Question

1. lemonade you drink $\frac{2}{7}$ of a pitcher of lemonade. your friend drinks $\frac{3}{14}$ of the pitcher. what fraction of the pitcher do you and your friend drink? (section 2.2)
2. football the table shows the statistics of a running back in a football game. did he gain more than 50 yards total? explain. (section 2.2)

quarter	1	2	3	4	total

Explanation:

Step1: Find common - denominator for lemonade problem

We need to add $\frac{2}{7}$ and $\frac{3}{14}$. The common denominator of 7 and 14 is 14. Rewrite $\frac{2}{7}$ as $\frac{2\times2}{7\times2}=\frac{4}{14}$.

Step2: Add the fractions

$\frac{4}{14}+\frac{3}{14}=\frac{4 + 3}{14}=\frac{7}{14}=\frac{1}{2}$

Step3: Calculate total yards for football problem

First, convert the mixed - numbers to improper fractions. $-8\frac{1}{2}=-\frac{17}{2}$, $42\frac{1}{2}=\frac{85}{2}$, $-2\frac{1}{4}=-\frac{9}{4}$.
The common denominator of 2 and 4 is 4. Rewrite $-\frac{17}{2}$ as $-\frac{34}{4}$ and $\frac{85}{2}$ as $\frac{170}{4}$.
Then, add the yardages: $-\frac{34}{4}+23+\frac{170}{4}-\frac{9}{4}$. Since $23=\frac{92}{4}$, we have $(-\frac{34}{4}+\frac{170}{4}-\frac{9}{4})+\frac{92}{4}=\frac{-34 + 170-9}{4}+\frac{92}{4}=\frac{127}{4}+\frac{92}{4}=\frac{127 + 92}{4}=\frac{219}{4}=54.75$

Answer:

1. $\frac{1}{2}$
2. Yes, because the total yards is $54.75$ yards which is more than 50 yards.