# Addition and Subtraction

Addition and subtraction are the simplest and most basic mathematical operations. Addition combines two or several quantities into a larger quantity (Adding – sign: +), while during subtraction, a number of objects is subtracted from a different number of objects (Subtracting – sign: -). Subtraction is the inverse operation of addition. It has two important property: commutativity and associativity. Commutativity means that the order of elements does not influence the result – you can switch places of the objects you want add and the result will be the same. Associativity means that the order in which you perform adding (when you are trying to add more than two numbers) is not important. For example:

a + (b + c) = (a + b) + c

Another important thing to remember is that adding zero to any other number does not change that number. Five + zero is always five and that is true for all other numbers when zero is added to them.

As for subtraction, it does not share the same properties as addition. When you subtract, the order of elements is very important. As you already know well, five minus three is not the same as three minus five. Zero is neutral in this operation as well – if zero is subtracted from any other number, that number does not change.

## Addition and subtraction exams for teachers

 Exam Name File Size Downloads Upload date Addition Positive integers Addition of positive integers – very easy 123.2 kB 4936 October 13, 2012 Addition of positive integers – easy 143.6 kB 2642 October 13, 2012 Addition of positive integers – medium 163.9 kB 3218 October 13, 2012 Addition of positive integers – hard 210.4 kB 3254 October 13, 2012 Positive decimals Addition of positive decimals – very easy 175.7 kB 1678 October 13, 2012 Addition of positive decimals – easy 186.3 kB 1620 October 13, 2012 Addition of positive decimals – medium 215.5 kB 1488 October 13, 2012 Addition of positive decimals – hard 222.4 kB 1463 October 13, 2012 Positive fractions Addition of positive fractions – very easy 186.4 kB 1753 October 13, 2012 Addition of positive fractions – easy 201.4 kB 1543 October 13, 2012 Addition of positive fractions – medium 596.3 kB 1484 October 13, 2012 Addition of positive fractions – medium-hard 613.2 kB 1286 October 13, 2012 Addition of positive fractions – hard 607.6 kB 1202 October 13, 2012 Addition of positive fractions – very hard 627.4 kB 1278 October 13, 2012 Positive mixed numbers Addition of positive mixed numbers – easy 195.1 kB 1573 October 13, 2012 Addition of positive mixed numbers – medium 606.2 kB 1287 October 13, 2012 Addition of positive mixed numbers – hard 628.6 kB 1376 October 13, 2012 Positive improper fractions Addition of positive improper fractions – very easy 176.8 kB 1148 October 13, 2012 Addition of positive improper fractions – easy 186.2 kB 1361 October 13, 2012 Addition of positive improper fractions – medium 589.7 kB 1073 October 13, 2012 Addition of positive improper fractions – medium-hard 597 kB 981 October 13, 2012 Addition of positive improper fractions – hard 576.2 kB 1111 October 13, 2012 Addition of positive improper fractions – very hard 587.1 kB 1126 October 13, 2012 Non positive integers Addition of integers – very easy 152.8 kB 1749 October 13, 2012 Addition of integers – easy 164.4 kB 1793 October 13, 2012 Addition of integers – medium 186.2 kB 1898 October 13, 2012 Addition of integers – medium-hard 199.4 kB 1472 October 13, 2012 Addition of integers – hard 587.8 kB 1382 October 13, 2012 Addition of integers – very hard 593.2 kB 1485 October 13, 2012 Non positive decimals Addition of decimals – very easy 198.1 kB 1139 October 13, 2012 Addition of decimals – easy 209.6 kB 1154 October 13, 2012 Addition of decimals – medium 234.1 kB 1104 October 13, 2012 Addition of decimals – medium-hard 593.2 kB 1134 October 13, 2012 Addition of decimals – hard 606.1 kB 1043 October 13, 2012 Addition of decimals – very hard 613.3 kB 1105 October 13, 2012 Non positive fractions Addition of fractions – very easy 587.5 kB 1192 October 13, 2012 Addition of fractions – easy 592.5 kB 1252 October 13, 2012 Addition of fractions – medium 617.8 kB 1221 October 13, 2012 Addition of fractions – medium-hard 634.7 kB 1141 October 13, 2012 Addition of fractions – hard 619.7 kB 1117 October 13, 2012 Addition of fractions – very hard 589.2 kB 1030 October 13, 2012 Non positive improper fractions Addition of improper fractions – very easy 225.6 kB 1133 October 13, 2012 Addition of improper fractions – easy 234.2 kB 1397 October 13, 2012 Addition of improper fractions – medium 601.8 kB 1120 October 13, 2012 Addition of improper fractions – medium-hard 619.2 kB 1074 October 13, 2012 Addition of improper fractions – hard 612 kB 1076 October 13, 2012 Addition of improper fractions – very hard 620.6 kB 1070 October 13, 2012 Addition and subtraction Integers Addition and subtraction of integers – very easy 152.3 kB 2041 October 13, 2012 Addition and subtraction of integers – easy 164.7 kB 2055 October 13, 2012 Addition and subtraction of integers – medium 185.9 kB 2190 October 13, 2012 Addition and subtraction of integers – medium-hard 193.7 kB 1513 October 13, 2012 Addition and subtraction of integers – hard 587.1 kB 1401 October 13, 2012 Addition and subtraction of integers – very hard 595.1 kB 1427 October 13, 2012 Decimals Addition and subtraction of decimals – very easy 196.1 kB 1177 October 13, 2012 Addition and subtraction of decimals – easy 203.6 kB 1241 October 13, 2012 Addition and subtraction of decimals – medium 229 kB 1209 October 13, 2012 Addition and subtraction of decimals – medium-hard 236 kB 1138 October 13, 2012 Addition and subtraction of decimals – hard 589.7 kB 1210 October 13, 2012 Addition and subtraction of decimals – very hard 589.7 kB 1145 October 13, 2012 Fractions Addition and subtraction of fractions – very easy 231.7 kB 1426 October 13, 2012 Addition and subtraction of fractions – easy 12.0 kB 1609 June 11, 2011 Addition and subtraction of fractions – medium 617.3 kB 1232 October 13, 2012 Addition and subtraction of fractions – medium-hard 633.6 kB 1118 October 13, 2012 Addition and subtraction of fractions – hard 631.9 kB 1103 October 13, 2012 Addition and subtraction of fractions – very hard 593.1 kB 1120 October 13, 2012 Mixed numbers Addition and subtraction of mixed numbers – easy 656.2 kB 1292 October 13, 2012 Addition and subtraction of mixed numbers – medium 632.6 kB 1140 October 13, 2012 Addition and subtraction of mixed numbers – hard 21.4 kB 1129 June 11, 2011 Improper fractions Addition and subtraction of improper fractions – very easy 218.5 kB 1107 October 13, 2012 Addition and subtraction of improper fractions – easy 11.2 kB 1280 June 11, 2011 Addition and subtraction of improper fractions – medium 601.8 kB 1063 October 13, 2012 Addition and subtraction of improper fractions – medium-hard 622.7 kB 969 October 13, 2012 Addition and subtraction of improper fractions – hard 624.2 kB 1002 October 13, 2012 Addition and subtraction of improper fractions – very hard 632.4 kB 1070 October 13, 2012

## Addition and subtraction worksheets for students

Students can practice learned by solving this worksheets:

 Worksheet Name File Size Downloads Upload date Addition and subtraction integers 557.5 kB 2547 October 14, 2012 Addition and subtraction decimals 566.1 kB 1548 October 14, 2012 Addition and subtraction fractions 660 kB 1604 October 14, 2012 Addition and subtraction mixed numbers 706.4 kB 1285 October 14, 2012 Addition and subtraction improper fractions 655.2 kB 1333 October 14, 2012