sandra bought four bags of nails the weights of bags in pounds (lb) are shown 2 5/6, 1 1/4, 2 1/4, 1 1/3 what is the closest weight of four bags of nails? I NEED AN EXPLANATION!!!!
8 lb
Hey there, nail enthusiast! Let's crunch some numbers and find the closest weight of those bags.
To add the weights together, we need to have a common denominator for the fractions. Let's convert the mixed numbers into improper fractions:
2 5/6 = (2 * 6 + 5) / 6 = 17/6
1 1/4 = (1 * 4 + 1) / 4 = 5/4
2 1/4 = (2 * 4 + 1) / 4 = 9/4
1 1/3 = (1 * 3 + 1) / 3 = 4/3
Now, we can calculate the total weight:
17/6 + 5/4 + 9/4 + 4/3
To simplify the fractions, we need to find a common denominator, which in this case is 12:
(17 * 2) / (6 * 2) + (5 * 3) / (4 * 3) + (9 * 3) / (4 * 3) + (4 * 4) / (3 * 4)
34/12 + 15/12 + 27/12 + 16/12
We add the numerators together and keep the common denominator:
(34 + 15 + 27 + 16) / 12
92/12
Now, we can simplify the fraction:
92 ÷ 12 = 7 remainder 8
So, the weight of the bags is 7 and 8/12 pounds.
And if you want an approximation, it's closest to 7.67 pounds.
Hope that explanation made you smile a little!
To find the closest weight of the four bags of nails, we need to add up the weights of each bag.
First, let's convert each mixed fraction into an improper fraction.
The first bag weighs 2 5/6 pounds. To convert it to an improper fraction, we multiply the whole number (2) by the denominator of the fraction (6) and add the numerator (5). The result is 17. So, the weight of the first bag is 17/6 pounds.
The second bag weighs 1 1/4 pounds. Converting it to an improper fraction, we have (1 * 4) + 1 = 5/4 pounds.
The third bag weighs 2 1/4 pounds. Converting it to an improper fraction, we have (2 * 4) + 1 = 9/4 pounds.
The fourth bag weighs 1 1/3 pounds. Converting it to an improper fraction, we have (1 * 3) + 1 = 4/3 pounds.
Now, let's add up all the weights:
17/6 + 5/4 + 9/4 + 4/3
To add fractions, we need a common denominator. In this case, the least common multiple (LCM) of 6, 4, and 3 is 12.
17/6 can be rewritten as 34/12 (multiply both numerator and denominator by 2).
5/4 remains the same.
9/4 remains the same.
4/3 can be rewritten as 16/12 (multiply both numerator and denominator by 4).
Now, we can add the fractions:
34/12 + 5/4 + 9/4 + 16/12
To add the fractions with a common denominator, we simply add the numerators:
(34 + 5 + 9 + 16) / 12 = 64/12 pounds
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
64/12 ÷ 4/4 = (64 ÷ 4) / (12 ÷ 4) = 16/3 pounds
Therefore, the closest weight of the four bags of nails is 16/3 pounds, or approximately 5 and 1/3 pounds.
Its 8 Ib (I did a hw with this question & got it right) :)
Change all of the fractions so that their denominators are 12.
Add the amounts of nails.
I'll be glad to check your answer.