Question

1. josiah is asked to simplify the expression $\frac{2}{3}+\frac{1}{2}(8 + 3\frac{1}{4})$. josiah incorrectly claims that the expression simplifies to $13\frac{1}{8}$. a. what is the correct value of the expression? b. what error did josiah likely make? 9. higher order thinking the table shows the temperatures of the water in 14 different beakers. what is the average temperature, rounded to the nearest tenth of a degree? temperatures in beakers temperature 4.5°c 3.7°c 4.3°c 4.1°c 2.9°c frequency 3 4 2 3 2 10. a swimming pool is draining at a constant rate. the table shows the proportional relationship between the change in the water level and the number of hours the pool has drained. complete the table to show the change in water level at 9 and 23 hours. draining swimming pool hours draining change in water level (in.) 2 -3.5 9 17 -29.75 23 11. in a classroom there are 6 students who are $5\frac{1}{2}$ feet tall, 2 students who are $4\frac{3}{4}$ feet tall, 4 students who are $4\frac{1}{4}$ feet tall, and 2 students who are 6 feet tall. which expression represents the mean height of the students in the classroom? a $\frac{6(5\frac{1}{2})+2(4\frac{3}{4})+4(4\frac{1}{4})+2(6)}{6\times2\times4\times2}$ b $\frac{6(5\frac{1}{2})+2(4\frac{3}{4})+4(4\frac{1}{4})+2(6)}{6 + 2+4 + 2}$ c $\frac{6(4\frac{1}{2})+2(5\frac{3}{4})+4(6\frac{1}{4})+4(6)}{6 + 2+4 + 2}$ d $\frac{6(4\frac{1}{2})+2(5\frac{1}{2})+4(6\frac{1}{4})+4(6)}{6 + 2+4 + 2}$

Explanation:

8.

a.

Step1: Simplify the expression inside the parentheses

First, calculate $8 + 3\frac{1}{4}=8+\frac{13}{4}=\frac{32 + 13}{4}=\frac{45}{4}$

Step2: Multiply by $\frac{1}{2}$

$\frac{1}{2}\times\frac{45}{4}=\frac{45}{8}$

Step3: Add $\frac{2}{3}$

Find a common - denominator, which is 24. $\frac{2}{3}=\frac{16}{24}$ and $\frac{45}{8}=\frac{135}{24}$
$\frac{16}{24}+\frac{135}{24}=\frac{16 + 135}{24}=\frac{151}{24}=6\frac{7}{24}$

Josiah likely did not follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). He may have added $\frac{2}{3}$ to 8 first instead of dealing with the parentheses operation $\frac{1}{2}(8 + 3\frac{1}{4})$ first.

Step1: Calculate the sum of the products of temperature and frequency

$(4.5\times3)+(3.7\times4)+(4.3\times2)+(4.1\times3)+(2.9\times2)$
$=13.5 + 14.8+8.6 + 12.3+5.8$
$=55$

Step2: Calculate the total frequency

$3 + 4+2 + 3+2=14$

Step3: Calculate the average

$\frac{55}{14}\approx3.9$

Answer:

$6\frac{7}{24}$

b.