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 2948 September 3, 2019
Multiplying positive integers – easy 143 kB 2946 September 3, 2019
Multiplying positive integers – medium 166.3 kB 3248 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 2719 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2124 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2334 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1974 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 1967 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 1792 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 1609 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 1781 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 1613 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1613 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 2407 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 2130 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 1826 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 1604 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 1615 September 3, 2019
Multiplying positive fractions – very hard 581 kB 1589 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1783 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 1807 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 1638 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1560 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 1568 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1530 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1574 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 1676 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 1565 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1523 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1468 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1532 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2147 September 3, 2019
Multiplying integers – easy 143.6 kB 2186 September 3, 2019
Multiplying integers – medium 173.3 kB 2142 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 1999 September 3, 2019
Multiplying integers – hard 565.9 kB 1788 September 3, 2019
Multiplying integers – very hard 568 kB 1682 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 2020 September 3, 2019
Multiplying decimals – easy 187 kB 2143 September 3, 2019
Multiplying decimals – medium 578.8 kB 1652 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1562 September 3, 2019
Multiplying decimals – hard 564.9 kB 1631 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1538 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1642 September 3, 2019
Multiplying fractions – easy 186.7 kB 1914 September 3, 2019
Multiplying fractions – medium 583.8 kB 1643 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1549 September 3, 2019
Multiplying fractions – hard 588 kB 1458 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1475 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1508 September 3, 2019
Multiplying mixed numbers – easy 209 kB 1678 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1545 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1390 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1418 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1397 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1449 September 3, 2019
Multiplying improper fractions – easy 174 kB 1492 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1458 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1369 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1386 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1386 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2479 September 3, 2019
Multiplying positive decimals 51.8 kB 1813 September 3, 2019
Multiplying positive fractions 632.1 kB 1621 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 1818 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1430 September 3, 2019
Non positive
Multiplying integers 166.8 kB 1852 September 3, 2019
Multiplying decimals 246.3 kB 1686 September 3, 2019
Multiplying fractions 393.1 kB 1689 September 3, 2019
Multiplying mixed numbers 412.4 kB 1576 September 3, 2019
Multiplying improper fractions 334.1 kB 1476 September 3, 2019