Paul is making loaves of raisin bread to sell at a fundraising event. The recipe calls for 1/3 cup of raisins for each loaf, and Paul has 3 1/4 cups of raisins
a) How many loaves can Paul make?
b) How many cups of raisins will he have left over?
a) To find out how many loaves Paul can make, we need to divide the total amount of raisins he has by the amount of raisins needed for each loaf.
First, let's convert 3 1/4 cups to an improper fraction:
3 1/4 = 4/4 + 1/4 = 5/4
Now we can divide the total amount of raisins by the amount needed for each loaf:
(5/4) ÷ (1/3) = (5/4) × (3/1) = 15/4 = 3 3/4
Therefore, Paul can make 3 3/4 loaves of raisin bread.
b) To find out how many cups of raisins Paul will have left over, we need to subtract the total amount of raisins needed for the loaves from the total amount of raisins he has.
The total amount of raisins needed for the loaves is (1/3) * (3 3/4) = 15/12 = 5/4 cups.
Now we can subtract:
(5/4) - (5/4) = 0
Therefore, Paul will have 0 cups of raisins left over.
To find out how many loaves Paul can make, we need to divide the total amount of raisins he has (3 1/4 cups) by the amount of raisins required for each loaf (1/3 cup).
a) To do the division, we can convert the mixed number (3 1/4) to an improper fraction, which is 13/4. Then we can divide 13/4 by 1/3:
(13/4) / (1/3)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(13/4) * (3/1)
Multiplying across the numerators and denominators gives us:
(39/4)
Since we can't have a fraction of a loaf, we need to round down to the nearest whole number. Thus, Paul can make 9 loaves of raisin bread.
b) To find out how many cups of raisins Paul will have left over, we can subtract the amount of raisins used for the loaves from the total amount of raisins he has:
Total amount of raisins - Amount of raisins used for loaves
3 1/4 cups - (1/3 cup/loaf * 9 loaves)
3 1/4 cups - (9/3 cups)
To subtract fractions with the same denominator, we subtract the numerators and keep the same denominator:
(13/4) - (9/4)
13 - 9 = 4
So, Paul will have 4/4 or 1 cup of raisins left over.
To find the number of loaves Paul can make, we need to divide the total amount of raisins he has by the amount of raisins required for each loaf.
a) To do this, we can set up a division problem:
Number of loaves = Total amount of raisins ÷ Amount of raisins per loaf
Total amount of raisins = 3 1/4 cups = 13/4 cups
Amount of raisins per loaf = 1/3 cup
Number of loaves = (13/4) cups ÷ (1/3) cup
To divide fractions, we multiply by the reciprocal of the second fraction:
Number of loaves = (13/4) cups * (3/1) cup
Multiplying the numerator and denominator of the fractions gives:
Number of loaves = (13 * 3) / (4 * 1) = 39/4 = 9 3/4 loaves
Therefore, Paul can make 9 3/4 loaves of raisin bread.
b) To find out how many cups of raisins he will have left over, we need to subtract the amount of raisins used from the total amount of raisins Paul has.
Amount of raisins used = Number of loaves * Amount of raisins per loaf
Amount of raisins used = (9 3/4 loaves) * (1/3 cup)
Converting 9 3/4 to an improper fraction:
Amount of raisins used = (39/4) * (1/3) cup
Multiplying the numerators and denominators of the fractions gives:
Amount of raisins used = (39 * 1) / (4 * 3) = 39/12 = 3 3/12 = 3/4 cup
To find the amount of raisins left over, we subtract the amount used from the total amount:
Amount of raisins left over = Total amount of raisins - Amount of raisins used
Amount of raisins left over = (13/4 cups) - (3/4 cups)
Amount of raisins left over = (13 - 3) / 4 cups = 10/4 cups = 2 1/2 cups
Therefore, Paul will have 2 1/2 cups of raisins left over.