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 3503 September 3, 2019
Multiplying positive integers – easy 143 kB 3505 September 3, 2019
Multiplying positive integers – medium 166.3 kB 3913 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 3194 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2556 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2802 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2432 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2378 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 2241 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 2027 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 2201 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 2001 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 2001 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 3053 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 2837 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 2267 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 2032 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 2042 September 3, 2019
Multiplying positive fractions – very hard 581 kB 1995 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 2242 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 2208 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 2070 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1957 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 1992 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1909 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1971 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 2082 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 1995 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1856 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1834 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1888 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2606 September 3, 2019
Multiplying integers – easy 143.6 kB 2716 September 3, 2019
Multiplying integers – medium 173.3 kB 2663 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 2458 September 3, 2019
Multiplying integers – hard 565.9 kB 2214 September 3, 2019
Multiplying integers – very hard 568 kB 2110 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2441 September 3, 2019
Multiplying decimals – easy 187 kB 2613 September 3, 2019
Multiplying decimals – medium 578.8 kB 2127 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1915 September 3, 2019
Multiplying decimals – hard 564.9 kB 2048 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1919 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 2209 September 3, 2019
Multiplying fractions – easy 186.7 kB 2468 September 3, 2019
Multiplying fractions – medium 583.8 kB 2103 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1895 September 3, 2019
Multiplying fractions – hard 588 kB 1794 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1872 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1923 September 3, 2019
Multiplying mixed numbers – easy 209 kB 2048 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1907 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1741 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1735 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1722 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1786 September 3, 2019
Multiplying improper fractions – easy 174 kB 1823 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1782 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1731 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1695 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1740 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2932 September 3, 2019
Multiplying positive decimals 51.8 kB 2200 September 3, 2019
Multiplying positive fractions 632.1 kB 2007 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 2184 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1757 September 3, 2019
Non positive
Multiplying integers 166.8 kB 2291 September 3, 2019
Multiplying decimals 246.3 kB 2043 September 3, 2019
Multiplying fractions 393.1 kB 2110 September 3, 2019
Multiplying mixed numbers 412.4 kB 1901 September 3, 2019
Multiplying improper fractions 334.1 kB 1764 September 3, 2019