Download Operaciones de Números Reales

Sección 1.2
Operaciones con
Números Reales
Copyright © 2013, 2010, 2006, 2003 Pearson Education, Inc.
La Recta Numérica
A number line is a line on which each point is associated
with a number.
–5 –4 –3 –2 –1
– 4.8
Negative Numbers
0
1
2
3
4
1.5
Positive Numbers
5
La Recta Numérica (cont)
Smaller numbers are on the left.
– 5 – 4– 3 – 2 – 1
–4<–1
“less
than”
0
1
2
3
4
5
2>–1
“greater
than”
Valor Absoluto
The absolute value of a number is the distance between
that number and zero on a number line.
| – 4| = 4
Símbolo
para valor
absoluto
|5| = 5
Distancia de 4 Distancia de 5
–5 –4 –3 –2 –1
0
1
2
3
4
5
Definición del Valor Absoluto
Absolute value of x:
 x, if x  0
x 
  x, if x  0
Example
Evaluate.
a. |2| = 2
b. |10| = 10
c. |0| = 0
d. |8 – 4| = |4| = 4
Regla 1.1
To add two real numbers with the same sign, add their
absolute values. The sum takes the common sign.
Ejemplo
Add (–3) + (–11).
3 + 11 = 14
Suma los valores absoluto
de 3 y 11.
(–3) + (–11) = –14
Se usa el signo negativo
porque sumamos dos
números negativos.
Ejemplo
Suma  1    1 
2  3
1  1
       3    2    5
2  3
6  6
6
Regla 1.2
To add to real numbers with different signs, find the
difference between their absolute values. The answer
takes the sign of the number with the larger absolute
value.
Ejemplo
Suma: 5 + (–9).
5 – 9 = –4
Subtract the absolute values of the
numbers 5 and 9.
A negative sign is used because the sign of the
larger number is negative.
Example
Add (–24) + (38).
38 – 24 = 14
Subtract the absolute values of the
numbers 24 and 38.
The answer is positive because the sign of
the larger number is positive.
Example
Add.
a. 2.8 + (–1.3) = 1.5
2  3
8  15 
b.       
 
5  4
20  20 
23
3

or  1
20
20
Example
Add (–56) + 6 + (–14).
Because addition is commutative, the numbers can be
added in any way.
(–56) + 6 + (–14)
– 50 + (–14)
– 64
or
(–56) + (–14) + 6
– 70
+6
– 64
Números Opuestos
Opposite numbers (or additive inverses) have the
same magnitude but different signs.
The opposite of 4 is – 4.
–5 –4 –3 –2 –1
0
1
2
4 + (–4) = 0
3
4
5
The sum of a number and
its opposite is zero.
Regla 1.3
To subtract b from a, add the opposite (additive inverse)
of b to a. Thus, a – b = a + (–b).
Ejemplo
6 – (–14).
Resta:
The opposite of 14 is 14.
6
–
(–14)
=6
+
(+14)
Change the subtraction to addition.
=
20
Perform the addition of the two
positive numbers.
Ejemplo
Resta
=
–6 – 14.
The opposite of 14 is 14.
–6
–
(14)
–6
+
(–14)
Change the subtraction to addition.
=
–20
Perform the addition of the two
negative numbers.
Ejemplo
Resta.
5 1

11 5
5 1 5  1
   
11 5 11  5 
Subtraction changed to
addition.
5 5
1 11
       
11 5   5 11
The LCD is 55.
25  11 

 
55  55 
Multiply the fractions.

14
55
Add the fractions.
Ejemplo
Resta:
–21 – (–13)
The opposite of –13 is 13.
–21 + (13)
Change the subtraction to
addition.
= –8
Perform the addition.
Ejemplo
Subtract.
a.  8  2  8  (2)  10
b. 23  28  23  (28)  5
c. 5  ( 3)  5  3  8
Regla 1.4
When you multiply or divide two real numbers with
different signs, the answer is a negative number.
Ejemplo
Evaluar.
a. –6(4) = –24
When multiplying two numbers
with different signs, the result is a
negative number.
b. 12(–9) = –108
Ejemplo
Evaluar.
a. –6 ÷ 2 = –3
When dividing two numbers with
different signs, the result is a
negative number.
b. 120 ÷ (–10) = –12
Ejemplo
Evaluar.
12 2


5 3
6
12 2  12  3 

     
5 3  5  2 1
18
3

or  3
5
5
Regla 1.5
When you multiply or divide two real numbers with like
signs, the answer is a positive number.
Ejemplo
Evaluar.
a. –75 × (–3) = 225
When multiplying two numbers
with the same sign, the result is a
positive number.
1
b.
  5   2     5   2   5
 12  3 
 12   3  18

 
 6  
Ejemplo
Evaluar.
a. –75 ÷ (–3) = 25
When dividing two numbers with
the same sign, the result is a
positive number.
1
b.
 5    3    5   2   5
 12   2   12   3  18

    6  
Orden de Operaciones Numéricas
If addition, subtraction, multiplication, and division are
written horizontally, do the operations in the following
order.
1. Do all multiplications and division from left to right.
2. Do all additions and subtractions from left to right.
Ejemplo
Evaluar.
24  2  4  2
24  2  4  2  12  4  2
 12  8
4
Ejemplo
Evaluar. 20  (4)  3  2  6  5
20  (4) 3  2  6  5  5  3  2  6  5
 15  2  6  5
 15  2  30
 13  30
 17
Ejemplo
Evaluar.
13  ( 3)
5( 2)  6( 3)
13  ( 3)
13  3

5( 2)  6( 3)
10  18
16

8
2
Ejemplo
3


Evaluar. 4 
3
1
5 
    
4
3
 4
1
5

4 
3
3
1
3
   
4
5
 4
3
3


 

4
 20 
15
3


 

20
 20 
15
3


20
20
18
9


20
10
To perform the division,
invert and multiply the
second fraction.
Multiply.
The LCD of the
fractions is 20.
Change the subtraction
to addition.
Add and simplify.