# 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. ## Multiplying exams for teachers

 Exam Name File Size Downloads Upload date Positive integers Multiplying positive integers – very easy 78 kB 2677 September 3, 2019 Multiplying positive integers – easy 143 kB 2681 September 3, 2019 Multiplying positive integers – medium 166.3 kB 2972 September 3, 2019 Multiplying positive integers – medium-hard 173.1 kB 2496 September 3, 2019 Multiplying positive integers – hard 561.5 kB 1911 September 3, 2019 Multiplying positive integers – very hard 571.8 kB 2124 September 3, 2019 Positive decimals Multiplying positive decimals – very easy 554.5 kB 1753 September 3, 2019 Multiplying positive decimals – easy 555.5 kB 1768 September 3, 2019 Multiplying positive decimals – medium 579.2 kB 1593 September 3, 2019 Multiplying positive decimals – medium-hard 580.2 kB 1437 September 3, 2019 Multiplying positive decimals – hard 569.5 kB 1578 September 3, 2019 Multiplying positive decimals – very hard 567.2 kB 1424 September 3, 2019 Positive fractions Multiplying positive fractions – very hard 567.2 kB 1424 September 3, 2019 Multiplying positive fractions – very easy 172.7 kB 2104 September 3, 2019 Multiplying positive fractions – easy 188.9 kB 1766 September 3, 2019 Multiplying positive fractions – medium 577.2 kB 1601 September 3, 2019 Multiplying positive fractions – medium-hard 591.9 kB 1419 September 3, 2019 Multiplying positive fractions – hard 575.7 kB 1430 September 3, 2019 Multiplying positive fractions – very hard 581 kB 1414 September 3, 2019 Positive mixed numbers Multiplying positive mixed numbers – very easy 176.8 kB 1600 September 3, 2019 Multiplying positive mixed numbers – easy 209.8 kB 1617 September 3, 2019 Multiplying positive mixed numbers – medium 585.6 kB 1441 September 3, 2019 Multiplying positive mixed numbers – medium-hard 592.9 kB 1373 September 3, 2019 Multiplying positive mixed numbers – hard 589.3 kB 1363 September 3, 2019 Multiplying positive mixed numbers – very hard 596.6 kB 1351 September 3, 2019 Positive improper fractions Multiplying positive improper fractions – very easy 166 kB 1405 September 3, 2019 Multiplying positive improper fractions – easy 169.9 kB 1502 September 3, 2019 Multiplying positive improper fractions – medium 571.6 kB 1375 September 3, 2019 Multiplying positive improper fractions – medium-hard 569.5 kB 1353 September 3, 2019 Multiplying positive improper fractions – hard 560.5 kB 1283 September 3, 2019 Multiplying positive improper fractions – very hard 571.8 kB 1351 September 3, 2019 Non positive integers Multiplying integers – very easy 137.9 kB 1958 September 3, 2019 Multiplying integers – easy 143.6 kB 1966 September 3, 2019 Multiplying integers – medium 173.3 kB 1913 September 3, 2019 Multiplying integers – medium-hard 173.5 kB 1805 September 3, 2019 Multiplying integers – hard 565.9 kB 1595 September 3, 2019 Multiplying integers – very hard 568 kB 1494 September 3, 2019 Non positive decimals Multiplying decimals – very easy 186.6 kB 1833 September 3, 2019 Multiplying decimals – easy 187 kB 1952 September 3, 2019 Multiplying decimals – medium 578.8 kB 1451 September 3, 2019 Multiplying decimals – medium-hard 577 kB 1377 September 3, 2019 Multiplying decimals – hard 564.9 kB 1421 September 3, 2019 Multiplying decimals – very hard 567.9 kB 1357 September 3, 2019 Non positive fractions Multiplying fractions – very easy 179.6 kB 1442 September 3, 2019 Multiplying fractions – easy 186.7 kB 1713 September 3, 2019 Multiplying fractions – medium 583.8 kB 1422 September 3, 2019 Multiplying fractions – medium-hard 589 kB 1374 September 3, 2019 Multiplying fractions – hard 588 kB 1292 September 3, 2019 Multiplying fractions – very hard 594.9 kB 1299 September 3, 2019 Non positive mixed numbers Multiplying mixed numbers – very easy 192.9 kB 1339 September 3, 2019 Multiplying mixed numbers – easy 209 kB 1500 September 3, 2019 Multiplying mixed numbers – medium 594.7 kB 1363 September 3, 2019 Multiplying mixed numbers – medium-hard 602.2 kB 1233 September 3, 2019 Multiplying mixed numbers – hard 586.3 kB 1247 September 3, 2019 Multiplying mixed numbers – very hard 591.3 kB 1232 September 3, 2019 Non positive improper fractions Multiplying improper fractions – very easy 171.2 kB 1284 September 3, 2019 Multiplying improper fractions – easy 174 kB 1321 September 3, 2019 Multiplying improper fractions – medium 574.7 kB 1282 September 3, 2019 Multiplying improper fractions – medium-hard 573.9 kB 1209 September 3, 2019 Multiplying improper fractions – hard 570.7 kB 1226 September 3, 2019 Multiplying improper fractions – very hard 577.4 kB 1223 September 3, 2019

## Multiplying worksheets for students

 Worksheet Name File Size Downloads Upload date Positive Multiplying positive integers 496.1 kB 2236 September 3, 2019 Multiplying positive decimals 51.8 kB 1612 September 3, 2019 Multiplying positive fractions 632.1 kB 1422 September 3, 2019 Multiplying positive mixed numbers 637.8 kB 1650 September 3, 2019 Multiplying positive improper fractions 594.6 kB 1253 September 3, 2019 Non positive Multiplying integers 166.8 kB 1650 September 3, 2019 Multiplying decimals 246.3 kB 1498 September 3, 2019 Multiplying fractions 393.1 kB 1469 September 3, 2019 Multiplying mixed numbers 412.4 kB 1395 September 3, 2019 Multiplying improper fractions 334.1 kB 1305 September 3, 2019