# Integer operations

Integer operations involve addition, subtraction, multiplication, and division between positive and negative numbers. Beads with whole numbers have specific sign rules.

The set of integers Z is negative and positive infinity, in addition to including zero, advancing from one to one.

A number is negative when there is a minus sign (-) in front of it. If there is no sign it means the number is positive.

## Addition and subtraction of whole numbers

To add or subtract whole numbers, you need to pay attention to their signs. If they are all positive, we add or subtract normally, like natural numbers.

When adding positive integers, we add their values ​​and the result will always be positive.

If all numbers are negative, we add their values ​​together and the result is always negative.

Note that we use parentheses in the second number so that the plus sign is not glued to the negative. It's just to organize and not have two signs together.

In this case, the plus sign can be omitted, like this:

To add a positive and a negative number, what we do in practice is subtract their values, the sign of the greater number prevailing.

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In the sum of 3 + (- 4) the signs are different, so we subtract their values:

When the highest value number is negative, the answer is also negative, like this:

### Sign rule for addition and subtraction

when are equal signs, the values ​​are added and the sign is repeated.

when are different signs, the values ​​are subtracted and the greater sign is used.

## Multiplication and division of whole numbers

To multiply or divide integers, operations must be performed normally, considering only their values.

The final value will be positive or negative depending only on whether they are the same or different. When multiplying or dividing integers of the same sign, the result will always be positive.

In cases of multiplying or dividing numbers with different signs, the result will always be negative.

### Sign rule for multiplication and division

when are equal signs, the result is always positive.

Which is to say that in multiplication and division "less with less is more".

when are different signs, the result is always negative.

Which is to say that in multiplication and division "more with less is less".

## Signs before parentheses

In the case of signs before expressions in parentheses we follow the rules:

Plus sign (+) before parentheses: the signs of the terms are kept the same.

Negative sign (-) before parentheses: signs are switched.

## Exercises for operations with solved integers

### Exercise 1

Solve additions and subtractions between whole numbers.

a) 55 + 23 =
b) -37 + 15 =
c) -157 -74 =
d) 86 - 102 =

a) 55 + 23 = 78
b) -37 + 15 = -22
c) -157 -74 = -231
d) 86 - 102 = -16

### Exercise 2

Solve multiplications and divisions between whole numbers.

a) 5. 23 =
b) -12. (-6) =
c) -10. 5 =
d) 56. (-4) =

a) 5. 23 = 115
b) -12. (-6) = 72
c) -10. 5 = -50
d) 56. (-4) = -224

### Exercise 3

Solve the numeric expression .

To solve the expression, we can use two modes:

1st way: solve the operations in parentheses and change the sign of the remaining term, as there is a negative sign before it.

2nd way: first change the signs of the terms in parentheses, as there is a negative sign before. Then perform the operations.

practice more integer exercises.

See too:

• Rational Numbers
• real numbers
• Natural Numbers
• irrational numbers
• Decimal numbers
• Numbers: what they are, history and sets
• History of numbers: origin and evolution of numbers
• Prime numbers
• Numerical sets
• Decimal Numbering System
• Numerical Sets Exercises
• Numerical Expressions
• 23 math exercises 7th grade
• 27 Basic Math exercises
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