Question

1. what integer is missing from the number line below?
2. what integer is missing from the number line below?

i can locate and compare rational numbers.

1. what rational number is missing from the number line below?
2. what is a reasonable estimate for the missing rational number below? why?
3. use the symbols <, >, or = to make each statement true.

a. $-\frac{6}{4}$ ______ $-\frac{3}{4}$
b. $\frac{2}{3}$ ______ $\frac{3}{8}$
c. $-\frac{5}{6}$ ______ $-\frac{1}{6}$

1. use the symbols <, >, or = to make each statement true.

a. -8.7 ______ -7.8
b. 3.29 ______ 3.09
c. -2.8 ______ -1.5
d. -17 ______ -17.0

Explanation:

Step1: Find number line 14 interval

The distance between -16 and -8 is $-8 - (-16) = 8$, with 2 intervals, so each interval is $\frac{8}{2}=4$.

Step2: Calculate missing value 14

The mark is 1 interval right of -8: $-8 + 4 = -4$.

Step3: Find number line 15 interval

Distance between -10 and -5 is $-5 - (-10)=5$, with 1 interval, so each interval is 5. The mark is 1 interval right of -10: $-10 + 5 = -7$.

Step4: Find number line 16 interval

Distance between -1 and 0 is $0 - (-1)=1$, with 2 intervals, so each interval is $\frac{1}{2}=0.5$. The mark is 1 interval right of -1: $-1 + 0.5 = -0.5 = -\frac{1}{2}$.

Step5: Estimate number line 17 value

The segment from -2 to 0 is split roughly into 2 equal parts, so the midpoint is $\frac{-2 + 0}{2} = -1$.

Step6: Compare fractions for 18a

For negative fractions, larger numerator means smaller value: $-\frac{6}{4} < -\frac{3}{4}$

Step7: Compare fractions for 18b

Convert to common denominator: $\frac{2}{3}=\frac{16}{24}$, $\frac{3}{8}=\frac{9}{24}$, so $\frac{16}{24} > \frac{9}{24}$

Step8: Compare fractions for 18c

For negative fractions, larger numerator means smaller value: $-\frac{5}{6} < -\frac{1}{6}$

Step9: Compare decimals for 19a

On number line, -8.7 is left of -7.8: $-8.7 < -7.8$

Step10: Compare decimals for 19b

3.29 has larger tenths place: $3.29 > 3.09$

Step11: Compare decimals for 19c

-2.8 is left of -1.5 on number line: $-2.8 < -1.5$

Step12: Compare values for 19d

-17 and -17.0 are equal: $-17 = -17.0$

Answer:

1. $-4$
2. $-7$
3. $-\frac{1}{2}$ (or $-0.5$)
4. $-1$ (it is the midpoint of -2 and 0, splitting the segment into two equal parts)

18.
a. $<$
b. $>$
c. $<$
19.
a. $<$
b. $>$
c. $<$
d. $=$