Let the number of math groups be x and the number of painting groups be 52-x.

1/2X = 3/7(52 X)

1/2X= 156/7-3/7X

1/2X+3/7X= 156/7

7/ 14X+6/ 14X = 156/7

13/ 14X= 156/7

x = 156/7÷ 13/ 14

X=24

Or X+( 1/2X÷3/7)=52.

X+7/6X=52

13/6X=52

X=24