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 3318 September 3, 2019
Multiplying positive integers – easy 143 kB 3340 September 3, 2019
Multiplying positive integers – medium 166.3 kB 3685 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 3052 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2430 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2660 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2270 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2260 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 2095 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 1879 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 2062 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 1889 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1889 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 2907 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 2702 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 2138 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 1880 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 1898 September 3, 2019
Multiplying positive fractions – very hard 581 kB 1851 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 2074 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 2092 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 1919 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1817 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 1850 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1814 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1863 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 1968 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 1851 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1760 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1728 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1782 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2453 September 3, 2019
Multiplying integers – easy 143.6 kB 2529 September 3, 2019
Multiplying integers – medium 173.3 kB 2480 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 2289 September 3, 2019
Multiplying integers – hard 565.9 kB 2053 September 3, 2019
Multiplying integers – very hard 568 kB 1949 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2313 September 3, 2019
Multiplying decimals – easy 187 kB 2455 September 3, 2019
Multiplying decimals – medium 578.8 kB 1950 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1814 September 3, 2019
Multiplying decimals – hard 564.9 kB 1892 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1813 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 2042 September 3, 2019
Multiplying fractions – easy 186.7 kB 2256 September 3, 2019
Multiplying fractions – medium 583.8 kB 1947 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1794 September 3, 2019
Multiplying fractions – hard 588 kB 1696 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1723 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1778 September 3, 2019
Multiplying mixed numbers – easy 209 kB 1921 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1782 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1613 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1644 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1642 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1689 September 3, 2019
Multiplying improper fractions – easy 174 kB 1723 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1688 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1614 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1608 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1622 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2799 September 3, 2019
Multiplying positive decimals 51.8 kB 2088 September 3, 2019
Multiplying positive fractions 632.1 kB 1873 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 2065 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1669 September 3, 2019
Non positive
Multiplying integers 166.8 kB 2145 September 3, 2019
Multiplying decimals 246.3 kB 1945 September 3, 2019
Multiplying fractions 393.1 kB 1983 September 3, 2019
Multiplying mixed numbers 412.4 kB 1808 September 3, 2019
Multiplying improper fractions 334.1 kB 1687 September 3, 2019