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1. how to add fractions with different denominators?
2. how to add improper fractions?
3. how to add mixed numbers?

Sagot :

1. In adding fractions with different denominators, you have to take the LCM (Least Common Multiple) of the denominators and then divide that LCM with each denominator and multiply them by the numerator.

[tex] \frac{2}{3}+ \frac{1}{4}= \frac{?}{?}[/tex]

The LCM of 3 and 4 is 12, so we will have:
[tex] \frac{2}{3}+ \frac{1}{4}= \frac{?}{12}[/tex] 

Then we divide 12 by the denominator 3, which gives us 4 (12/3=4), then multiply that answer to 2, which makes it 8 (4*2).
[tex] \frac{2}{3}+ \frac{1}{4}= \frac{8+?}{12}[/tex] 

But we still have to add the other fraction. Do the same with it. Try it!
If you did the correct procedure, you will be able to get the answer [tex]\frac{11}{12}[/tex]

2. Adding improper fractions is just the same with adding our usual fractions, whether they have the same denominator or not.

3. If you are given with a mixed number and another fraction, you have to make the mixed number an improper fraction first.

In order to do that, you just multiply the denominator by the whole number and add the numerator, and the value that you get will be your new numerator.

[tex]5 \frac{3}{4}= \frac{(5*4)+3}{4} = \frac{23}{4} [/tex]

The second case is that if you have two mixed numbers. This is easier.

You just have to add the whole numbers together and then add the fractions and combine them.

[tex]5 \frac{3}{4}+3 \frac{1}{3}=8 \frac{13}{12}=\frac{109}{12}[/tex]

But, you can also do it by making both of them improper fractions then doing the addition. The answer is the same. :) 

Though the problem with that process is that you will get larger values to add and multiply which will take a bit of time. But you have the freedom to choose. 

Hope that helps. Good luck!