# Fraction Addition

#### toponlinetool

##### New member
Can anyone please provide answer- 2/5 + 3/8 =?

#### Narwalalpaca12\$

##### Junior Member
Well first you need to find the common denominator of both numbers. The common denominator is the least common multiple the denominator (the number at the bottom) of both numbers have. Once you’ve figured that out, you multiply the top numbers of what you multiplied the bottom

#### HallsofIvy

##### Elite Member
Though it may not be the least common denominator, you can always get a common denominator by multiplying the two denominator, here 8 and 5, together.

#### Mr. Bland

##### Junior Member
Observe that $$\displaystyle \frac{x}{x} = 1$$ for any fraction where $$\displaystyle x \ne 0$$. Also note that when multiplying some number by 1, the result will be the same number you started with. You can use this fact to change the denominator in a fraction:

$$\displaystyle \frac{2}{5} = \frac{2}{5} * 1$$

$$\displaystyle \frac{2}{5} = \frac{2}{5} * \frac{8}{8}$$

$$\displaystyle \frac{2}{5} = \frac{16}{40}$$

$$\displaystyle \frac{3}{8} = \frac{3}{8} * \frac{5}{5} = \frac{15}{40}$$​

The fractions $$\displaystyle \frac{8}{8}$$ and $$\displaystyle \frac{5}{5}$$ were chosen because they were formed from the denominators of the "other" fraction, which ensures both of the fractions now have a denominator of $$\displaystyle 8 * 5 = 40$$. With the denominators equivalent, adding $$\displaystyle \frac{16}{40} + \frac{15}{40}$$ becomes trivial.

#### firemath

##### Full Member
Where is Khan?

Please follow the forum guidelines as enunciated by "Read Before Posting."

Where are you stuck? What have you done on the problem so far?

#### Otis

##### Senior Member
For students, there are lots of lessons and examples available on the Internet. Search keywords like how to add fractions, to find written and video sites -- like this one.

If you see something you don't understand, tell us what it is. If you need more help, please show us what you tried, so we can see where you need help.

#### toponlinetool

##### New member
Well first you need to find the common denominator of both numbers. The common denominator is the least common multiple the denominator (the number at the bottom) of both numbers have. Once you’ve figured that out, you multiply the top numbers of what you multiplied the bottom
Thanks...I followed your instructions, & got the answer- 31/40

#### toponlinetool

##### New member
Observe that $$\displaystyle \frac{x}{x} = 1$$ for any fraction where $$\displaystyle x \ne 0$$. Also note that when multiplying some number by 1, the result will be the same number you started with. You can use this fact to change the denominator in a fraction:

$$\displaystyle \frac{2}{5} = \frac{2}{5} * 1$$​
$$\displaystyle \frac{2}{5} = \frac{2}{5} * \frac{8}{8}$$​
$$\displaystyle \frac{2}{5} = \frac{16}{40}$$​
$$\displaystyle \frac{3}{8} = \frac{3}{8} * \frac{5}{5} = \frac{15}{40}$$​

The fractions $$\displaystyle \frac{8}{8}$$ and $$\displaystyle \frac{5}{5}$$ were chosen because they were formed from the denominators of the "other" fraction, which ensures both of the fractions now have a denominator of $$\displaystyle 8 * 5 = 40$$. With the denominators equivalent, adding $$\displaystyle \frac{16}{40} + \frac{15}{40}$$ becomes trivial.
Thank u very much..

#### toponlinetool

##### New member
Though it may not be the least common denominator, you can always get a common denominator by multiplying the two denominator, here 8 and 5, together.
Thanks for the help.

#### toponlinetool

##### New member
For students, there are lots of lessons and examples available on the Internet. Search keywords like how to add fractions, to find written and video sites -- like this one.

If you see something you don't understand, tell us what it is. If you need more help, please show us what you tried, so we can see where you need help.

Ok. Thanks..

#### toponlinetool

##### New member
Hi. There's no need to type those hyphens. Some people might see them as negative signs.

ok.. will remember next time..thanx