Say that we have two fractions (with different denominators, I assume that's what you're asking about):
$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{5}}}}$$
To add or subtract fractions, the denominators need to be the same. This is called a common denominator.
Basically, the common denominator is when the denominators are the same (i.e. common):
So to make the denominators the same, we need to find the least common denominator. That is, we need to find the least common multiple, the lowest number you can multiply both numbers with. Like this:
The least common denominator for $${\frac{{\mathtt{2}}}{{\mathtt{3}}}}$$ and $${\frac{{\mathtt{4}}}{{\mathtt{5}}}}$$ is then 15.
To change the denominator of a fraction, you multiply the fraction with the needed number to get the denominator to match with (in this case, it's 15 your denominator should be). Let's see:
In fraction 1: To get 3 (the denominator) to 15, you have to multiply by 5. But you have to threw in a $${\frac{{\mathtt{5}}}{{\mathtt{5}}}}$$, so you now multiply both the sides of the fraction. So then: $${\frac{{\mathtt{2}}}{{\mathtt{3}}}}$$ * $${\frac{{\mathtt{5}}}{{\mathtt{5}}}}$$. This makes $${\frac{{\mathtt{10}}}{{\mathtt{15}}}}$$. Taada, you've got it to the common denominator.
In fraction 2: The same drill. To get 5 to 15, you have to multiply by 3. And that automatically goes for the numerator too. $${\frac{{\mathtt{4}}}{{\mathtt{5}}}}$$ * $${\frac{{\mathtt{3}}}{{\mathtt{3}}}}$$ = $${\frac{{\mathtt{12}}}{{\mathtt{15}}}}$$.
Now you can add your fractions normally:
$${\frac{{\mathtt{10}}}{{\mathtt{15}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{12}}}{{\mathtt{15}}}} = {\frac{{\mathtt{22}}}{{\mathtt{15}}}}$$
Say that we have two fractions (with different denominators, I assume that's what you're asking about):
$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{5}}}}$$
To add or subtract fractions, the denominators need to be the same. This is called a common denominator.
Basically, the common denominator is when the denominators are the same (i.e. common):
So to make the denominators the same, we need to find the least common denominator. That is, we need to find the least common multiple, the lowest number you can multiply both numbers with. Like this:
The least common denominator for $${\frac{{\mathtt{2}}}{{\mathtt{3}}}}$$ and $${\frac{{\mathtt{4}}}{{\mathtt{5}}}}$$ is then 15.
To change the denominator of a fraction, you multiply the fraction with the needed number to get the denominator to match with (in this case, it's 15 your denominator should be). Let's see:
In fraction 1: To get 3 (the denominator) to 15, you have to multiply by 5. But you have to threw in a $${\frac{{\mathtt{5}}}{{\mathtt{5}}}}$$, so you now multiply both the sides of the fraction. So then: $${\frac{{\mathtt{2}}}{{\mathtt{3}}}}$$ * $${\frac{{\mathtt{5}}}{{\mathtt{5}}}}$$. This makes $${\frac{{\mathtt{10}}}{{\mathtt{15}}}}$$. Taada, you've got it to the common denominator.
In fraction 2: The same drill. To get 5 to 15, you have to multiply by 3. And that automatically goes for the numerator too. $${\frac{{\mathtt{4}}}{{\mathtt{5}}}}$$ * $${\frac{{\mathtt{3}}}{{\mathtt{3}}}}$$ = $${\frac{{\mathtt{12}}}{{\mathtt{15}}}}$$.
Now you can add your fractions normally:
$${\frac{{\mathtt{10}}}{{\mathtt{15}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{12}}}{{\mathtt{15}}}} = {\frac{{\mathtt{22}}}{{\mathtt{15}}}}$$
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