Jan mixes 1 1/3 cups of white flour,, 1 3/4 cups of whole wheat flour, and 2/3 cup of rye flour. About what fraction of the mixture is whole wheat flour? Solve and explain how you got your answer.
white:wheat:rye = 4/3 : 7/4 : 2/3 = 16:21:8
wheat/total = 21/(16+21+8) = 21/45 = 7/15
To find the fraction of the mixture that is whole wheat flour, we need to add up all the amounts of flour used and then calculate the ratio of whole wheat flour to the total amount of flour.
First, let's convert the mixed numbers to improper fractions:
1 1/3 = (3 * 1 + 1)/3 = 4/3
1 3/4 = (4 * 1 + 3)/4 = 7/4
Now, let's add up the amounts of flour:
4/3 + 7/4 + 2/3
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
Now, let's rewrite each fraction with a denominator of 12:
4/3 = (4/3) * (4/4) = 16/12
7/4 = (7/4) * (3/3) = 21/12
2/3 = (2/3) * (4/4) = 8/12
Adding the fractions:
16/12 + 21/12 + 8/12 = 45/12
Now, we can see the fraction of whole wheat flour by dividing the amount of whole wheat flour by the total amount of flour:
(21/12) / (45/12)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(21/12) * (12/45)
The numerators of the fractions cancel each other out:
(21/1) * (1/45) = 21/45
Thus, the fraction of the mixture that is whole wheat flour is 21/45.