Equivalent Fractions to print

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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...

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®Arturo Ramo García.-Record of intellectual property of Teruel (Spain) No 141, of 29-IX-1999
Plaza Playa de Aro, 3, 1º DO 44002-TERUEL