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Matemática GeneralProf. Egberto Hernández
E-mail: [email protected]
Website: www.profehernandez.weebly.com
Cel: 787-240-9446
Fracciones
• Fracciones Propias
• Fracciones Impropias
• Fracciones Aparentes
Fracciones Propias
• Son aquellas donde el numerador es menor que el denominador
• Ejemplo:
–1/2
–7/8
–3/16
Fracciones Impropias
• son aquellas donde el numerador es mayor que el denominador
• Ejemplo:
–4/2
–8/7
–16/4
Fracciones Aparentes
• Son aquellas donde el numerador es igual a l denominador
• Ejemplo:
–2/2
–8/8
–16/16
Numeros MixtosMatematica General
Números Mixtos
Escritura de números mixtos como fracciones impropias
Escritura de fracciones impropiascomo números mixtos
Graficación de fracciones y números mixtos
Multiplicación y División de Números Mixtos
Multiplicación y División de Números Mixtos
Números Mixtos
SUMA Y RESTA DE NÚMEROS MIXTOS
Suma de Números Mixtos
Suma de Números Mixtos
Resta de Números Mixtos
Resta de Números Mixtos
Números Mixtos
ORDEN DE OPERACIONES
Orden de Operaciones
Fracciones Propias
• Son aquellas donde el numerador es menor que el denominador
• Ejemplo:
–1/2
–7/8
–3/16
Fracciones Impropias
• son aquellas donde el numerador es mayor que el denominador
• Ejemplo:
–4/2
–8/7
–16/4
Fracciones Aparentes
• Son aquellas donde el numerador es igual al denominador
• Ejemplo:
–2/2
–8/8
–16/16
• Julianna hizo 20 chocolates y quiere guardarlos en envases que contengan la misma cantidad.
– De cuantas formas distintas puede guardar los chocolates?
• Pilar desea hacer una receta de una bebida para una fiesta. Para la receta, se necesita ¼ taza de azucar y ella tiene 2 tazas.
– Cuantas veces puede hacer la receta de la bebida, si utiliza todo el azucar que tiene?
• Un ciclista debe recorrer 105 km. El primer dia recorre 1/3 del camino y el segundo dia 2/5 dejando el resto para el tercer dia.
– Cuantos kilometros recorre cada dia?
• Luis tiene una colección de 96 postales. Los 3/8 son de paisajes, los 5/12 de monumentos y el resto de barcos.
Ejercicios Practica
• Repaso
– Fracciones
– Cap #3
• ej. 48
Decimales
• Existen tres tipos de números decimales
–Números decimales exactos
–Números decimales periódicos• Periódico puro
• Periódico mixto
–Números decimales no exactos y no periódicos
Decimales
• Existen tres tipos de números decimales
–Números decimales exactos
•Tienen un numero limitado de cifras decimales
Decimales
• Existen tres tipos de números decimales
–Números decimales periódicos• Tienen un numero ilimitados de
decimales
• Periódico puro – la cifra se repiten a partir del punto
• Periódico mixto – la cifra no se repite a partir del punto
Decimales
• Existen tres tipos de números decimales
–Números decimales no exactos y no periódicos
• Tienen un numero ilimitado de cifras decimales no periódicas
Suma o Resta
• Colocamos los números, de forma que lospuntos decimales estén en la misma columnay se añaden los ceros necesarios para quetodos tengan el mismo numero de decimales.
• Sumamos o restamos como si fueran númerosnaturales, manteniendo el punto en su lugarcorrespondiente.
Suma o Resta
• Ejercicios
Multiplicando
• Para Multiplicar un numero decimal por launidad seguida de ceros desplazamos el puntohacia la derecha tantos lugares como cerostenga la unidad.
Math FlashFractions I
By Monica Yuskaitis
Parts of a Fraction
3
4
= the number of parts
= the total number of
parts that equal a
whole
Parts of a Fraction
3
4
= numerator
= denominator
Which number is circled?
3
4 = denominator
Which number is circled?
3
4
= numerator
¾ looks like
1/43
4 1/4
1/4
¾ looks like
1/4
3
4 1/4
1/4
¾ looks like
3
4
1/4
1/4
1/4
What fraction of the balls are purple?
3
4
What fraction of the balls are purple?
1
4
What fraction of the balls are purple?
1
6
What fraction of the balls are purple?
4
6
What fraction of the rectangle is purple?
4
6
What fraction of the rectangle is purple?
2
6
What fraction of the pie is purple?
4
4
What fraction of the pie is purple?
3
4
What fraction of the musical instruments have strings?
2
5
What fraction of the arrowshit the bullseye?
1
3
What fraction of the pins areknocked down?
3
10
Credits
Clipart from “Clip Art 125,000”
by T/Maker a subsidiary of
Broderbund
Math FlashFractions II
By Monica Yuskaitis
How many halves are in a whole?
21/2 1/2
How many quarters are in a whole?
41/4 1/4
1/4 1/4
How many eighths are in a whole?
8
1/8 1/8
1/8 1/8
1/8 1/8
1/8 1/8
How many eighths are in a quarter?
21/4
1/8
1/8
How many eighths are in a half?
41/2
1/8 1/8
1/8 1/8
How many quarters are in a half?
21/4
1/41/2
How many thirds are in a whole?
31/3
1/3 1/3
How many sixths are in a whole?
61/6
1/6 1/6
1/6 1/6
1/6
How many sixths are in a third?
21/6
1/6
1/3
How many sixths are in a half?
31/6
1/21/6
1/6
How many fifths are in a whole?
51/5 1/5
1/5 1/5
1/5
How many tenths are in a whole?
101/10 1/10
1/10
1/10
1/10
1/10
1/10
1/10 1/10
1/10
How many tenths are in a fifth?
21/5
1/10
1/10
How many tenths are in a half?
51/10
1/10
1/10
1/10
1/10 1/2
Fractions VISimplifying Fractions
By Monica Yuskaitis
Factor
• A number that divides evenly into another.
Factors of 24 are 1,2, 3, 4, 6, 8, 12 and 24.
What are the factors of 9?
Factors of 9 are 1, 3 and 9.
What are the factors of 10?
Factors of 10 are 1, 5 and 10.
What are the factors of 7?
Factors of 7 are 1 and 7.
What are the factors of 56?
Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
Common Factor
When two numbers have the same factor it is called a common factor.
A common factor of 12 and 6 is 3.
Name a Common Factor of 9 and 27?
1, 3, 9
Name a Common Factor of 4 and 8?
1, 2, 4
Name a Common Factor of 4 and 8?
1, 2, 4
Name a Common Factor of 15 and 30?
1, 3, 5, 15
Name a Common Factor of 12 and 48?
1, 2, 3, 4, 6, 12
Name a Common Factor of 9 and 21?
1, 3, 9,
Name a Common Factor of 10 and 25?
1, 5, 10
Name a Common Factor of 3 and 4?
1
Simplest Form
• When the only common factor of the numerator and denominator is 1, the fraction is in simplest form.
34
34÷
11 =
Greatest Common Factor
• The greatest common factor is the largest factor between two numbers.
12 = 1, 2, 3, 4, 6, 12
18 = 1, 2, 3, 6, 9, 18
What is the Greatest Common Factor?
8 = 1, 2, 4, 8
12 = 1, 2, 3, 4, 6, 12
What is the Greatest Common Factor?
8 = 1, 2, 4, 8
14 = 1, 2, 7,14
What is the Greatest Common Factor?
6 = 1, 2, 3, 6
18 = 1, 2, 3, 6, 9, 15
What is the Greatest Common Factor?
6 = 1, 2, 3, 6
12 = 1, 2, 3, 4, 6, 12
What is the Greatest Common Factor?
8 = 1, 2, 4, 8
16 = 1, 2, 4, 8, 16
What is the Greatest Common Factor?
8 = 1, 2, 4, 8
10 = 1, 2, 5, 10
What is the Greatest Common Factor?
3 = 1, 3
6 = 1, 2, 3, 6
What is the Greatest Common Factor?
4 = 1, 2, 4
6 = 1, 2, 3, 6
What is the Greatest Common Factor?
7 = 1, 7,
21 = 1, 3, 7, 21
What is the Greatest Common Factor?
15 = 1, 3, 5, 15
24 = 1, 2, 3, 8, 12, 24
How to Find the Simplest Form of a Fraction
• Find the greatest common factor of the numerator and the denominator and divide both the numerator and the denominator by that number.
1218
23÷
66 =
Simplify or Reduce This Fraction
1218
23
÷66
=
Simplify or Reduce This Fraction
921
37
÷33
=
Simplify or Reduce This Fraction
1220
35
÷44
=
Simplify or Reduce This Fraction
1015
23
÷55
=
Simplify or Reduce This Fraction
1016
58
÷22
=
Simplify or Reduce This Fraction
1216
34
÷44
=
Simplify or Reduce This Fraction
312
14
÷33
=
Simplify or Reduce This Fraction
28
14
÷22
=
Simplify or Reduce This Fraction
24
12
÷22
=
Simplify or Reduce This Fraction
69
23
÷33
=
Simplify or Reduce This Fraction
68
34
÷22
=