Question

How do you simplify $ \dfrac{4}{5} + \dfrac{2}{9} $ ?

Answer 1

Hint: First we take the given simplify $ \dfrac{4}{5} + \dfrac{2}{9} $ . We know that the LCM (Lowest Common Multiple). One way to find the least common multiple is,
List the multiples of the given numbers.
Find the multiples common to the given numbers.
Select the smallest common multiple.
After that we add the numerator, and then we get the numerator value.
Finally we get the improper fraction. We convert the improper fraction to the mixed numbers.

Complete step by step answer:
The given simplify is $ \dfrac{4}{5} + \dfrac{2}{9} $
We know that the LCM (Lowest Common Multiple).
The LCM (Lowest Common Multiple) of $ 5 $ and $ 9 $ is $ 45 $ , hence we get
$ \Rightarrow \dfrac{4}{5} + \dfrac{2}{9} = \dfrac{{(4 \times 9) + (2 \times 5)}}{{45}} $
Now we multiply the first term $ 4 $ by $ 9 $ and the second term $ 2 $ by $ 5 $ in the numerator, hence we get
$ = \dfrac{{36 + 10}}{{45}} $
Add the numerator, hence we get
$ = \dfrac{{46}}{{45}} $
$ \Rightarrow \dfrac{4}{5} + \dfrac{2}{9} = \dfrac{{46}}{{45}} $

The solution gets the improper fraction. The improper fraction is $ \dfrac{{46}}{{45}} $

Note: We convert improper fraction to mixed number.
Let us consider $ \dfrac{{46}}{{45}} $ is improper fraction
Here we will show you how to convert the improper fraction $ \dfrac{{46}}{{45}} $ to a mixed number. We start by setting up the fraction below.
$ \dfrac{{46}}{{45}} $
Step $ 1 $ : Calculate out how many times the denominator goes into the numerator. To do that, divide $ 46 $ by $ 45 $ and keep only what is to the left of the decimal point:
$ \Rightarrow \dfrac{{46}}{{45}} = 1.022 $
$ \Rightarrow x = 1 $
Step $ 2 $ - Find New Numerator
Multiply the answer from step $ 1 $ by the denominator and deduct that from the original numerator.
$ 46 - (45 \times 1) = 1 $
Step $ 3 $ - Get solution
Keep the original denominator and use the answers from step $ 1 $ and step $ 2 $ to get the answer. $ \dfrac{{46}}{{45}} $ as a mixed number is:
$ 1\dfrac{1}{{45}} $