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 3796 September 3, 2019
Multiplying positive integers – easy 143 kB 3800 September 3, 2019
Multiplying positive integers – medium 166.3 kB 4250 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 3442 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2769 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 3056 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2640 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2612 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 2442 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 2233 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 2422 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 2212 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 2212 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 3289 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 3083 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 2485 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 2212 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 2242 September 3, 2019
Multiplying positive fractions – very hard 581 kB 2183 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 2443 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 2408 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 2267 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 2133 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 2180 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 2095 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 2167 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 2288 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 2187 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 2034 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 2015 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 2074 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2830 September 3, 2019
Multiplying integers – easy 143.6 kB 2981 September 3, 2019
Multiplying integers – medium 173.3 kB 2927 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 2673 September 3, 2019
Multiplying integers – hard 565.9 kB 2404 September 3, 2019
Multiplying integers – very hard 568 kB 2304 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2656 September 3, 2019
Multiplying decimals – easy 187 kB 2875 September 3, 2019
Multiplying decimals – medium 578.8 kB 2344 September 3, 2019
Multiplying decimals – medium-hard 577 kB 2096 September 3, 2019
Multiplying decimals – hard 564.9 kB 2240 September 3, 2019
Multiplying decimals – very hard 567.9 kB 2132 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 2465 September 3, 2019
Multiplying fractions – easy 186.7 kB 2738 September 3, 2019
Multiplying fractions – medium 583.8 kB 2341 September 3, 2019
Multiplying fractions – medium-hard 589 kB 2079 September 3, 2019
Multiplying fractions – hard 588 kB 1977 September 3, 2019
Multiplying fractions – very hard 594.9 kB 2054 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 2117 September 3, 2019
Multiplying mixed numbers – easy 209 kB 2264 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 2142 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1897 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1899 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1884 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1961 September 3, 2019
Multiplying improper fractions – easy 174 kB 2007 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1978 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1902 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1867 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1908 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 3193 September 3, 2019
Multiplying positive decimals 51.8 kB 2429 September 3, 2019
Multiplying positive fractions 632.1 kB 2229 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 2355 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1945 September 3, 2019
Non positive
Multiplying integers 166.8 kB 2541 September 3, 2019
Multiplying decimals 246.3 kB 2291 September 3, 2019
Multiplying fractions 393.1 kB 2315 September 3, 2019
Multiplying mixed numbers 412.4 kB 2099 September 3, 2019
Multiplying improper fractions 334.1 kB 1928 September 3, 2019