I am also having trouble figuring out the below:
Eva wants to make two pieces of pottery. She needs 3/5 pound of clay one piece and 7/10 pound of clay for the other piece. She has three bags of clay that weigh 4/5 pound each. How many bags of clay will Eva need to make both pieces of pottery? How many pounds of clay will she have left over?
Convert to decimals to clarify.
.6 + .7 = 1.3 lbs
1.3/.8 = ?
To figure out how many bags of clay Eva will need to make both pieces of pottery, we first need to add up the amounts of clay needed for each piece.
The first piece requires 3/5 pound of clay, and the second piece requires 7/10 pound of clay.
To add these fractions, we need a common denominator. The smallest number that both 5 and 10 divide evenly into is 10.
So, multiplying the numerator and denominator of 3/5 by 2, we get 6/10 pound of clay for the first piece.
Now, we can add the two fractions:
6/10 + 7/10 = 13/10 pound of clay.
To see how many bags of clay Eva needs, we need to divide 13/10 by the weight of each bag of clay, which is 4/5 pound.
To divide by a fraction, we multiply by its reciprocal. So we have:
(13/10) ÷ (4/5) = (13/10) * (5/4).
Multiplying across:
(13/10) * (5/4) = (13 * 5) / (10 * 4) = 65/40.
Now, to simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 5:
(65/5) / (40/5) = 13/8
So Eva will need 13/8, or one and five eighths, bags of clay to make both pieces of pottery.
To find out how much clay she will have left over, we need to subtract the total amount of clay used from the total amount of clay she has.
The total amount of clay she has is 3 bags, each weighing 4/5 pound. To find the total weight, we multiply 4/5 by 3:
3 * (4/5) = 12/5.
So Eva has 12/5 pound of clay.
Subtracting the total amount of clay used (13/8 pound) from the total amount she has (12/5 pound), we perform:
(12/5) - (13/8) = (96/40) - (65/40) = 31/40.
Therefore, Eva will have 31/40 pound of clay left over.