sandra bought four bags of nails for a carpentry project. the weights of the bags (lb) are shown.
2 5/6, 1 1/4, 2 1/4, 1 1/3
which is closest to the total weight of four bags of nails?
I NEED THE ANSWER AND EXPLANATION
a 10
b 8
c 6
d 4
common denominator for the fractions is 12
2 + 1 + 2 + 1 + 10/12 + 3/12 + 3/12 + 4/12
8
69
To find the total weight of the four bags of nails, we need to add up the weights of each bag.
Given weights:
Bag 1: 2 5/6 lb
Bag 2: 1 1/4 lb
Bag 3: 2 1/4 lb
Bag 4: 1 1/3 lb
To add these fractions, we need to find a common denominator. The least common multiple of 6, 4, and 3 is 12.
Now, let's convert the mixed numbers to improper fractions:
Bag 1: 2 5/6 = (2 * 6 + 5) / 6 = 17 / 6
Bag 2: 1 1/4 = (1 * 4 + 1) / 4 = 5 / 4
Bag 3: 2 1/4 = (2 * 4 + 1) / 4 = 9 / 4
Bag 4: 1 1/3 = (1 * 3 + 1) / 3 = 4 / 3
Now, we can add the fractions:
17/6 + 5/4 + 9/4 + 4/3
To add these fractions, we need a common denominator of 12:
(17/6) x (2/2) = 34/12
(5/4) x (3/3) = 15/12
(9/4) x (3/3) = 27/12
(4/3) x (4/4) = 16/12
Now, adding the fractions:
34/12 + 15/12 + 27/12 + 16/12 = 92/12
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4:
92/12 รท 4/4 = 23/3
Therefore, the total weight of the four bags of nails is 23/3 lb.
Now, let's find the closest option:
a) 10 lb
b) 8 lb
c) 6 lb
d) 4 lb
Calculating the decimal value of 23/3, we get approximately 7.67 lb.
Comparing this result to the given options, the closest value is option b) 8 lb.
So, the closest weight to the total weight of the four bags of nails is 8 lb.