John is cooking cupcakes. The recipe calls for 3 3/10 cups of flour. He accidentally put in 3 5/8 cups. How many extra cups did he put in?
To solve this problem, we need to find the difference between the correct amount of flour (3 3/10 cups) and the amount that John actually put in (3 5/8 cups).
First, let's convert 3 3/10 to an improper fraction:
3 3/10 = (3 * 10 + 3)/10 = 33/10.
Next, let's convert 3 5/8 to an improper fraction:
3 5/8 = (3 * 8 + 5)/8 = 29/8.
Now, let's find the difference between the two fractions:
33/10 - 29/8.
To subtract fractions, we need to find a common denominator. In this case, the common denominator is 10 * 8 = 80.
Therefore, the equation becomes:
(33/10) * (8/8) - (29/8) * (10/10) = 264/80 - 290/80.
Now, let's subtract the two fractions:
264/80 - 290/80 = (264 - 290)/80 = -26/80.
Finally, let's simplify the fraction as much as possible:
-26/80 = -13/40.
So, John put in an extra 13/40 cups of flour.
To find out how many extra cups of flour John put in, we need to subtract the correct amount of flour from the amount he actually put in.
The correct amount of flour according to the recipe is 3 3/10 cups.
John accidentally put in 3 5/8 cups of flour.
To subtract these fractions, we need to make sure they have a common denominator. The lowest common denominator for 10 and 8 is 40.
Now, let's convert both fractions to have a denominator of 40.
3/10 is equivalent to 12/40 (multiplied numerator and denominator by 4).
5/8 is equivalent to 25/40 (multiplied numerator and denominator by 5).
So, the correct amount of flour is 12/40 cups, and John actually put in 25/40 cups.
To find the difference, we subtract the correct amount from the actual amount:
25/40 - 12/40 = 13/40.
Therefore, John put in an extra 13/40 cups of flour.
To find out how many extra cups John put in, we need to calculate the difference between the amount he put in (3 5/8 cups) and the required amount (3 3/10 cups).
Step 1: Convert the mixed numbers to improper fractions.
3 5/8 cups = (3 * 8 + 5) / 8 = 29/8 cups
3 3/10 cups = (3 * 10 + 3) / 10 = 33/10 cups
Step 2: Subtract the required amount from the amount put in.
29/8 - 33/10
To subtract fractions with different denominators, we need to find a common denominator.
Step 3: Find the common denominator.
The common denominator of 8 and 10 is 40.
Step 4: Convert the fractions to have a common denominator.
29/8 = (29 * 5) / (8 * 5) = 145/40
33/10 = (33 * 4) / (10 * 4) = 132/40
Step 5: Subtract the fractions.
145/40 - 132/40 = (145 - 132) / 40 = 13/40
Therefore, John put in an extra 13/40 cups of flour.