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 2870 September 3, 2019
Multiplying positive integers – easy 143 kB 2871 September 3, 2019
Multiplying positive integers – medium 166.3 kB 3165 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 2649 September 3, 2019
Multiplying positive integers – hard 561.5 kB 2053 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2265 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1900 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 1901 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 1723 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 1554 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 1707 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 1551 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1551 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 2324 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 2002 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 1736 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 1535 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 1547 September 3, 2019
Multiplying positive fractions – very hard 581 kB 1534 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1730 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 1737 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 1566 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1491 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 1491 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1463 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1518 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 1619 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 1499 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1463 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1400 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1465 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 2082 September 3, 2019
Multiplying integers – easy 143.6 kB 2113 September 3, 2019
Multiplying integers – medium 173.3 kB 2063 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 1931 September 3, 2019
Multiplying integers – hard 565.9 kB 1721 September 3, 2019
Multiplying integers – very hard 568 kB 1620 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1957 September 3, 2019
Multiplying decimals – easy 187 kB 2079 September 3, 2019
Multiplying decimals – medium 578.8 kB 1573 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1494 September 3, 2019
Multiplying decimals – hard 564.9 kB 1567 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1482 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1571 September 3, 2019
Multiplying fractions – easy 186.7 kB 1846 September 3, 2019
Multiplying fractions – medium 583.8 kB 1571 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1488 September 3, 2019
Multiplying fractions – hard 588 kB 1398 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1418 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1448 September 3, 2019
Multiplying mixed numbers – easy 209 kB 1617 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1489 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1338 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1361 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1344 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1393 September 3, 2019
Multiplying improper fractions – easy 174 kB 1437 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1397 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1316 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1337 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1330 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2402 September 3, 2019
Multiplying positive decimals 51.8 kB 1736 September 3, 2019
Multiplying positive fractions 632.1 kB 1544 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 1763 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1364 September 3, 2019
Non positive
Multiplying integers 166.8 kB 1790 September 3, 2019
Multiplying decimals 246.3 kB 1620 September 3, 2019
Multiplying fractions 393.1 kB 1613 September 3, 2019
Multiplying mixed numbers 412.4 kB 1514 September 3, 2019
Multiplying improper fractions 334.1 kB 1421 September 3, 2019