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 2166 January 1, 1970
Multiplying positive integers – easy 0 B 2179 January 1, 1970
Multiplying positive integers – medium 0 B 2344 January 1, 1970
Multiplying positive integers – medium-hard 0 B 1988 January 1, 1970
Multiplying positive integers – hard 0 B 1551 January 1, 1970
Multiplying positive integers – very hard 0 B 1721 January 1, 1970
Positive decimals
Multiplying positive decimals – very easy 0 B 1409 January 1, 1970
Multiplying positive decimals – easy 0 B 1424 January 1, 1970
Multiplying positive decimals – medium 0 B 1273 January 1, 1970
Multiplying positive decimals – medium-hard 0 B 1146 January 1, 1970
Multiplying positive decimals – hard 0 B 1285 January 1, 1970
Multiplying positive decimals – very hard 0 B 1163 January 1, 1970
Positive fractions
Multiplying positive fractions – very hard 0 B 1163 January 1, 1970
Multiplying positive fractions – very easy 0 B 1706 January 1, 1970
Multiplying positive fractions – easy 0 B 1428 January 1, 1970
Multiplying positive fractions – medium 0 B 1271 January 1, 1970
Multiplying positive fractions – medium-hard 0 B 1162 January 1, 1970
Multiplying positive fractions – hard 0 B 1169 January 1, 1970
Multiplying positive fractions – very hard 0 B 1169 January 1, 1970
Positive mixed numbers
Multiplying positive mixed numbers – very easy 0 B 1283 January 1, 1970
Multiplying positive mixed numbers – easy 0 B 1303 January 1, 1970
Multiplying positive mixed numbers – medium 0 B 1145 January 1, 1970
Multiplying positive mixed numbers – medium-hard 0 B 1117 January 1, 1970
Multiplying positive mixed numbers – hard 0 B 1117 January 1, 1970
Multiplying positive mixed numbers – very hard 0 B 1103 January 1, 1970
Positive improper fractions
Multiplying positive improper fractions – very easy 0 B 1132 January 1, 1970
Multiplying positive improper fractions – easy 0 B 1241 January 1, 1970
Multiplying positive improper fractions – medium 0 B 1119 January 1, 1970
Multiplying positive improper fractions – medium-hard 0 B 1118 January 1, 1970
Multiplying positive improper fractions – hard 0 B 1046 January 1, 1970
Multiplying positive improper fractions – very hard 0 B 1109 January 1, 1970
Non positive integers
Multiplying integers – very easy 0 B 1674 January 1, 1970
Multiplying integers – easy 0 B 1577 January 1, 1970
Multiplying integers – medium 0 B 1548 January 1, 1970
Multiplying integers – medium-hard 0 B 1464 January 1, 1970
Multiplying integers – hard 0 B 1308 January 1, 1970
Multiplying integers – very hard 0 B 1196 January 1, 1970
Non positive decimals
Multiplying decimals – very easy 0 B 1431 January 1, 1970
Multiplying decimals – easy 0 B 1636 January 1, 1970
Multiplying decimals – medium 0 B 1149 January 1, 1970
Multiplying decimals – medium-hard 0 B 1081 January 1, 1970
Multiplying decimals – hard 0 B 1133 January 1, 1970
Multiplying decimals – very hard 0 B 1105 January 1, 1970
Non positive fractions
Multiplying fractions – very easy 0 B 1184 January 1, 1970
Multiplying fractions – easy 0 B 1371 January 1, 1970
Multiplying fractions – medium 0 B 1133 January 1, 1970
Multiplying fractions – medium-hard 0 B 1104 January 1, 1970
Multiplying fractions – hard 0 B 1060 January 1, 1970
Multiplying fractions – very hard 0 B 1072 January 1, 1970
Non positive mixed numbers
Multiplying mixed numbers – very easy 0 B 1088 January 1, 1970
Multiplying mixed numbers – easy 0 B 1243 January 1, 1970
Multiplying mixed numbers – medium 0 B 1125 January 1, 1970
Multiplying mixed numbers – medium-hard 0 B 1022 January 1, 1970
Multiplying mixed numbers – hard 0 B 1039 January 1, 1970
Multiplying mixed numbers – very hard 0 B 1015 January 1, 1970
Non positive improper fractions
Multiplying improper fractions – very easy 0 B 1040 January 1, 1970
Multiplying improper fractions – easy 0 B 1069 January 1, 1970
Multiplying improper fractions – medium 0 B 1053 January 1, 1970
Multiplying improper fractions – medium-hard 0 B 985 January 1, 1970
Multiplying improper fractions – hard 0 B 1026 January 1, 1970
Multiplying improper fractions – very hard 0 B 1020 January 1, 1970

 

Multiplying worksheets for students

Worksheet Name File Size Downloads Upload date
Positive
Multiplying positive integers 0 B 1820 January 1, 1970
Multiplying positive decimals 0 B 1334 January 1, 1970
Multiplying positive fractions 0 B 1178 January 1, 1970
Multiplying positive mixed numbers 0 B 1410 January 1, 1970
Multiplying positive improper fractions 0 B 1053 January 1, 1970
Non positive
Multiplying integers 0 B 1344 January 1, 1970
Multiplying decimals 0 B 1228 January 1, 1970
Multiplying fractions 0 B 1209 January 1, 1970
Multiplying mixed numbers 0 B 1144 January 1, 1970
Multiplying improper fractions 0 B 1098 January 1, 1970


Multiplying knowledge test