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 3591 September 3, 2019
Multiplying positive integers – easy 143 kB 3571 September 3, 2019
Multiplying positive integers – medium 166.3 kB 3995 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 3253 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2605 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2877 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2484 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2434 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 2292 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 2072 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 2248 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 2044 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 2044 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 3112 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 2896 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 2320 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 2075 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 2088 September 3, 2019
Multiplying positive fractions – very hard 581 kB 2038 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 2288 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 2259 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 2118 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1994 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 2033 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1948 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 2026 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 2136 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 2041 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1895 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1872 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1933 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2664 September 3, 2019
Multiplying integers – easy 143.6 kB 2780 September 3, 2019
Multiplying integers – medium 173.3 kB 2740 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 2512 September 3, 2019
Multiplying integers – hard 565.9 kB 2258 September 3, 2019
Multiplying integers – very hard 568 kB 2164 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2505 September 3, 2019
Multiplying decimals – easy 187 kB 2679 September 3, 2019
Multiplying decimals – medium 578.8 kB 2178 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1958 September 3, 2019
Multiplying decimals – hard 564.9 kB 2094 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1971 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 2276 September 3, 2019
Multiplying fractions – easy 186.7 kB 2550 September 3, 2019
Multiplying fractions – medium 583.8 kB 2175 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1938 September 3, 2019
Multiplying fractions – hard 588 kB 1837 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1922 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1968 September 3, 2019
Multiplying mixed numbers – easy 209 kB 2101 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1953 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1774 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1771 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1761 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1832 September 3, 2019
Multiplying improper fractions – easy 174 kB 1873 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1830 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1772 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1736 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1777 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2992 September 3, 2019
Multiplying positive decimals 51.8 kB 2252 September 3, 2019
Multiplying positive fractions 632.1 kB 2054 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 2225 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1797 September 3, 2019
Non positive
Multiplying integers 166.8 kB 2352 September 3, 2019
Multiplying decimals 246.3 kB 2103 September 3, 2019
Multiplying fractions 393.1 kB 2159 September 3, 2019
Multiplying mixed numbers 412.4 kB 1950 September 3, 2019
Multiplying improper fractions 334.1 kB 1803 September 3, 2019