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 0 B 2214 January 1, 1970
Multiplying positive integers – easy 0 B 2214 January 1, 1970
Multiplying positive integers – medium 0 B 2407 January 1, 1970
Multiplying positive integers – medium-hard 0 B 2023 January 1, 1970
Multiplying positive integers – hard 0 B 1582 January 1, 1970
Multiplying positive integers – very hard 0 B 1754 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1431 January 1, 1970
Multiplying positive decimals – easy 0 B 1453 January 1, 1970
Multiplying positive decimals – medium 0 B 1302 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1165 January 1, 1970
Multiplying positive decimals – hard 0 B 1307 January 1, 1970
Multiplying positive decimals – very hard 0 B 1183 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1183 January 1, 1970
Multiplying positive fractions – very easy 0 B 1755 January 1, 1970
Multiplying positive fractions – easy 0 B 1470 January 1, 1970
Multiplying positive fractions – medium 0 B 1300 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1185 January 1, 1970
Multiplying positive fractions – hard 0 B 1187 January 1, 1970
Multiplying positive fractions – very hard 0 B 1192 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1316 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1332 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1167 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1135 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1138 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1122 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1157 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1263 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1142 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1134 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1066 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1123 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1700 January 1, 1970
Multiplying integers – easy 0 B 1609 January 1, 1970
Multiplying integers – medium 0 B 1582 January 1, 1970
Multiplying integers – medium-hard 0 B 1489 January 1, 1970
Multiplying integers – hard 0 B 1338 January 1, 1970
Multiplying integers – very hard 0 B 1227 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1479 January 1, 1970
Multiplying decimals – easy 0 B 1666 January 1, 1970
Multiplying decimals – medium 0 B 1172 January 1, 1970
Multiplying decimals – medium-hard 0 B 1105 January 1, 1970
Multiplying decimals – hard 0 B 1148 January 1, 1970
Multiplying decimals – very hard 0 B 1124 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1202 January 1, 1970
Multiplying fractions – easy 0 B 1399 January 1, 1970
Multiplying fractions – medium 0 B 1153 January 1, 1970
Multiplying fractions – medium-hard 0 B 1127 January 1, 1970
Multiplying fractions – hard 0 B 1077 January 1, 1970
Multiplying fractions – very hard 0 B 1090 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1117 January 1, 1970
Multiplying mixed numbers – easy 0 B 1269 January 1, 1970
Multiplying mixed numbers – medium 0 B 1146 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1039 January 1, 1970
Multiplying mixed numbers – hard 0 B 1056 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1034 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1075 January 1, 1970
Multiplying improper fractions – easy 0 B 1103 January 1, 1970
Multiplying improper fractions – medium 0 B 1076 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 1007 January 1, 1970
Multiplying improper fractions – hard 0 B 1039 January 1, 1970
Multiplying improper fractions – very hard 0 B 1035 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 1853 January 1, 1970
Multiplying positive decimals 0 B 1362 January 1, 1970
Multiplying positive fractions 0 B 1202 January 1, 1970
Multiplying positive mixed numbers 0 B 1435 January 1, 1970
Multiplying positive improper fractions 0 B 1068 January 1, 1970
Non positive
Multiplying integers 0 B 1376 January 1, 1970
Multiplying decimals 0 B 1253 January 1, 1970
Multiplying fractions 0 B 1237 January 1, 1970
Multiplying mixed numbers 0 B 1163 January 1, 1970
Multiplying improper fractions 0 B 1118 January 1, 1970


Multiplying knowledge test