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 4141 September 3, 2019
Multiplying positive integers – easy 143 kB 4107 September 3, 2019
Multiplying positive integers – medium 166.3 kB 4623 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 3783 September 3, 2019
Multiplying positive integers – hard 561.5 kB 3059 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 3392 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2931 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2880 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 2705 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 2522 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 2739 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 2493 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 2493 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 3595 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 3509 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 2796 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 2441 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 2550 September 3, 2019
Multiplying positive fractions – very hard 581 kB 2480 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 2744 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 2670 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 2570 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 2408 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 2433 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 2359 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 2468 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 2579 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 2496 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 2280 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 2315 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 2366 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 3148 September 3, 2019
Multiplying integers – easy 143.6 kB 3305 September 3, 2019
Multiplying integers – medium 173.3 kB 3310 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 3044 September 3, 2019
Multiplying integers – hard 565.9 kB 2701 September 3, 2019
Multiplying integers – very hard 568 kB 2610 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2940 September 3, 2019
Multiplying decimals – easy 187 kB 3210 September 3, 2019
Multiplying decimals – medium 578.8 kB 2654 September 3, 2019
Multiplying decimals – medium-hard 577 kB 2382 September 3, 2019
Multiplying decimals – hard 564.9 kB 2528 September 3, 2019
Multiplying decimals – very hard 567.9 kB 2450 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 2744 September 3, 2019
Multiplying fractions – easy 186.7 kB 3072 September 3, 2019
Multiplying fractions – medium 583.8 kB 2644 September 3, 2019
Multiplying fractions – medium-hard 589 kB 2368 September 3, 2019
Multiplying fractions – hard 588 kB 2270 September 3, 2019
Multiplying fractions – very hard 594.9 kB 2347 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 2408 September 3, 2019
Multiplying mixed numbers – easy 209 kB 2575 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 2525 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 2148 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 2178 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 2160 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 2206 September 3, 2019
Multiplying improper fractions – easy 174 kB 2290 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 2275 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 2209 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 2120 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 2200 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 3521 September 3, 2019
Multiplying positive decimals 51.8 kB 2746 September 3, 2019
Multiplying positive fractions 632.1 kB 2530 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 2631 September 3, 2019
Multiplying positive improper fractions 594.6 kB 2220 September 3, 2019
Non positive
Multiplying integers 166.8 kB 2846 September 3, 2019
Multiplying decimals 246.3 kB 2583 September 3, 2019
Multiplying fractions 393.1 kB 2612 September 3, 2019
Multiplying mixed numbers 412.4 kB 2354 September 3, 2019
Multiplying improper fractions 334.1 kB 2187 September 3, 2019