Question

in 29 - 31, use the table at the right.

1. communicate and justify suppose you plot the lengths in the table on a number line. which track members long - jump length would be represented by the point closest to, but not equal to, 0 on the number line? explain.
2. delias relative long - jump length was recorded as 0. what does this mean?
3. check for reasonableness which track members did not qualify for the state championship? construct an argument to explain how you know.
4. analyze and persevere order - 6\frac{1}{4}, - 6.35, - 6\frac{1}{5}, and - 6.1 from greatest to least. explain.
5. higher order thinking tyler says there are infinitely many rational numbers between 0 and 1. do you agree? explain.
6. which could be a value for m?
7. which inequalities are true? select all that apply.

\\(\frac{13}{2}>\frac{25}{4}\\)
\\(-9.82 < - 7.6\\)
\\(-26.45>-24.8\\)
\\(-\frac{3}{5}< - \frac{1}{10}\\)
\\(-9\frac{1}{3}>4\frac{3}{4}\\)
track members long jump length relative to state qualifying distance
theresa - 5.625 in.
ann 2 in.
shirley - 3 in.
delia 0 in.

Explanation:

Step1: Analyze question 30

Delia's relative long - jump length is 0. This means her long - jump length is equal to the state qualifying distance.

Step2: Analyze question 31

Theresa's long - jump length is - 5.625 in. and Shirley's is - 3 in. Since negative values mean their jump lengths are less than the state qualifying distance, Theresa and Shirley did not qualify for the state championship.

Step3: Analyze question 32

Convert the mixed numbers to decimals: $-6\frac{1}{4}=-6.25$, $-6\frac{1}{5}=-6.2$. Then compare: $-6.1>-6.2>-6.25>-6.35$. So the order from greatest to least is $-6.1, - 6\frac{1}{5},-6\frac{1}{4},-6.35$.

Step4: Analyze question 33

A rational number is a number that can be written as $\frac{a}{b}$ where $a$ and $b$ are integers and $b
eq0$. Between 0 and 1, we can have $\frac{1}{2},\frac{1}{3},\frac{1}{4},\cdots$. There are infinitely many rational numbers of the form $\frac{1}{n}$ where $n$ is a positive integer greater than 1. So, yes, there are infinitely many rational numbers between 0 and 1.

Step5: Analyze question 34

From the number - line, $m$ is between $-\frac{3}{4}$ and $-\frac{1}{4}$. $-\frac{2}{3}\approx - 0.67$ which is between $-\frac{3}{4}=-0.75$ and $-\frac{1}{4}=-0.25$. So $m =-\frac{2}{3}$ is a possible value.

Step6: Analyze question 35

• For $\frac{13}{2}=\frac{26}{4}$, so $\frac{13}{2}>\frac{25}{4}$ is true.
• For negative numbers, the larger the absolute value, the smaller the number. Since $|-9.82| = 9.82$ and $|-7.6| = 7.6$, $-9.82<-7.6$ is true.
• Since $|-26.45| = 26.45$ and $|-24.8| = 24.8$, $-26.45<-24.8$, so $-26.45>-24.8$ is false.
• Convert to decimals: $-\frac{3}{5}=-0.6$ and $-\frac{1}{10}=-0.1$, so $-\frac{3}{5}<-\frac{1}{10}$ is true.
• $-9\frac{1}{3}$ is negative and $4\frac{3}{4}$ is positive, so $-9\frac{1}{3}>4\frac{3}{4}$ is false.

Answer:

1. It means Delia's long - jump length is equal to the state qualifying distance.
2. Theresa and Shirley did not qualify because their long - jump lengths ( - 5.625 in and - 3 in) are less than the state qualifying distance.
3. $-6.1, - 6\frac{1}{5},-6\frac{1}{4},-6.35$
4. Yes, because there are infinitely many rational numbers of the form $\frac{1}{n}$ where $n$ is a positive integer greater than 1 between 0 and 1.
5. C. $-\frac{2}{3}$
6. $\frac{13}{2}>\frac{25}{4}$, $-9.82<-7.6$, $-\frac{3}{5}<-\frac{1}{10}$