Katrina is building a deck. She cuts 3 lengths of wood from a 72-inch board. The first length is 30 3.4 inches. The second length is 12 1.4 inches. And the third length is 16 1.4 inches. How much of the original board remains after Katrina makes her cuts?

Common denominators!

If you have to add ... 3 fractions with 4 as the denominators:

Then you can combine the numerators:

a/c + b/c = (a+b) / c and a/d + b/d + c/d = (a+b+c) / d

Let's plug in the numbers.

a=3, b=1, c=1, d = 4

3/4 + 1/4 + 1/4 = 5/4 or 1 1/4!

So the equation for the problem:

Lt = L1 + L2 + L3 + L4 or

L4 = Lt - L1 - L2 - L3 Plug in the numbers

L4 (remains) = L total, 72 - L1 (first cut at 30 3/4) - L2 (second cut 12 1/4) - L3 (16 1/4)

So 72 - 30 - 12 - 16 - 3/4 - 1/4 - 1/4 = ?

(break this down into simple terms and do it in your head ...

72 - 30 = 42, 42 - 21 = 30, 30 - 16 = 14, 14 - 3/4 = 13 1/4 - 1//4 = 13 - 1/4 = 12 3/4!