Solve Online Equivalent Fractions

Fraction is defined as an equal amount of one whole object. It can be represented as " a / b " where 'a' denotes the value called numerator and 'b' denotes the value called denominator and q not equal to zero.

Equivalent Fractions:

Equivalent fractions are defined as a fraction that have the same value or represent the same part of an object. If a box is cut into two pieces, each piece is also one-half of the boxes.

Example:

It will be recalled that any number divided by itself is 1. For example, l/l, 2/2, 3/3, 4/4, and all other numbers formed in this way, have the value 1. For again, any number is multiplied by 1 then it is equivalent to that number itself. For example, 1 times 2 is 2, 1 times 3 is 3, 1 times l/2 is l/2, etc.

These facts are used in changing the form of a fraction to an equivalent form which is more convenient for use in a particular problem.

For example, if 1 in the form 2/2 is multiplied by 3/4, the product will still have a value of 3/5 but will be in a different form, as follows:

2 / 2 * 3 / 5 = 6 / 8

Since 1/2 equals 2/4, the reverse must also be true; that is 2/4 must be equal to1/2..This can likewise be verified on a ruler. We have already seen that 4/8 is the same as 1/2 12/16 equals 3/4 and 2/8 equals 1/4. We see that dividing both terms of a fraction by the same number does not change the value of the fraction.

Fundamental rule of Fractions:

The fundamental rule of fractions is given as follows:

Multiplying both numerator and denominator by the same number because it does not change the value of the fraction. It is one of the most important steps used in dealing with equaling the fractions.

The fundamental rule is used in the following examples:

1. Change 1/3 to twelfths. This problem is set up as follows:

1 / 3 = ? / 12

The first step is to find how many number of 3’s are contained in 12. The solution is 4, therefore we know that the multiplier for both terms of the fraction is 4, as follows:

4 / 4 * 1 / 3 = 3 / 12

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2. What fraction with a numerator of 6 is equal to 3/4?

6 / ? = 3 / 4

Solution:

We note that 6 contain 3 twice; therefore we need to double the numerator of the right-hand fraction to make it equivalent to the numerator of the fraction we seek. We can multiply both number of 3/4 by 2, obtaining 8 as the denominator of the new fraction, as follows:

6 / 8 = 3 / 4 *2 / 2