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### Course: Arithmetic (all content)>Unit 5

Lesson 10: Decomposing fractions

# Decomposing a fraction visually

Sal uses a tape diagram to decompose 7/9. Created by Sal Khan.

## Want to join the conversation?

• How do you add numbers with different denominators (EXAMPLE: 3/9 + 2/6)?
• You would need to convert the fractions so that they have the same denominator, and then add them by adding the values in the numerators and keeping the denominator the same. To convert a fraction into a different denominator, you have to multiply the numerator and denominator by the same number (in order to keep the actual value the same). The easiest way to convert two fractions to the same denominator is to make each denominator the least common multiple of the two previous denominators. With all that out of the way, let's see that example:
3/9 + 2/6
The least common multiple between 9 and 6 is 18 (you can learn how to find LCMs by using the search box in the top of any Khan Academy screen, if you don't know already). So, we multiply each fraction to get 18
3/9 * 2/2 = 6/18
2/6 * 3/3 = 6/18
Now, you have two fractions with the same denominator, so you can add them as normal:
6/18 + 6/18 = (6 + 6) / 18 = 12/18 = 2/3
(Note: you could have made the problem lots easier by simplifying the fractions at the beginning into 1/3 and 1/3 and then just adding those, but that would defeat the purpose of learning how to add unlike denominators.)
• can you do 1/9 + 6/9 - 1/9 + 1/9?
• I think of it this way:
(1/9 + 6/9) - (1/9 + 1/9)
= (7/9) - (2/9)
= 5/9
So the answer would be 5/9
I remember being taught the MDAS (Multiplication, Division, Addition, Subtraction) method (which tells you which operations you would do first in given equation). For the problem you posed, I added all terms that needed to be added then I moved on to tackle the terms that needed to be substracted....Hope this helped.
• what happends if you have a improper fration
• then you have to change to a mixed number for example if you have 5/2 you could change it to 2 and 1/2
• In Thailand, we didn't learn decomposing a fraction
I want to know how important is it?
• It's very practical and applicable to real life. It's important.
• At cant Sal use 4/9+3/9 instead of 2/9+3/9+2/9?
• Yes that would work too. In fact there are many more possibilities, can you find more?

There are actually infinitely many ways to represent 7/9 (or any number really). Sal just gave 3 examples here, hoping to give the viewers some insight into fractions.
• How do you add fractions with diffrent dennminators

In short, you need to convert the denominator into a common denominator.
You can do it by a method called cross multiplication (I'm not sure but at least that's what I called it).

``a   c- + -b   da * d + c * b-------------    b * d``

The cross means multiplying the denominator on the other side.
``a   c- \ -b   da   c- / -b   d``
• could u take away the denominator and pretend that it is 2+3+2=7
• You would be multiplying the fractions by the denominator (if it's the same for all of them) but technically yes.
• Sal says "times two ninths" but meant "plus two ninths.