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 4082 September 3, 2019
Multiplying positive integers – easy 143 kB 4054 September 3, 2019
Multiplying positive integers – medium 166.3 kB 4562 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 3727 September 3, 2019
Multiplying positive integers – hard 561.5 kB 3000 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 3321 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2866 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2823 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 2657 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 2471 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 2680 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 2433 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 2433 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 3542 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 3446 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 2742 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 2394 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 2493 September 3, 2019
Multiplying positive fractions – very hard 581 kB 2423 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 2688 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 2614 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 2518 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 2357 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 2389 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 2306 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 2413 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 2526 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 2439 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 2222 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 2252 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 2311 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 3088 September 3, 2019
Multiplying integers – easy 143.6 kB 3235 September 3, 2019
Multiplying integers – medium 173.3 kB 3252 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 2976 September 3, 2019
Multiplying integers – hard 565.9 kB 2649 September 3, 2019
Multiplying integers – very hard 568 kB 2556 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2883 September 3, 2019
Multiplying decimals – easy 187 kB 3162 September 3, 2019
Multiplying decimals – medium 578.8 kB 2599 September 3, 2019
Multiplying decimals – medium-hard 577 kB 2324 September 3, 2019
Multiplying decimals – hard 564.9 kB 2471 September 3, 2019
Multiplying decimals – very hard 567.9 kB 2392 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 2690 September 3, 2019
Multiplying fractions – easy 186.7 kB 3017 September 3, 2019
Multiplying fractions – medium 583.8 kB 2593 September 3, 2019
Multiplying fractions – medium-hard 589 kB 2313 September 3, 2019
Multiplying fractions – hard 588 kB 2213 September 3, 2019
Multiplying fractions – very hard 594.9 kB 2292 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 2358 September 3, 2019
Multiplying mixed numbers – easy 209 kB 2520 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 2470 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 2096 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 2127 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 2107 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 2152 September 3, 2019
Multiplying improper fractions – easy 174 kB 2241 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 2221 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 2155 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 2067 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 2153 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 3464 September 3, 2019
Multiplying positive decimals 51.8 kB 2690 September 3, 2019
Multiplying positive fractions 632.1 kB 2476 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 2576 September 3, 2019
Multiplying positive improper fractions 594.6 kB 2168 September 3, 2019
Non positive
Multiplying integers 166.8 kB 2793 September 3, 2019
Multiplying decimals 246.3 kB 2531 September 3, 2019
Multiplying fractions 393.1 kB 2561 September 3, 2019
Multiplying mixed numbers 412.4 kB 2296 September 3, 2019
Multiplying improper fractions 334.1 kB 2137 September 3, 2019