Fun with Fractions

Fractions:
A part of a whole is called a fraction.
Nickel = 5 cents
Dime = 10 cents
Dollar = 100 cents
All are parts of a dollar. Hence, they can be represented as follows.
Nickel = one twentieth of a dollar (1/20).
Dime = One tenth of a dollar (1/10).
Cent = one hundredth of a dollar (1/100).
We can exchange 2 nickels for a dime. It means that the monetary value of 2 nickels and a dime are equal. When we represent them as fractions, we get
2 nickels = 2 X 1/20 = 2/20
1 Dime = 1/10
Thus 2/20 = 1/10. Even though their numerators and denominators are different.

What is Equivalent Fractions?
Fractions, having same value but with different numerators and denominators are called equivalent fractions.
Example: 1/3 and 3/9
Though the fractions look different, their values are same. If we divide both numerator and denominator of 3/9 by 3, we get the same fraction of 1/3.
Similarly, if we multiply both numerator and denominator of 1/3 by 3, we get 3/9 which is equivalent t0 the other fraction.

Fractions Equivalent
Fractions, which are Equivalent, have two properties.
(1) Fractions will have same value.
(2) The numerator and denominator of one of the fractions will have a common factor.
Example:
1/3 = 1 x 3/3 x 3
The numerator and denominator of 3/9 can be reduced, as both are factors of 3.

Equivalent fractions Definition:
Fractions with different numerators and denominators having same value are called Equivalent fractions.

 Equivalent Fractions:
Let is learn how to find the equivalent fractions. There is a simple method of finding equivalent fractions.  They can be obtained by either dividing or multiplying both numerator and denominator of a fraction by the same number.
Example:
6/8= 6 ? 2/ 8 ? 2 =3/4. Hence, ¾ and 6/8 are equivalent fractions.
6/7 = 6 x 9/ 7 x 9 = 54/63. Hence, 6/7 and 54/63 are equivalent fractions.
Checking for equivalent fractions:
Two fractions are equal if the product of numerator of one fraction with denominator of the other is equal to the product of the other two numbers.
Explanation: Two fractions A/B and C/D are equal if product of a and d is equal to product of b and c.
A / B = C / D if
A x D = B x C.

What is an equivalent fractions?
A fraction that has the same value but with different numerator and denominator is an equivalent fractions.