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 2603 September 3, 2019
Multiplying positive integers – easy 143 kB 2604 September 3, 2019
Multiplying positive integers – medium 166.3 kB 2881 September 3, 2019
Multiplying positive integers – medium-hard 173.1 kB 2430 September 3, 2019
Multiplying positive integers – hard 561.5 kB 1856 September 3, 2019
Multiplying positive integers – very hard 571.8 kB 2064 September 3, 2019
Positive decimals
Multiplying positive decimals – very easy 554.5 kB 1703 September 3, 2019
Multiplying positive decimals – easy 555.5 kB 1703 September 3, 2019
Multiplying positive decimals – medium 579.2 kB 1535 September 3, 2019
Multiplying positive decimals – medium-hard 580.2 kB 1390 September 3, 2019
Multiplying positive decimals – hard 569.5 kB 1534 September 3, 2019
Multiplying positive decimals – very hard 567.2 kB 1381 September 3, 2019
Positive fractions
Multiplying positive fractions – very hard 567.2 kB 1381 September 3, 2019
Multiplying positive fractions – very easy 172.7 kB 2015 September 3, 2019
Multiplying positive fractions – easy 188.9 kB 1703 September 3, 2019
Multiplying positive fractions – medium 577.2 kB 1546 September 3, 2019
Multiplying positive fractions – medium-hard 591.9 kB 1375 September 3, 2019
Multiplying positive fractions – hard 575.7 kB 1382 September 3, 2019
Multiplying positive fractions – very hard 581 kB 1366 September 3, 2019
Positive mixed numbers
Multiplying positive mixed numbers – very easy 176.8 kB 1550 September 3, 2019
Multiplying positive mixed numbers – easy 209.8 kB 1562 September 3, 2019
Multiplying positive mixed numbers – medium 585.6 kB 1396 September 3, 2019
Multiplying positive mixed numbers – medium-hard 592.9 kB 1329 September 3, 2019
Multiplying positive mixed numbers – hard 589.3 kB 1319 September 3, 2019
Multiplying positive mixed numbers – very hard 596.6 kB 1307 September 3, 2019
Positive improper fractions
Multiplying positive improper fractions – very easy 166 kB 1362 September 3, 2019
Multiplying positive improper fractions – easy 169.9 kB 1453 September 3, 2019
Multiplying positive improper fractions – medium 571.6 kB 1332 September 3, 2019
Multiplying positive improper fractions – medium-hard 569.5 kB 1314 September 3, 2019
Multiplying positive improper fractions – hard 560.5 kB 1246 September 3, 2019
Multiplying positive improper fractions – very hard 571.8 kB 1313 September 3, 2019
Non positive integers
Multiplying integers – very easy 137.9 kB 1914 September 3, 2019
Multiplying integers – easy 143.6 kB 1900 September 3, 2019
Multiplying integers – medium 173.3 kB 1843 September 3, 2019
Multiplying integers – medium-hard 173.5 kB 1742 September 3, 2019
Multiplying integers – hard 565.9 kB 1544 September 3, 2019
Multiplying integers – very hard 568 kB 1443 September 3, 2019
Non positive decimals
Multiplying decimals – very easy 186.6 kB 1782 September 3, 2019
Multiplying decimals – easy 187 kB 1898 September 3, 2019
Multiplying decimals – medium 578.8 kB 1405 September 3, 2019
Multiplying decimals – medium-hard 577 kB 1332 September 3, 2019
Multiplying decimals – hard 564.9 kB 1378 September 3, 2019
Multiplying decimals – very hard 567.9 kB 1312 September 3, 2019
Non positive fractions
Multiplying fractions – very easy 179.6 kB 1394 September 3, 2019
Multiplying fractions – easy 186.7 kB 1651 September 3, 2019
Multiplying fractions – medium 583.8 kB 1367 September 3, 2019
Multiplying fractions – medium-hard 589 kB 1324 September 3, 2019
Multiplying fractions – hard 588 kB 1249 September 3, 2019
Multiplying fractions – very hard 594.9 kB 1252 September 3, 2019
Non positive mixed numbers
Multiplying mixed numbers – very easy 192.9 kB 1295 September 3, 2019
Multiplying mixed numbers – easy 209 kB 1461 September 3, 2019
Multiplying mixed numbers – medium 594.7 kB 1327 September 3, 2019
Multiplying mixed numbers – medium-hard 602.2 kB 1201 September 3, 2019
Multiplying mixed numbers – hard 586.3 kB 1212 September 3, 2019
Multiplying mixed numbers – very hard 591.3 kB 1202 September 3, 2019
Non positive improper fractions
Multiplying improper fractions – very easy 171.2 kB 1249 September 3, 2019
Multiplying improper fractions – easy 174 kB 1283 September 3, 2019
Multiplying improper fractions – medium 574.7 kB 1246 September 3, 2019
Multiplying improper fractions – medium-hard 573.9 kB 1175 September 3, 2019
Multiplying improper fractions – hard 570.7 kB 1194 September 3, 2019
Multiplying improper fractions – very hard 577.4 kB 1190 September 3, 2019

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 496.1 kB 2182 September 3, 2019
Multiplying positive decimals 51.8 kB 1569 September 3, 2019
Multiplying positive fractions 632.1 kB 1382 September 3, 2019
Multiplying positive mixed numbers 637.8 kB 1619 September 3, 2019
Multiplying positive improper fractions 594.6 kB 1221 September 3, 2019
Non positive
Multiplying integers 166.8 kB 1596 September 3, 2019
Multiplying decimals 246.3 kB 1455 September 3, 2019
Multiplying fractions 393.1 kB 1422 September 3, 2019
Multiplying mixed numbers 412.4 kB 1351 September 3, 2019
Multiplying improper fractions 334.1 kB 1273 September 3, 2019