A box of nails weighs 56 5/8 pounds. If you used 3 3/16 pounds of nails yesterday, and another 7 3/4 pounds today, how many pounds of nails are left?
To calculate the weight of nails left, subtract the weights of the nails used from the weight of the box of nails: 56 5/8 pounds - 3 3/16 pounds - 7 3/4 pounds = 56 5/8 pounds - (3*2/16 pounds + 3/16 pounds) - (7*2/4 pounds + 3/4 pounds)
56 5/8 pounds = 56 + 5/8 pounds = 56 + 5*2/16 pounds + 5/8 pounds = 56 + 10/16 pounds + 5/8 pounds = 56 + 10/16 pounds + 10/16 pounds = 56 + 20/16 pounds = 57 4/16 pounds = 57 1/4 pounds
3 3/16 pounds = 56/16 pounds + 3/16 pounds = 59/16 pounds
7 3/4 pounds = 7*2/4 pounds + 3/4 pounds = 14/4 pounds + 3/4 pounds = 17/4 pounds
Weight of nails left = 57 1/4 pounds - 59/16 pounds - 17/4 pounds = 57 1/4 pounds - (3*16/16 pounds + 11/16 pounds) - 68/16 pounds = 57 1/4 pounds - 48/16 pounds - 68/16 pounds = 57 1/4 pounds - 116/16 pounds = 57 pounds - 8/16 pounds = 56 8/16 pounds = 56 1/2 pounds
There are 56 1/2 pounds of nails left. Answer: \boxed{56\frac{1}{2}}.
To find out how many pounds of nails are left, we need to subtract the weights of the nails used from the weight of the box.
First, let's convert the mixed numbers to improper fractions:
56 5/8 pounds = 56 + 5/8 = (56*8 + 5) / 8 = 453/8 pounds
3 3/16 pounds = 3 + 3/16 = (3*16 + 3) / 16 = 51/16 pounds
7 3/4 pounds = 7 + 3/4 = (7*4 + 3) / 4 = 31/4 pounds
Next, we subtract the weights of the nails used from the weight of the box:
453/8 - 51/16 - 31/4
To subtract fractions, we need a common denominator:
The first fraction already has a denominator of 8, so we don't need to make any changes.
The second fraction has a denominator of 16, so we multiply the numerator and denominator by 2 to get:
51/16 = (51*2)/(16*2) = 102/32
The third fraction has a denominator of 4, so we multiply the numerator and denominator by 8 to get:
31/4 = (31*8)/(4*8) = 248/32
Now we can subtract the fractions:
453/8 - 102/32 - 248/32
Since the denominators are the same, we can subtract the numerators directly:
(453 - 102 - 248) / 32 = 103/32
Therefore, there are 103/32 pounds of nails left.
To find out how many pounds of nails are left, we need to subtract the weights of nails used from the total weight of the box.
First, we need to convert all the mixed fractions into improper fractions to make calculations easier.
56 5/8 pounds is equivalent to 56 + 5/8 = (56 * 8 + 5) / 8 = 453/8 pounds.
3 3/16 pounds is equivalent to 3 + 3/16 = (3 * 16 + 3) / 16 = 51/16 pounds.
7 3/4 pounds is equivalent to 7 + 3/4 = (7 * 4 + 3) / 4 = 31/4 pounds.
Now, let's calculate the remaining weight of nails by subtracting the weights used from the total weight:
453/8 pounds - 51/16 pounds - 31/4 pounds
To subtract fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 8, 16, and 4 is 16.
Converting each fraction to have a denominator of 16:
(453/8 pounds) * (2/2) = 906/16 pounds
(51/16 pounds) * (1/1) = 51/16 pounds
(31/4 pounds) * (4/4) = 124/16 pounds
Now we can subtract:
906/16 pounds - 51/16 pounds - 124/16 pounds
Combining the numerators:
(906 - 51 - 124)/16 pounds
Simplifying the expression in the numerator:
731/16 pounds
Therefore, there are 731/16 pounds or approximately 45.6875 pounds of nails left.