Question

What is the product of \[\dfrac{1}{5},\dfrac{5}{6}\] and \[\dfrac{4}{9}\]?

Answer 1

Hint: Here we have a product of three fractions. Multiplication of fraction is just like the multiplication of two given real numbers. We can apply a simple method for multiplying fractions. That is, the product of fraction is equal to product of numerators divided by product of the denominators.

Complete step by step solution:
We have,
\[\dfrac{1}{5},\dfrac{5}{6}\] and \[\dfrac{4}{9}\].
Suppose if we have a fraction \[\dfrac{a}{b}\], here ‘a’ is called the numerator and ‘b’ is called the denominator.
As we know that we have the product of fractions. We need to multiply the numerator and the denominators.
Then we have,
\[ \Rightarrow \dfrac{{1 \times 5 \times 4}}{{5 \times 6 \times 9}}\]
\[ \Rightarrow \dfrac{{20}}{{270}}\].
This is the required result. We can simplify it further.
Divining by 10
 \[ \Rightarrow \dfrac{2}{{27}}\]. This is the exact form.
\[ \Rightarrow 0.074\]. This is the decimal form.
So, the correct answer is “ 0.074”.

Note: We know that there are different types of fractions.
Proper fraction: In these fraction, the numerator is lesser in value than the denominator. for example \[\dfrac{4}{9}\]. Improper fraction: In these fractions, the numerator is greater than the denominator. for examples \[\dfrac{9}{4}\]. Mixed fraction: A mixed fraction is obtained by adding a non-zero integer and a proper fraction. For example \[2\dfrac{4}{9}\]