my family has a $6000/ month budget. we spend 1/3 of our budget on food, 1/4 on our mortgage, 1/5 for clothing, and 1/10 for childcare. How much money is left for other expenses

1/3 + 1/4 + 1/5 + 1/10 = 53/60

So, you have 7/60 of the total left over.