Question

nit 2 test - tues

1. ①2 3/4 + 1 1/4

②3/5 + 2/3
③4 3/7 + 2 1/2
④2/3 - 1/5

1. model (draw)

3/5×2/3

1. model (draw)

4/5÷3/4
sum of 0.7 + 0.64
difference of 0.94 - 0.6
the product of 5.32·4.3
the quotient of 45.7÷1.83
mean, median, mode: 4,6,7,6,9,3,5,2 and range
dot plot detective
case 1: hours spent studying
below is a dot - plot showing the number of hours 13 students studied for a math test.
questions:

1. how many students studied at least 4 hours?
2. what is the most common number of hours students studied?
3. how many total students are represented?
4. what is the range of hours studied?
5. what percentage of students studied 3 or more hours?

case 2: favorite ice cream flavors
a class of students voted on their favorite ice cream flavor. the dot plot shows the results.
questions:

1. which flavor is the most popular?
2. how many students voted for vanilla or mint?
3. which flavor received the least votes?
4. what is the total number of votes?
5. what fraction of the class voted for chocolate?

case 3: be the analyst!
dot plot: number of books read in a month
questions:

1. how many students read fewer than 2 books?
2. what is the median number of books read?
3. if the student who read 4 books read 2 books next month, how would that affect the dot plot?
4. which is greater: the mean or the median? explain why.

Explanation:

Step1: Calculate 2\frac{3}{5}+1\frac{1}{5}

First convert to improper - fractions: $2\frac{3}{5}=\frac{2\times5 + 3}{5}=\frac{13}{5}$ and $1\frac{1}{5}=\frac{1\times5+1}{5}=\frac{6}{5}$. Then $\frac{13}{5}+\frac{6}{5}=\frac{13 + 6}{5}=\frac{19}{5}=3\frac{4}{5}$

Step2: Calculate $\frac{3}{5}+\frac{2}{3}$

Find a common denominator, which is $5\times3 = 15$. Then $\frac{3}{5}=\frac{3\times3}{5\times3}=\frac{9}{15}$ and $\frac{2}{3}=\frac{2\times5}{3\times5}=\frac{10}{15}$. So $\frac{3}{5}+\frac{2}{3}=\frac{9}{15}+\frac{10}{15}=\frac{9 + 10}{15}=\frac{19}{15}=1\frac{4}{15}$

Step3: Calculate $4\frac{3}{7}+2\frac{1}{2}$

Convert to improper - fractions: $4\frac{3}{7}=\frac{4\times7+3}{7}=\frac{31}{7}$ and $2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}$. The common denominator is $7\times2=14$. $\frac{31}{7}=\frac{31\times2}{7\times2}=\frac{62}{14}$ and $\frac{5}{2}=\frac{5\times7}{2\times7}=\frac{35}{14}$. Then $\frac{31}{7}+\frac{5}{2}=\frac{62}{14}+\frac{35}{14}=\frac{62 + 35}{14}=\frac{97}{14}=6\frac{13}{14}$

Step4: Calculate $\frac{2}{3}-\frac{1}{5}$

The common denominator is $3\times5 = 15$. $\frac{2}{3}=\frac{2\times5}{3\times5}=\frac{10}{15}$ and $\frac{1}{5}=\frac{1\times3}{5\times3}=\frac{3}{15}$. So $\frac{2}{3}-\frac{1}{5}=\frac{10}{15}-\frac{3}{15}=\frac{10 - 3}{15}=\frac{7}{15}$

Step5: Calculate $\frac{3}{5}\times\frac{2}{3}$

Multiply the numerators and denominators: $\frac{3\times2}{5\times3}=\frac{6}{15}=\frac{2}{5}$

Step6: Calculate $\frac{4}{5}\div\frac{3}{4}$

Dividing by a fraction is the same as multiplying by its reciprocal. So $\frac{4}{5}\div\frac{3}{4}=\frac{4}{5}\times\frac{4}{3}=\frac{4\times4}{5\times3}=\frac{16}{15}=1\frac{1}{15}$

Step7: Calculate $0.7 + 0.64$

$0.7+0.64=1.34$

Step8: Calculate $0.94 - 0.6$

$0.94−0.6 = 0.34$

Step9: Calculate $5.32\times4.3$

$5.32\times4.3=(5 + 0.32)\times4.3=5\times4.3+0.32\times4.3=21.5+1.376 = 22.876$

Step10: Calculate $45.7\div1.83$

$45.7\div1.83=\frac{45.7}{1.83}\approx24.97$

Step11: Calculate the mean, median, mode, and range of 4, 6, 7, 6, 9, 3, 5, 2

1. **Mean**:
- First find the sum: $4 + 6+7 + 6+9+3+5+2=42$.
- There are 8 numbers. So the mean is $\frac{42}{8}=5.25$
2. **Median**:
- Arrange the numbers in ascending order: 2, 3, 4, 5, 6, 6, 7, 9.
- Since there are 8 numbers, the median is the average of the 4th and 5th numbers. $\frac{5 + 6}{2}=5.5$
3. **Mode**:
- The number 6 appears twice, more frequently than other numbers. So the mode is 6.
4. **Range**:
- The range is the difference between the largest and smallest numbers. $9−2 = 7$

For the dot - plot questions:

Case 1: Hours Spent Studying

1. **Number of students who studied at least 4 hours**: There are 3 students who studied 4 hours and 2 students who studied 5 hours. So $3 + 2=5$ students.
2. **Most common number of hours**: The most common number of hours is 3 (since there are 4 dots above 3).
3. **Total number of students**: Count all the dots, there are 12 students.
4. **Range of hours studied**: The largest value is 5 and the smallest is 1. So the range is $5 - 1=4$.
5. **Percentage of students who studied 3 or more hours**: There are $4+3 + 2=9$ students who studied 3 or more hours. The total number of students is 12. So the percentage is $\frac{9}{12}\times100\% = 75\%$

Case 2: Favorite Ice - Cream Flavors

6. **Most popular flavor**: Chocolate is the most popular flavor (5 votes).
7. **Number of students who voted for Vanilla or Mint**: Vanilla has 3 votes and Mint has 4 votes. So $3 + 4=7$ students.
8. **Flavor with the least votes**: Cookies & Cream has the least votes (1 vote).
9. **Total number of votes**: $5+3 + 4+2+1=15$ votes.
10. **Fraction of the class that voted for Chocolate**: $\frac{5}{15}=\frac{1}{3}$

Case 3: Number of Books Read in a Month

11. **Number of students who read fewer than 2 books**: There are 3 students who read 0 books and 4 students who read 1 book. So $3 + 4=7$ students.
12. **Median number of books read**: There are 12 students. Arrange the data in order. The 6th and 7th values are both 2. So the median is 2.
13. **Effect on the dot - plot if the student who read 4 books read 2 books next month**: The dot above 4 would move to above 2.
14. **Which is greater, the mean or the median**:
- Calculate the mean: $(0\times3+1\times4 + 2\times3+3\times2+4\times1)\div12=(0 + 4+6 + 6+4)\div12=\frac{20}{12}\approx1.67$. The median is 2. So the median is greater.

Answer:

1. $3\frac{4}{5}$, $1\frac{4}{15}$, $6\frac{13}{14}$, $\frac{7}{15}$, $\frac{2}{5}$, $1\frac{1}{15}$, $1.34$, $0.34$, $22.876$, $24.97$, Mean: $5.25$, Median: $5.5$, Mode: 6, Range: 7
2. Case 1: 5 students, 3 hours, 12 students, 4 hours, 75%

Case 2: Chocolate, 7 students, Cookies & Cream, 15 votes, $\frac{1}{3}$
Case 3: 7 students, 2 books, The dot above 4 moves to above 2, Median is greater.