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 2629 September 3, 2019
Multiplying positive integers – easy 143 kB 2638 September 3, 2019
Multiplying positive integers – medium 166.3 kB 2918 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 2457 September 3, 2019
Multiplying positive integers – hard 561.5 kB 1878 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2089 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1722 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 1726 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 1555 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 1412 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 1551 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 1400 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1400 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 2039 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 1726 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 1568 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 1392 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 1401 September 3, 2019
Multiplying positive fractions – very hard 581 kB 1385 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1569 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 1585 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 1413 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1347 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 1337 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1325 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1381 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 1473 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 1352 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1330 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1262 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1330 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 1931 September 3, 2019
Multiplying integers – easy 143.6 kB 1929 September 3, 2019
Multiplying integers – medium 173.3 kB 1872 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 1771 September 3, 2019
Multiplying integers – hard 565.9 kB 1568 September 3, 2019
Multiplying integers – very hard 568 kB 1467 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1801 September 3, 2019
Multiplying decimals – easy 187 kB 1923 September 3, 2019
Multiplying decimals – medium 578.8 kB 1423 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1350 September 3, 2019
Multiplying decimals – hard 564.9 kB 1394 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1330 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1412 September 3, 2019
Multiplying fractions – easy 186.7 kB 1675 September 3, 2019
Multiplying fractions – medium 583.8 kB 1389 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1344 September 3, 2019
Multiplying fractions – hard 588 kB 1265 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1273 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1314 September 3, 2019
Multiplying mixed numbers – easy 209 kB 1476 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1344 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1211 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1231 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1214 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1264 September 3, 2019
Multiplying improper fractions – easy 174 kB 1299 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1259 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1191 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1205 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1203 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2200 September 3, 2019
Multiplying positive decimals 51.8 kB 1586 September 3, 2019
Multiplying positive fractions 632.1 kB 1398 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 1634 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1237 September 3, 2019
Non positive
Multiplying integers 166.8 kB 1613 September 3, 2019
Multiplying decimals 246.3 kB 1473 September 3, 2019
Multiplying fractions 393.1 kB 1440 September 3, 2019
Multiplying mixed numbers 412.4 kB 1367 September 3, 2019
Multiplying improper fractions 334.1 kB 1285 September 3, 2019