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 3055 September 3, 2019
Multiplying positive integers – easy 143 kB 3070 September 3, 2019
Multiplying positive integers – medium 166.3 kB 3360 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 2818 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2214 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2430 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 2060 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 2050 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 1881 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 1689 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 1863 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 1695 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1695 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 2508 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 2337 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 1907 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 1684 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 1692 September 3, 2019
Multiplying positive fractions – very hard 581 kB 1663 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1861 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 1886 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 1722 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1631 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 1650 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1615 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1646 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 1756 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 1652 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1592 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1543 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1610 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2234 September 3, 2019
Multiplying integers – easy 143.6 kB 2289 September 3, 2019
Multiplying integers – medium 173.3 kB 2241 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 2083 September 3, 2019
Multiplying integers – hard 565.9 kB 1865 September 3, 2019
Multiplying integers – very hard 568 kB 1759 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2107 September 3, 2019
Multiplying decimals – easy 187 kB 2226 September 3, 2019
Multiplying decimals – medium 578.8 kB 1740 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1637 September 3, 2019
Multiplying decimals – hard 564.9 kB 1706 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1615 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1765 September 3, 2019
Multiplying fractions – easy 186.7 kB 2005 September 3, 2019
Multiplying fractions – medium 583.8 kB 1735 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1622 September 3, 2019
Multiplying fractions – hard 588 kB 1527 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1545 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1587 September 3, 2019
Multiplying mixed numbers – easy 209 kB 1750 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1617 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1455 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1484 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1466 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1518 September 3, 2019
Multiplying improper fractions – easy 174 kB 1555 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1521 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1438 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1450 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1451 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2575 September 3, 2019
Multiplying positive decimals 51.8 kB 1903 September 3, 2019
Multiplying positive fractions 632.1 kB 1695 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 1892 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1503 September 3, 2019
Non positive
Multiplying integers 166.8 kB 1940 September 3, 2019
Multiplying decimals 246.3 kB 1759 September 3, 2019
Multiplying fractions 393.1 kB 1770 September 3, 2019
Multiplying mixed numbers 412.4 kB 1648 September 3, 2019
Multiplying improper fractions 334.1 kB 1541 September 3, 2019