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.

Z equals left brace minus infinity comma space... space comma space minus 4 comma space minus 3 comma space minus 2 comma space minus 1 comma space 0 comma space 1 comma space 2 comma space 3 comma space 4 comma space... space comma infinite space right brace

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.

marks space 3 space plus space 4 space equals space 7 space marks space 15 space plus space 3 space equals space 18 space marks space 258 space plus space 12 space equals space 270

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

minus 3 space plus space left parenthesis minus 4 right parenthesis space equals space minus 7 space marks space minus 15 space plus space left parenthesis minus 3 right parenthesis space equals space minus 18 space marks space minus 258 space plus space left parenthesis minus 12 right parenthesis space equals space minus 270

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:

minus 3 space plus space left parenthesis minus 4 right parenthesis space equals space minus 3 space minus 4 space equals space minus 7

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:

4 space minus space 3 space equals space 1

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

3 space plus space left parenthesis minus 4 right parenthesis space equals space minus 1

Sign rule for addition and subtraction

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

mark space 9 space plus space 7 space equals space 16 space mark space minus 9 space more space left parenthesis minus 7 right parenthesis space equals space minus 9 space minus space 7 space equals space minus 16

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

mark space 9 space minus space 7 space equals space 2 space left parenthesis positive comma space because straight space the space nine straight space is greater space square space and positive space parenthesis right. space marks space minus 9 space plus space 7 space equals minus 2 space negative left parenthesis comma space because straight space the space nine square space is greater space square space and negative space parentheses right.

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.

space mark 3 space multiplication sign space 2 space equals space 6 mark space minus 3 space multiplication sign space left parenthesis minus 2 right parenthesis space equals 6 marks space 10 space divided by space 2 space equals space 5 marks space minus 10 space divided by space left parenthesis minus 2 right parenthesis space equals space 5

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

minus 3 space multiplication sign space 2 equals space minus 6 marks space 10 space divided by space left parenthesis minus 2 right parenthesis equals minus 5

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".

learn more about whole numbers.

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.

mark space 2 space plus space left parenthesis minus 4 space plus space 3 right parenthesis space equal to space 2 space minus 4 space plus space 3 space
mark space 2 space plus space left parenthesis minus 1 right parenthesis space equals space 2 space minus space 1

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

mark space 2 space minus space left parenthesis minus 4 space plus space 3 space right parenthesis space equal to space 2 space plus space 4 space less space 3 space
mark space 2 space minus space left parenthesis minus 1 right parenthesis space equals space 2 space plus space 1

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 45 space plus space 23 space less space left parenthesis minus 17 space more space 9 space minus 12 right parenthesis space plus space 3.

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.

45 space plus space 23 space less space left parenthesis minus 17 space plus space 9 space minus 12 right parenthesis space plus space 3 equals 45 space plus space 23 space less space left parenthesis minus 8 space minus 12 right parenthesis space plus space 3 equals 45 space plus space 23 space minus space left parenthesis minus 20 right parenthesis space plus space 3 equals 45 space plus space 23 space plus space 20 space plus space 3 equals 91

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

45 space plus space 23 space less space left parenthesis minus 17 space plus space 9 space minus 12 right parenthesis space plus space 3 equals 45 space plus space 23 space plus space 17 space less space 9 space plus 12 space plus space 3 equals 85 space minus space 9 space plus space 12 space plus space 3 space equals 76 space plus space 12 space plus space 3 equal space to 91

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
  • 6th grade math exercises
  • 27 Basic Math exercises
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