patel squeezed oranges so that his family could have fresh - squeezed juice for breakfast. he squeezed…

patel squeezed oranges so that his family could have fresh - squeezed juice for breakfast. he squeezed $\frac{13}{15}$ cups from the first orange, $\frac{1}{5}$ cups from the second orange, $\frac{9}{20}$ cups from the third orange, $\frac{5}{11}$ cups from the fourth orange, and $\frac{7}{15}$ cups from the fifth orange. patel estimates that he needs 3 cups of orange juice for his family. about how much more orange juice does he need to reach his estimate?\n$\frac{1}{2}$ cups\n1 cups\n$1\frac{1}{2}$ cups\n$2\frac{1}{2}$ cups

patel squeezed oranges so that his family could have fresh - squeezed juice for breakfast. he squeezed $\frac{13}{15}$ cups from the first orange, $\frac{1}{5}$ cups from the second orange, $\frac{9}{20}$ cups from the third orange, $\frac{5}{11}$ cups from the fourth orange, and $\frac{7}{15}$ cups from the fifth orange. patel estimates that he needs 3 cups of orange juice for his family. about how much more orange juice does he need to reach his estimate?\n$\frac{1}{2}$ cups\n1 cups\n$1\frac{1}{2}$ cups\n$2\frac{1}{2}$ cups

Answer

Explanation:

Step1: Find the total amount of juice squeezed

First, find a common - denominator for the fractions $\frac{13}{15},\frac{1}{5},\frac{9}{20},\frac{5}{11},\frac{7}{15}$. The least common multiple of 15, 5, 20, 11 is 660. $\frac{13}{15}=\frac{13\times44}{15\times44}=\frac{572}{660}$; $\frac{1}{5}=\frac{1\times132}{5\times132}=\frac{132}{660}$; $\frac{9}{20}=\frac{9\times33}{20\times33}=\frac{297}{660}$; $\frac{5}{11}=\frac{5\times60}{11\times60}=\frac{300}{660}$; $\frac{7}{15}=\frac{7\times44}{15\times44}=\frac{308}{660}$. The sum $S=\frac{572 + 132+297+300+308}{660}=\frac{1609}{660}\approx2.44$ cups.

Step2: Calculate the remaining amount of juice needed

He needs 3 cups. The remaining amount $R = 3-\frac{1609}{660}$. $3=\frac{3\times660}{660}=\frac{1980}{660}$. $R=\frac{1980 - 1609}{660}=\frac{371}{660}\approx0.56$ cups, which is closest to $\frac{1}{2}$ cup.

Answer:

A. $\frac{1}{2}$ cups