Question

What is the fraction $\dfrac{4}{9}$ simplified?

Answer 1

Hint: Now we know that a fraction is simplified when the numerator and denominator has no common factors. Hence we will factorize the numerator and denominator and then cancel the common factors. Hence we will get a simplified fraction.

Complete step by step solution:
First let us understand the concept of fractions. A fraction is a number which represents a part of the whole. To understand this let us take an example. Suppose we had 2 apples and 1 was taken away then we say that 1 out of 2 apples were taken. This is represented numerically as $\dfrac{1}{2}$ . Now here 1 is called the numerator of the fraction and 2 is called the denominator of the fraction. Now let us understand some properties of fraction. The value of fraction does not change when we multiply the numerator and denominator by the same constant. Suppose we have the fraction $\dfrac{2}{3}$ then on multiplying the numerator and denominator by 2 we get the fraction as $\dfrac{4}{6}$ .
Now note that both the fractions are equal, that is $\dfrac{2}{3}=\dfrac{4}{6}$ .
Now hence we can say that the same fraction can be written in infinite forms.
Now let us understand the term simplified fractions. Simplified fractions are fractions such that the numerator and denominator have no common fraction. Hence it cannot be reduced further to simple form.
Now to convert the fractions in simple form we will factorize the numerator and denominator. Then we will cancel common factors. Hence we will get the given fraction in simplest form.
Now the given fraction is $\dfrac{4}{9}$ .
On factoring the numerator and denominator we get, $\dfrac{2\times 2}{3\times 3}$ .
Since there are no common factors we can say the fraction is already in its simplest form.

Note: Now note that the value of fraction changes if we add or subtract the numerator and denominator by the same term. Hence we can only multiply or divide the numerator and denominator while solving them. Also note that the denominator of the fraction can never be 0.