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 3805 September 3, 2019
Multiplying positive integers – easy 143 kB 3810 September 3, 2019
Multiplying positive integers – medium 166.3 kB 4260 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 3452 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2780 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 3062 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2647 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2620 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 2451 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 2243 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 2431 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 2222 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 2222 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 3298 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 3095 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 2494 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 2220 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 2250 September 3, 2019
Multiplying positive fractions – very hard 581 kB 2191 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 2451 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 2417 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 2275 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 2142 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 2188 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 2104 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 2176 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 2295 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 2198 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 2042 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 2023 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 2082 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2837 September 3, 2019
Multiplying integers – easy 143.6 kB 2987 September 3, 2019
Multiplying integers – medium 173.3 kB 2936 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 2683 September 3, 2019
Multiplying integers – hard 565.9 kB 2412 September 3, 2019
Multiplying integers – very hard 568 kB 2311 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2668 September 3, 2019
Multiplying decimals – easy 187 kB 2884 September 3, 2019
Multiplying decimals – medium 578.8 kB 2355 September 3, 2019
Multiplying decimals – medium-hard 577 kB 2107 September 3, 2019
Multiplying decimals – hard 564.9 kB 2249 September 3, 2019
Multiplying decimals – very hard 567.9 kB 2141 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 2474 September 3, 2019
Multiplying fractions – easy 186.7 kB 2747 September 3, 2019
Multiplying fractions – medium 583.8 kB 2350 September 3, 2019
Multiplying fractions – medium-hard 589 kB 2087 September 3, 2019
Multiplying fractions – hard 588 kB 1985 September 3, 2019
Multiplying fractions – very hard 594.9 kB 2061 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 2125 September 3, 2019
Multiplying mixed numbers – easy 209 kB 2273 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 2150 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1906 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1907 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1892 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1973 September 3, 2019
Multiplying improper fractions – easy 174 kB 2014 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1988 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1910 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1877 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1917 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 3204 September 3, 2019
Multiplying positive decimals 51.8 kB 2436 September 3, 2019
Multiplying positive fractions 632.1 kB 2236 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 2362 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1950 September 3, 2019
Non positive
Multiplying integers 166.8 kB 2553 September 3, 2019
Multiplying decimals 246.3 kB 2300 September 3, 2019
Multiplying fractions 393.1 kB 2322 September 3, 2019
Multiplying mixed numbers 412.4 kB 2107 September 3, 2019
Multiplying improper fractions 334.1 kB 1934 September 3, 2019