gemmox wrote:
Where does the 10 come from.. I understand that the inner ratio's cancel themselves out, but unfortunately my brain power is failing me!
![Crying or Very sad :cry:](./images/smilies/crying.png)
w/x =
5/4 and w/z =
10/3.
To combine ratios with a COMMON ELEMENT, the common element must be represented by the SAME VALUE in each ratio.
Here, the element common to both ratios is w.
In the first ratio, w is represented by 5.
In the second ratio, w is represented by 10.
The LCM (lowest common multiple) of these two values is 10.
Thus, we want w to be represented by 10 in each ratio.
But we must take care not to CHANGE the value of either ratio: if we multiply the top of a ratio by a factor, we must multiply the bottom of the ratio by the SAME factor, so that the value of the ratio doesn't change:
w/x = 5/4 = (5*
2)/(4*
2) =
10/8.
w/z =
10/3.
Combining the ratios, we get:
w : x : z = 10:8:3.
Another example:
If we want to combine a:b = 2:3 and b:c = 5:4, we get:
a/b = 2/3 = (2*5)/(3*5) = 10/15.
b/c = 5/4 = (5*3)/(4*3) = 15/12.
Thus:
a
![:b:](//cdn.jsdelivr.net/gh/twitter/twemoji@latest/assets/svg/1f171.svg)
c = 10:15:12.
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