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 2748 September 3, 2019
Multiplying positive integers – easy 143 kB 2756 September 3, 2019
Multiplying positive integers – medium 166.3 kB 3051 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 2556 September 3, 2019
Multiplying positive integers – hard 561.5 kB 1964 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2170 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1803 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 1811 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 1639 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 1475 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 1621 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 1462 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1462 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 2192 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 1819 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 1645 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 1456 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 1463 September 3, 2019
Multiplying positive fractions – very hard 581 kB 1454 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1639 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 1658 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 1483 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1410 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 1398 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1381 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1439 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 1536 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 1413 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1385 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1313 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1383 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 1995 September 3, 2019
Multiplying integers – easy 143.6 kB 2013 September 3, 2019
Multiplying integers – medium 173.3 kB 1964 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 1844 September 3, 2019
Multiplying integers – hard 565.9 kB 1633 September 3, 2019
Multiplying integers – very hard 568 kB 1532 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1865 September 3, 2019
Multiplying decimals – easy 187 kB 1991 September 3, 2019
Multiplying decimals – medium 578.8 kB 1490 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1413 September 3, 2019
Multiplying decimals – hard 564.9 kB 1472 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1393 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1487 September 3, 2019
Multiplying fractions – easy 186.7 kB 1754 September 3, 2019
Multiplying fractions – medium 583.8 kB 1477 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1411 September 3, 2019
Multiplying fractions – hard 588 kB 1320 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1340 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1369 September 3, 2019
Multiplying mixed numbers – easy 209 kB 1543 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1403 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1267 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1280 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1264 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1313 September 3, 2019
Multiplying improper fractions – easy 174 kB 1357 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1315 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1237 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1262 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1253 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2293 September 3, 2019
Multiplying positive decimals 51.8 kB 1653 September 3, 2019
Multiplying positive fractions 632.1 kB 1461 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 1685 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1285 September 3, 2019
Non positive
Multiplying integers 166.8 kB 1689 September 3, 2019
Multiplying decimals 246.3 kB 1529 September 3, 2019
Multiplying fractions 393.1 kB 1525 September 3, 2019
Multiplying mixed numbers 412.4 kB 1435 September 3, 2019
Multiplying improper fractions 334.1 kB 1347 September 3, 2019