Question

nit 2 test - tues. 1. ①2\frac{2}{3}+1\frac{2}{5} ②\frac{3}{5}+\frac{2}{3} ③4\frac{3}{7}+2\frac{1}{2} ④\frac{2}{3}-\frac{1}{5} 2. model (draw) \frac{3}{5}\times\frac{2}{3} 3. model (draw) \frac{4}{4}div\frac{3}{4} 4. sum of 0.7 + 0.64 5. difference of 0.94 - 0.6 6. the product of 5.32cdot4.3 7. the quotient of 45.7div1.83 8. the 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 12 students studied for a math test. questions: 1. how many students studied for 3 hours? 2. what is the most common number of hours studied? 3. how many students studied for more than 4 hours? 4. what is the range of hours studied? 5. what percent of students studied for 2 hours or less? case 2: favorite ice cream flavors a class of students voted on their favorite ice - cream flavor. the dot plot shows the results. questions: 6. which flavor is the most popular? 7. how many students voted for vanilla or mint? 8. which flavor received the least votes? 9. what is the total number of votes? 10. what fraction of the class voted for chocolate? case 3: be the analyst! dot plot: number of books read in a month questions: 11. how many students read fewer than 3 books? 12. what is the median number of books read? 13. if the student who read 4 books read 5 books instead, how would the dot - plot change? 14. which is greater, the mean or the median? explain why.

Explanation:

Step1: Solve 1.a: Convert mixed - numbers to improper fractions

$2\frac{2}{3}+1\frac{2}{5}=\frac{2\times3 + 2}{3}+\frac{1\times5+2}{5}=\frac{8}{3}+\frac{7}{5}$
Find a common denominator (15) and add: $\frac{8\times5}{3\times5}+\frac{7\times3}{5\times3}=\frac{40}{15}+\frac{21}{15}=\frac{40 + 21}{15}=\frac{61}{15}=4\frac{1}{15}$

Step2: Solve 1.b: Find a common denominator (15)

$\frac{3}{5}+\frac{2}{3}=\frac{3\times3}{5\times3}+\frac{2\times5}{3\times5}=\frac{9}{15}+\frac{10}{15}=\frac{9 + 10}{15}=\frac{19}{15}=1\frac{4}{15}$

Step3: Solve 1.c: Convert mixed - numbers to improper fractions

$4\frac{3}{7}+2\frac{1}{2}=\frac{4\times7+3}{7}+\frac{2\times2 + 1}{2}=\frac{31}{7}+\frac{5}{2}$
Find a common denominator (14) and add: $\frac{31\times2}{7\times2}+\frac{5\times7}{2\times7}=\frac{62}{14}+\frac{35}{14}=\frac{62+35}{14}=\frac{97}{14}=6\frac{13}{14}$

Step4: Solve 1.d: Find a common denominator (15)

$\frac{2}{3}-\frac{1}{5}=\frac{2\times5}{3\times5}-\frac{1\times3}{5\times3}=\frac{10}{15}-\frac{3}{15}=\frac{10 - 3}{15}=\frac{7}{15}$

Step5: Solve 2: Multiply fractions

$\frac{3}{5}\times\frac{2}{3}=\frac{3\times2}{5\times3}=\frac{6}{15}=\frac{2}{5}$
To draw a model, you can draw a rectangle divided into 5 equal parts, shade 3 of them to represent $\frac{3}{5}$, then divide those 3 shaded parts into 3 equal sub - parts and shade 2 of the sub - parts out of the 3 shaded parts. The final shaded part out of the whole rectangle represents $\frac{2}{5}$.

Step6: Solve 3: Divide fractions

$\frac{4}{4}\div\frac{3}{4}=\frac{4}{4}\times\frac{4}{3}=\frac{4\times4}{4\times3}=\frac{16}{12}=\frac{4}{3}=1\frac{1}{3}$
To draw a model, you can draw 4 equal parts (representing $\frac{4}{4}$), and then show how many groups of $\frac{3}{4}$ are in it.

Step7: Solve 4: Add decimals

$0.7+0.64 = 1.34$

Step8: Solve 5: Subtract decimals

$0.94−0.6=0.34$

Step9: Solve 6: Multiply decimals

$5.32\times4.3=5.32\times(4 + 0.3)=5.32\times4+5.32\times0.3=21.28+1.596 = 22.876$

Step10: Solve 7: Divide decimals

$45.7\div1.83=\frac{45.7}{1.83}\approx24.97$ (rounded to two decimal places)

Step11: Solve 8: Find mean, median, mode and range for data set {4,6,7,6,9,3,5,2}

1. Mean:

Sum of data values: $4 + 6+7+6+9+3+5+2=42$
Number of data values $n = 8$
Mean $\bar{x}=\frac{42}{8}=5.25$

1. Median:

Arrange data in ascending order: $2,3,4,5,6,6,7,9$
Since $n = 8$ (even), median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values. $\frac{4 + 5}{2}=4.5$

1. Mode:

The mode is 6 (it appears 2 times, more frequently than other values)

1. Range:

Range=Max - Min=$9 - 2=7$

Answer:

1.a: $4\frac{1}{15}$; 1.b: $1\frac{4}{15}$; 1.c: $6\frac{13}{14}$; 1.d: $\frac{7}{15}$; 2: $\frac{2}{5}$; 3: $1\frac{1}{3}$; 4: $1.34$; 5: $0.34$; 6: $22.876$; 7: $\approx24.97$; 8: Mean: $5.25$, Median: $4.5$, Mode: $6$, Range: $7$