LogFAQs > #962603628

Super Slash posted...

Here's another one. I always forget the intuition behind word problems. I know they're just fancier ways of writing out expressions.

A baby's t-shirt requires 8/9 yards of fabric. How many t-shirts can be made from 104 yards?

To grow intuition you need understanding.
Break it into smaller easier problems to grow understanding.

If a t-shirt takes 1 yard of fabric, how many t-shirts can be made with 10 yards?
10, that's easy.
If a t-shirt takes 1/2 yards of fabric (.5 or one-half), how many can be made with 10 yards?
20. Either count them out: 1/2, 1, 1 and 1/2, 2, 2 and 1/2... or divide 10 by 1/2, or 10 by .5. Do you understand dividing by fractions (it's the same thing you just did).
Then take it to the next level, 8/9 yards per t-shirt with 104 yards.

Another approach is to look at the units.
You have (8/9) yards/shirt. You can see that as 8 yards per 9 shirts or (some number) yards per shirt. You also have 104 yards. You want the units to become shirts.
8 Yards __104 yards
--------- ---------
9 Shirt _______1
You can cancel units just like canceling numbers. So divide yards by yards/shirt.
104 yards _9 shirts
--------- --------
1 _________8 yards
The yards cancel and your left with 1049 shirts divided by 8. (Underscores for spacing. )