Answer:
![\frac{12}{35}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B35%7D)
Step-by-step explanation:
Given :
→ For Purple People Eater, she used 3 pints of red paint for every 5 pints of blue paint.
i.e, The ratio of red paint to blue paint is 3:5
→ For Purple Majesty, she used a blue to red paint ratio of 7 to 4.
i.e, The ratio of red paint to blue paint is 4:7
To find :
1) Compare the ratios of red paint to blue paint.
![\frac{3}{5}\times \frac{4}{7}=\frac{12}{35}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B7%7D%3D%5Cfrac%7B12%7D%7B35%7D)
2) The ratio for Purple People Eater can be expressed in fraction form as :
![=\frac{3}{5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B5%7D)
3) The ratio for Purple Majesty can be expressed in fraction form as :
![=\frac{7}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7%7D%7B4%7D)
4) To compare these fractions, rewrite them with a common denominator
For common denominator
Multiply numerator and denominator by 4 in ![\frac{3}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D)
![\Rightarrow\frac{3\times 4}{5\times4}=\frac{12}{20}](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7B3%5Ctimes%204%7D%7B5%5Ctimes4%7D%3D%5Cfrac%7B12%7D%7B20%7D)
Multiply numerator and denominator by 5 in ![\frac{7}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B4%7D)
![\Rightarrow\frac{7\times 5}{5\times4}=\frac{35}{20}](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7B7%5Ctimes%205%7D%7B5%5Ctimes4%7D%3D%5Cfrac%7B35%7D%7B20%7D)
Common denominator is 20