Equivalent Fractions 
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1. Equivalent Fractions.
Montse has 6/8 of one chocolate and John has 3/4 of another chocolate. They have the same amount of chocolate.
If we multiply the two digits of the fraction by 2, its value does not change. 3/4 = 3x2/4x2 = 6/8.
We can also say that when we divide the two digits of the fraction by a number, its value is not altered.
Example: 6/8 = 6:2 / 8:2 = 3/4.
Answer these questions:
1/3 is equal to... 

2/5 is equal to... 

4/7 is equal to... 

2/4 is equal to... 
2. Amplified Fractions.
1/2 is equal to 2/4. The blue Parts of the two pictures are the same. The numerator an8xd the denominator of 1/2 are multiplied by 2 (the multiplication sign is the symbol (.) or (x).)
An amplified fraction is obtained by multiplying the numerator and the denominator by the same number, other than zero.
Examples: 1/3 = 1x4/3x4 = 4/12; 2/7 = 2x3/7x3 = 6/21.
Do these exercises:
What are the amplified fraction of 3/4? 

What are the amplified fraction of 1/7 ? 

¿What are the amplified fraction of 2/5 ? 

¿What are the amplified fraction of 5/8 ? 
3. Simplified Fractions.
The fraction 2/5 has been obtained by dividing each term of 6/15 by 3.
6/15 = 6:3 / 15:3 = 2/5.
If we divide the numerator and the denominator of a fraction by the same number, we obtain a simplified fraction.
Examples: 8/12 = 8:2 / 12:2 = 4/6 = 2/3; 3/9 = 3:3 / 9:3 = 1/3.
What is the correct fraction?
What are the simplified fraction of 4/8 ? 

What are the simplified fraction of 6/9 ? 

What are the simplified fraction of 10/18 ? 

What are the simplified fraction of 6/15 ? 
4. Irreducible Fraction.
The Fraction 12/18 has been simplified twice: 12/18 = 6/9 = 2/3. The fraction 2/3 cannot be simplified any further and it is called irreducible fraction.
In general, a fraction a / b is called irreducible when its terms have no any common divisor, except 1.
Simplify it and obtain an irreducible fraction
18/72 is equal to... 

60/90 is equal to... 

36/48 is equal to... 

10/6 is equal to... 
5 Reductions of fractions to a common denominator.
The Fractions 3/6, 4/6 and 8/6 have the same denominators (6). Fractions 4/5, 3/12, 6/22 and 4/15 have different denominators.
We will reduce to a common denominator the next fractions 2/3, 5/6 and 3/4.
We multiply the two digits of the fraction 2/3 by the denominators of the other two (6 and 4).
We multiply the two digits of the fraction 5/6 by the denominators of the other two (3 and 4).
We multiply the two digits of the fraction 3/4 by the denominators of the other two (6 and 3).
These have become: 48/72, 60/72 and 54/72.
To reduce fractions to a common denominator, we multiply the numerator and the denominator of each fraction by the denominators of the others.
Reduce these fractions to a common denominator:
2/3 y 2/5... 

1/4 y 4/9... 

2/5, 1/3 y 1/4... 

3/7 y 5/9... 
 Educational applications

Mathematics 
 In Spanish 
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®Arturo Ramo García.Record of intellectual property of Teruel (Spain)
No 141, of 29IX1999
Plaza Playa de Aro, 3, 1º DO 44002TERUEL