals – easy 555.5 kB 2556 September 3, 2019 Multiplying positive decimals – medium 579.2 kB 2401 September 3, 2019 Multiplying positive decimals – medium-hard 580.2 kB 2180 September 3, 2019 Multiplying positive decimals – hard 569.5 kB 2371 September 3, 2019 Multiplying positive decimals – very hard 567.2 kB 2159 September 3, 2019 Positive fractions Multiplying positive fractions – very hard 567.2 kB 2159 September 3, 2019 Multiplying positive fractions – very easy 172.7 kB 3229 September 3, 2019 Multiplying positive fractions – easy 188.9 kB 3033 September 3, 2019 Multiplying positive fractions – medium 577.2 kB 2439 September 3, 2019 Multiplying positive fractions – medium-hard 591.9 kB 2168 September 3, 2019 Multiplying positive fractions – hard 575.7 kB 2193 September 3, 2019 Multiplying positive fractions – very hard 581 kB 2140 September 3, 2019 Positive mixed numbers Multiplying positive mixed numbers – very easy 176.8 kB 2400 September 3, 2019 Multiplying positive mixed numbers – easy 209.8 kB 2362 September 3, 2019 Multiplying positive mixed numbers – medium 585.6 kB 2221 September 3, 2019 Multiplying positive mixed numbers – medium-hard 592.9 kB 2090 September 3, 2019 Multiplying positive mixed numbers – hard 589.3 kB 2135 September 3, 2019 Multiplying positive mixed numbers – very hard 596.6 kB 2051 September 3, 2019 Positive improper fractions Multiplying positive improper fractions – very easy 166 kB 2117 September 3, 2019 Multiplying positive improper fractions – easy 169.9 kB 2244 September 3, 2019 Multiplying positive improper fractions – medium 571.6 kB 2138 September 3, 2019 Multiplying positive improper fractions – medium-hard 569.5 kB 1990 September 3, 2019 Multiplying positive improper fractions – hard 560.5 kB 1973 September 3, 2019 Multiplying positive improper fractions – very hard 571.8 kB 2034 September 3, 2019 Non positive integers Multiplying integers – very easy 137.9 kB 2782 September 3, 2019 Multiplying integers – easy 143.6 kB 2919 September 3, 2019 Multiplying integers – medium 173.3 kB 2874 September 3, 2019 Multiplying integers – medium-hard 173.5 kB 2624 September 3, 2019 Multiplying integers – hard 565.9 kB 2368 September 3, 2019 Multiplying integers – very hard 568 kB 2272 September 3, 2019 Non positive decimals Multiplying decimals – very easy 186.6 kB 2619 September 3, 2019 Multiplying decimals – easy 187 kB 2826 September 3, 2019 Multiplying decimals – medium 578.8 kB 2305 September 3, 2019 Multiplying decimals – medium-hard 577 kB 2062 September 3, 2019 Multiplying decimals – hard 564.9 kB 2203 September 3, 2019 Multiplying decimals – very hard 567.9 kB 2092 September 3, 2019 Non positive fractions Multiplying fractions – very easy 179.6 kB 2418 September 3, 2019 Multiplying fractions – easy 186.7 kB 2693 September 3, 2019 Multiplying fractions – medium 583.8 kB 2303 September 3, 2019 Multiplying fractions – medium-hard 589 kB 2049 September 3, 2019 Multiplying fractions – hard 588 kB 1941 September 3, 2019 Multiplying fractions – very hard 594.9 kB 2020 September 3, 2019 Non positive mixed numbers Multiplying mixed numbers – very easy 192.9 kB 2084 September 3, 2019 Multiplying mixed numbers – easy 209 kB 2225 September 3, 2019 Multiplying mixed numbers – medium 594.7 kB 2072 September 3, 2019 Multiplying mixed numbers – medium-hard 602.2 kB 1865 September 3, 2019 Multiplying mixed numbers – hard 586.3 kB 1865 September 3, 2019 Multiplying mixed numbers – very hard 591.3 kB 1850 September 3, 2019 Non positive improper fractions Multiplying improper fractions – very easy 171.2 kB 1929 September 3, 2019 Multiplying improper fractions – easy 174 kB 1975 September 3, 2019 Multiplying improper fractions – medium 574.7 kB 1932 September 3, 2019 Multiplying improper fractions – medium-hard 573.9 kB 1868 September 3, 2019 Multiplying improper fractions – hard 570.7 kB 1832 September 3, 2019 Multiplying improper fractions – very hard 577.4 kB 1877 September 3, 2019

## Multiplying worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Multiplying positive integers 496.1 kB 3149 September 3, 2019 Multiplying positive decimals 51.8 kB 2394 September 3, 2019 Multiplying positive fractions 632.1 kB 2189 September 3, 2019 Multiplying positive mixed numbers 637.8 kB 2325 September 3, 2019 Multiplying positive improper fractions 594.6 kB 1912 September 3, 2019 Non positive Multiplying integers 166.8 kB 2497 September 3, 2019 Multiplying decimals 246.3 kB 2249 September 3, 2019 Multiplying fractions 393.1 kB 2281 September 3, 2019 Multiplying mixed numbers 412.4 kB 2058 September 3, 2019 Multiplying improper fractions 334.1 kB 1895 September 3, 2019