How do you add two fractions? I have a fraction I am trying to solve. I know the answer already, as

veneciasp 2022-07-02 Answered
How do you add two fractions?
I have a fraction I am trying to solve. I know the answer already, as Wolfram says it is $\frac{143}{300}$.
The fraction is:

Please explain why and how your method works.
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Answers (2)

Immanuel Glenn
Answered 2022-07-03 Author has 12 answers
Null has given you a good way. Here's a way without worrying about the LCM:
$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$
In the example,
$\frac{5}{12}+\frac{3}{50}=\frac{\left(5\right)\left(50\right)+\left(12\right)\left(3\right)}{\left(12\right)\left(50\right)}=\frac{286}{600}=\frac{143}{300}$
The price of not worrying about the LCM is that you get an answer $286/600$ , that isn't in lowest terms, so you have the extra step at the end of reducing the fraction.
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Rebecca Villa
Answered 2022-07-04 Author has 3 answers
The fractions need to have the same denominator in order to add them together. The denominator must be the least common multiple of the two denominators, or a multiple of it. The least common multiple of 12 and 50 is 300.
First multiply $5/12$ by $25/25$. Since $25/25=1$ the product is the same as the original fraction. You simply multiply the numerators together and the denominators together:
$\frac{5}{12}×\frac{25}{25}=\frac{125}{300}$
Then multiply $3/50$ by $6/6$ . Again, the product is the same as the original fraction:
$\frac{3}{50}×\frac{6}{6}=\frac{18}{300}$
Now both fractions have the same denominator and you can simply add the numerators:
$\frac{125}{300}+\frac{18}{300}=\frac{143}{300}$
Did you like this example?

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