Try thinking of \(\displaystyle \overline{AE}\) as a number line with endpoint \(\displaystyle A\) at 0, and endpoint \(\displaystyle E\) at 8. \(\displaystyle C\), the midpoint of \(\displaystyle \overline{AE}\), would be at 4. \(\displaystyle B\), the midpoint of \(\displaystyle \overline{AC}\), would be at 2; \(\displaystyle D\), the midpoint of \(\displaystyle \overline{BE}\) - whose endpoints are at 2 and 8 - would be at 5. 

\(\displaystyle AE = 8\); \(\displaystyle DE = 8-5 = 3\)

\(\displaystyle \overline{DE}\) is \(\displaystyle \frac{DE}{AE} = \frac{3}{8}\) of \(\displaystyle \overline{AE}\).

Try thinking of \(\displaystyle \overline{AE}\) as a number line with endpoint \(\displaystyle A\) at 0, and endpoint \(\displaystyle E\) at 8. \(\displaystyle C\), the midpoint of \(\displaystyle \overline{AE}\), would be at 4. \(\displaystyle B\), the midpoint of \(\displaystyle \overline{AC}\), would be at 2; \(\displaystyle D\), the midpoint of \(\displaystyle \overline{BE}\) - whose endpoints are at 2 and 8 - would be at 5. 

\(\displaystyle AE = 8\); \(\displaystyle AD = 5\)

Therefore, 

\(\displaystyle \overline{AD}\) is \(\displaystyle \frac{AD}{AE } \cdot 100 \% = \frac{5}{8} \cdot 100 \% = 62\frac{1}{2} \%\) of \(\displaystyle \overline{AE}\)

Convert \(\displaystyle \frac{5}{9}\) to a decimal by dividing 5 by 9.

\(\displaystyle \frac{5}{9} = 0.555...\), so it falls between 0.55 and 0.56 on the number line. Point \(\displaystyle B\) is the correct response.

\(\displaystyle \pi \approx 3.14\), so

\(\displaystyle 3.1 < \pi < 3.2\)

\(\displaystyle 3.1 - 3< \pi- 3 < 3.2 - 3\)

\(\displaystyle 0.1 < \pi- 3 < 0.2\)

Point \(\displaystyle B\) is in this range, so this is the correct response.

\(\displaystyle \pi \approx 3.14\), so

\(\displaystyle 3.1 < \pi < 3.15\)

\(\displaystyle 2 \times 3.1 < 2 \times \pi < 2 \times 3.15\)

\(\displaystyle 6.2 < 2 \pi < 6.3\)

Point \(\displaystyle C\) falls between 6.2 and 6.3 on the number line, so this is the correct choice.

\(\displaystyle \pi \approx 3.14\), so \(\displaystyle 4 - \pi \approx 4 - 3.14 = 0.86\).

Therefore, \(\displaystyle 0.8< 4 - \pi < 0.9\).

Of the four points, \(\displaystyle D\) falls in this range, so it is the correct response.

On a number line, negative numbers lie to the left of zero and positive numbers lie to the right. To count the distance, count the slots between the two numbers:

There are TWO units between -2 and 0, and there are SEVEN units between 0 and 7. Together, there are NINE units between them.

On a number line, the negative numbers lie to the left of zero and positive numbers lie to the right. To visualize the distance between numbers, look at the units:

-3 and 0 are 3 units apart.

-1 and 2 are 3 units apart

-2 and 2 are 4 units apart. This is the greatest distance.

Looking at a number line, you can visualize the distance between positive and negative numbers:

There are THREE units between -2 and 1

There are SIX units between 1 and 7.

There are SEVEN units between -2 and 5, so this is the greatest distance.

The first step is to find out the values of A and B by counting the units between the given numbers.

A) The distance between -2 and 5 on a number line is 7.

B) The distance between -1 and 3 on a number line is 4.

\(\displaystyle A - B = 7 - 4 = 3\)