Ronnie and Josiah each bought a package of the same kind of cookies at the store. Rodney 8 1/2 package of cookies on Monday and 1/3 of the same package on Tuesday. Josiah ate 512 of his package on Monday and 1/2 of the package on Tuesday. Who ate more? How much more?
Add up each persons fractions, then subtract the two people's totals to see who ate more : )
To compare who ate more, we need to calculate the total amount of cookies eaten by each person.
Ronnie ate 8 1/2 + 1/3 package of cookies. To add these fractions, we first need to find a common denominator, which in this case is 6.
8 1/2 can be written as 8 3/6 and 1/3 can be written as 2/6. Adding these fractions together gives us:
8 3/6 + 2/6 = 11/6
So, Ronnie ate a total of 11/6 packages of cookies.
Josiah ate 512 of his package on Monday and 1/2 of the package on Tuesday. To add these together, we need to convert 512 into a fraction of a whole package.
Since there are 6 equal parts in a whole package, each part represents 512/6 = 85 1/3 cookies.
So, Josiah ate 85 1/3 + 1/2 of a package of cookies, which can be written as:
85 1/3 + 1/2 = 256/3 + 3/6
= 256/3 + 1/2
= (256 * 2 + 3) / (3 * 2)
= 515/6
Therefore, Josiah ate a total of 515/6 packages of cookies.
To determine who ate more, we compare the fractions: 11/6 (Ronnie) and 515/6 (Josiah).
To make the comparison easier, we can convert both fractions to decimals.
11/6 ≈ 1.83
515/6 ≈ 85.83
From the calculations, we can see that Josiah ate more cookies than Ronnie.
The difference in the amount of cookies eaten can be calculated by subtracting the fraction of cookies Ronnie ate from the fraction of cookies Josiah ate:
515/6 - 11/6 = 504/6 = 84
Therefore, Josiah ate 84 more cookies than Ronnie.
To find out who ate more cookies and how much more, we need to calculate the total number of cookies each person ate.
Let's start with Ronnie:
On Monday, Ronnie ate 8 1/2 packages of cookies. To add the number of cookies, we need to convert the mixed number into an improper fraction:
8 1/2 = (8 * 2 + 1) / 2 = 17 / 2
So, Ronnie ate 17/2 packages of cookies on Monday.
On Tuesday, Ronnie ate 1/3 of a package of cookies.
To add Monday and Tuesday together, we need to make the denominators the same:
17/2 + 1/3
To do this, we find a common denominator, which is 6 in this case:
(17/2) * (3/3) = 51/6 (converting the fraction to a fraction with the denominator 6)
1/3 * (2/2) = 2/6 (converting the fraction to a fraction with the denominator 6)
Now, we can add the two fractions together:
51/6 + 2/6 = 53/6
Therefore, Ronnie ate a total of 53/6 packages of cookies.
Now, let's move on to Josiah:
On Monday, Josiah ate 512 of his package of cookies.
On Tuesday, Josiah ate 1/2 of his package of cookies.
To add Monday and Tuesday together, we need to find a common denominator. However, since both fractions already have a denominator of 2, we don't need to perform any conversions.
Now, we can add the two fractions together:
512/2 + 1/2 = 513/2
Therefore, Josiah ate a total of 513/2 packages of cookies.
To compare who ate more, we need to compare the two totals:
Ronnie: 53/6 packages
Josiah: 513/2 packages
To compare fractions with different denominators, we need to make them have the same denominator. In this case, we can find a common denominator by multiplying the denominators together:
6 * 2 = 12
Now, let's convert the fractions to have 12 as the denominator:
(Ronnie) 53/6 * 2/2 = 106/12
(Josiah) 513/2 * 6/6 = 3078/12
Comparing the numerators, we can see that Josiah ate more cookies, as 3078/12 is greater than 106/12.
To find out how much more Josiah ate, we subtract Ronnie's total from Josiah's total:
3078/12 - 106/12 = 2972/12
Therefore, Josiah ate 2972/12 packages more than Ronnie.
Simplifying the fraction, we get:
248/1
So, Josiah ate 248 packages more than Ronnie.