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Equivalent rational number:

If we multiply the rational number (say \(a / b\) ) by a certain non-zero integer (say \(c\)), on both numerator and denominator, the product is equal to the same rational number.

Example:

Let us assume \(a / b\) is a rational number, $\frac{a}{b}$ \(=\) $\frac{1}{2}$.

Multiply $\frac{1}{2}$ by the non zero integer \(2\) on numerator and denominator.

We get $\frac{1}{2}=\frac{1\times 2}{2\times 2}=\frac{2}{4}$

Therefore, $\frac{1}{2}$ \(=\) $\frac{2}{4}$

Here, $\frac{1}{2}$ and $\frac{2}{4}$ are

**equivalent rational numbers.****Using this method, we can make an equivalent rational number.**

Standard form of rational number:

In the above example, we obtain the equivalent rational number by multiplying the rational number by certain non zero integer.

Similarly,

To obtain the standard form of (simplified form) rational number, the rational number should be divided by the common factor other than \(1\).

That is, consider a rational number $\frac{a}{b}$, the only common factor of \(a\) and \(b\) is \(1\) and \(b\) is positive, and then the rational number is said to be in standard form.

Example:

**Reduce the following to the standard form:**

**1)**$\frac{10}{8}$

The given numerator and denominator have the same common factor of 2.

Therefore let us divide the rational number by the common factor 2.

$\frac{10}{8}=\frac{10\xf7(2)}{8\xf7(2)}=\frac{5}{4}$

**Therefore the standard form of**$\frac{10}{8}$

**is**$\frac{5}{4}$.

**2)**$\frac{-15}{24}$

The given numerator and denominator have the same common factor of 3.

Therefore let us divide the rational number by the common factor 3.

$\frac{-15}{24}=\frac{-15\xf7(3)}{24\xf7(3)}=\frac{-5}{8}$

**Therefore the standard form of**$\frac{-15}{24}$

**is**$\frac{-5}{8}$.

**Applying the above method, we reduce the rational numbers to the standard form.**