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 3873 September 3, 2019
Multiplying positive integers – easy 143 kB 3872 September 3, 2019
Multiplying positive integers – medium 166.3 kB 4322 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 3517 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2835 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 3121 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2699 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2671 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 2498 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 2290 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 2494 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 2285 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 2285 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 3354 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 3173 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 2542 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 2264 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 2306 September 3, 2019
Multiplying positive fractions – very hard 581 kB 2243 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 2502 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 2470 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 2320 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 2189 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 2244 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 2154 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 2223 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 2343 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 2246 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 2086 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 2079 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 2132 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2886 September 3, 2019
Multiplying integers – easy 143.6 kB 3037 September 3, 2019
Multiplying integers – medium 173.3 kB 3013 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 2767 September 3, 2019
Multiplying integers – hard 565.9 kB 2466 September 3, 2019
Multiplying integers – very hard 568 kB 2365 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2720 September 3, 2019
Multiplying decimals – easy 187 kB 2955 September 3, 2019
Multiplying decimals – medium 578.8 kB 2407 September 3, 2019
Multiplying decimals – medium-hard 577 kB 2148 September 3, 2019
Multiplying decimals – hard 564.9 kB 2295 September 3, 2019
Multiplying decimals – very hard 567.9 kB 2198 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 2530 September 3, 2019
Multiplying fractions – easy 186.7 kB 2804 September 3, 2019
Multiplying fractions – medium 583.8 kB 2405 September 3, 2019
Multiplying fractions – medium-hard 589 kB 2124 September 3, 2019
Multiplying fractions – hard 588 kB 2030 September 3, 2019
Multiplying fractions – very hard 594.9 kB 2105 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 2176 September 3, 2019
Multiplying mixed numbers – easy 209 kB 2332 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 2265 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1946 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1952 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1938 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 2020 September 3, 2019
Multiplying improper fractions – easy 174 kB 2059 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 2040 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1962 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1923 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1971 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 3256 September 3, 2019
Multiplying positive decimals 51.8 kB 2496 September 3, 2019
Multiplying positive fractions 632.1 kB 2285 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 2406 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1997 September 3, 2019
Non positive
Multiplying integers 166.8 kB 2600 September 3, 2019
Multiplying decimals 246.3 kB 2349 September 3, 2019
Multiplying fractions 393.1 kB 2377 September 3, 2019
Multiplying mixed numbers 412.4 kB 2155 September 3, 2019
Multiplying improper fractions 334.1 kB 1978 September 3, 2019