What is a reasonable estimate for the sum of 4 1/8+3 2/3+5 1/2

A responsible estimate would be 14.

You estimate each of the mixed numbers to the nearest whole number:

4 1/8=4 because 1/8 is less than 1/2 so the number stays the same

3 2/3=4 because 2/3 is grater than 1/2

5 1/2 = 6 because 1/2 is equal to 1/2 which means you estimate up.

So 4+4+6=14

First, mentally add the whole numbers.

4+3+5=12

Now, look at the fractions. 1/8, 2/3, and 1/2.

2/3 is bigger than 1/2, so you can add in another whole number.

12+1=13

1/8 is tiny, and won't add a whole lot to the mix, so just leave that.

A reasonable estimate would be 13 1/8