at the northgate fabric store, there are 5 scrap pieces of cloth. their lengths are 1/2 yrd, 3/10 tard, 5/6 yard, 1/3 yard, and 2/5 yard. how much total fabric does the owner have?

Answer: 71/30 or 2 and 11/30 yards

Work:

You need to add each fraction together in order to find the total amount of fabric. You should do this by finding common denominators (the number on the bottom of the fraction) and then combining fractions.

Since the order of adding doesn't matter, you should combine the fractions that are the easiest first. Start with adding 1/2 and 1/3. The common denominator is 6, since that is the LCM of 2 and 3. The fractions then become 3/6 and 2/6 which combine into 5/6. It is then easy to add the other 5/6 of a yard from the question to the 5/6 you have just found into 10/6.

Then come over to the 3/10 and 2/5 yard pieces which can be easily added together using 10 as the common denominator. These two fractions added together become 7/10.

The final step is to add the 7/10 plus the 10/6. The common denominator is 30, as it is the LCM of 10 and 6. The new fractions become 21/30 plus 50/30 which equals 71/30.