Convert all fractions to have the same denominator.
To convert, we must find the least common multiple of the two denominators of the fractions:
Multiples of 4: {4,8,12,16,20}
Multiples of 5: {5,10,15,20}
The least common multiple of 4 and 5 is 20.
Multiply the fractions by a number that will result in the denominator being 20:
![\frac{3}{4} * \frac{5}{5} = \frac{15}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20%2A%20%5Cfrac%7B5%7D%7B5%7D%20%3D%20%5Cfrac%7B15%7D%7B20%7D)
![\frac{2}{5} * \frac{4}{4} = \frac{8}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%20%2A%20%5Cfrac%7B4%7D%7B4%7D%20%3D%20%5Cfrac%7B8%7D%7B20%7D%20)
The equation should now look like this:
![\frac{15}{20} = w + \frac{8}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B20%7D%20%3D%20w%20%2B%20%5Cfrac%7B8%7D%7B20%7D)
Subtract both sides by 8/20 to get w by itself:
![\frac{15}{20} - \frac{8}{20} = \frac{7}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B20%7D%20-%20%5Cfrac%7B8%7D%7B20%7D%20%3D%20%5Cfrac%7B7%7D%7B20%7D%20)
![w = \frac{7}{20}](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B7%7D%7B20%7D%20)
The value of w is 7/20.