1. circle all of the following numbers are equal to $-\frac{4}{5}$?
$\frac{4}{5}, -\frac{5}{4}, \frac{-4}{5}, \frac{-4}{-5}, -\frac{8}{10}$

2. write the rational number represented by each letter as a decimal.
number line with -2, -1, 0, 1, points a, d, b, c
a:__________ b:__________ c:__________ d:__________

3. write the rational number represented by each letter as a fraction.
number line with -2, -1, 0, 1, points a, b, c
a:__________ b:__________ c:__________ d:__________

4. sketch a number line and mark each rational number on it.
order the numbers from greatest to least.
$-2.25, \frac{5}{4}, -1.5, -\frac{1}{8}, 0.9$

5. in each pair, circle the rational number is greater? explain how you know.
a) $-7.3, -7.2$
b) $\frac{4}{5}, \frac{5}{4}$
c) $1.2, -1.3$
d) $-\frac{10}{13}, -\frac{10}{11}$

6. diver a is 2.3 m below sea level.
diver b is 1.7 m below sea level.
diver c is 3.2 m below sea level.

a) draw a vertical number line to show the location of the divers.
b) which diver is farthest from the surface? explain your thinking.

Question

1. circle all of the following numbers are equal to $-\frac{4}{5}$?
$\frac{4}{5}, -\frac{5}{4}, \frac{-4}{5}, \frac{-4}{-5}, -\frac{8}{10}$

2. write the rational number represented by each letter as a decimal.
number line with -2, -1, 0, 1, points a, d, b, c
a:__________ b:__________ c:__________ d:__________

3. write the rational number represented by each letter as a fraction.
number line with -2, -1, 0, 1, points a, b, c
a:__________ b:__________ c:__________ d:__________

4. sketch a number line and mark each rational number on it.
order the numbers from greatest to least.
$-2.25, \frac{5}{4}, -1.5, -\frac{1}{8}, 0.9$

5. in each pair, circle the rational number is greater? explain how you know.
a) $-7.3, -7.2$
b) $\frac{4}{5}, \frac{5}{4}$
c) $1.2, -1.3$
d) $-\frac{10}{13}, -\frac{10}{11}$

6. diver a is 2.3 m below sea level.
diver b is 1.7 m below sea level.
diver c is 3.2 m below sea level.

a) draw a vertical number line to show the location of the divers.
b) which diver is farthest from the surface? explain your thinking.

Accepted Answer

### Question 1
# Explanation:
## Step1: Simplify each fraction
- $\frac{4}{5}$: Positive, not equal to $-\frac{4}{5}$.
- $-\frac{5}{4}$: Simplify, $-\frac{5}{4}
eq -\frac{4}{5}$.
- $\frac{-4}{5}$: Equals $-\frac{4}{5}$.
- $\frac{-4}{-5}$: Simplify to $\frac{4}{5}$, not equal.
- $-\frac{8}{10}$: Simplify by dividing numerator and denominator by 2: $-\frac{4}{5}$.

# Answer: $\frac{-4}{5}$, $-\frac{8}{10}$

### Question 2 (Assuming each segment between integers is divided into 10 parts for simplicity, adjust based on actual number line divisions. Here, let's assume between -2 and -1, -1 and 0, 0 and 1, there are 10 small ticks each, so each tick is 0.1)
# Explanation:
## Step1: Find A
A is 2 ticks to the right of -2? Wait, no, looking at the number line: from -2, moving right, A is at -2 + 0.8? Wait, maybe better: between -2 and -1, how many ticks? Let's see, from -2 to -1, the distance is 1. If there are, say, 10 ticks (so each is 0.1), then A is at -2 + 0.8? Wait, no, the number line: -2, then A, then towards -1. Wait, maybe the number line has, between -2 and -1, 10 intervals? So each interval is 0.1. So A is at -1.8? Wait, no, let's re-examine:

Wait, the number line: -2, then A, then several ticks, then -1, then D, then ticks, then B near 0, then C near 1.

Wait, maybe between -2 and -1, there are 10 small marks, so each mark is 0.1. So A is 2 marks to the right of -2? No, -2 + 0.2? No, that would be -1.8? Wait, no, -2 + 0.2 is -1.8? Wait, no: -2 + 0.1 is -1.9, +0.2 is -1.8, etc. Wait, maybe the number line is divided into, say, 5 parts between -2 and -1? Let's assume that between -2 and -1, there are 5 intervals, so each is 0.2. Then A is at -2 + 0.4 = -1.6? Wait, this is ambiguous without exact tick marks. But let's proceed with common number line divisions.

Alternatively, maybe the number line has:

- Between -2 and -1: 10 units (each 0.1), so A is at -1.8 (2 units left of -1.6? No, maybe the first tick after -2 is -1.9, then -1.8, etc. Let's assume:

A: -1.8 (if 2 ticks right of -2, each 0.1)

B: -0.1 (1 tick left of 0)

C: 0.7 (7 ticks right of 0)

D: -0.9 (1 tick right of -1)

But this is an assumption. Alternatively, if between -2 and -1, there are 5 intervals (each 0.2), then:

A: -2 + 0.4 = -1.6

D: -1 + 0.1 = -0.9 (if 1 interval right of -1, each 0.1)

B: -0.1 (1 interval left of 0, each 0.1)

C: 0.7 (7 intervals right of 0, each 0.1)

But since the problem is to write as decimal, let's use standard divisions. Let's assume:

A: -1.8 (if 2 ticks from -2 towards -1, each 0.1)

B: -0.1 (1 tick left of 0)

C: 0.7 (7 ticks right of 0)

D: -0.9 (1 tick right of -1)

# Answer:
A: -1.8
B: -0.1
C: 0.7
D: -0.9

### Question 3 (Assuming number line with -2 to -1 divided into 5 parts, each 0.2, so fraction is 1/5 per part; -1 to 0 divided into 5 parts, 0 to 1 divided into 5 parts)
# Explanation:
## Step1: Find A
A is 1 part right of -2, so -2 + 0.2 = -1.8 = $-\frac{9}{5}$? Wait, no, if between -2 and -1, there are 5 intervals, each is 1/5. So A is at -2 + 1*(1/5) = -2 + 0.2 = -1.8 = $-\frac{9}{5}$? Wait, no, -2 is -10/5, so -10/5 + 1/5 = -9/5.

B: Between -1 and 0, 2 parts right of -1, so -1 + 2*(1/5) = -3/5? Wait, no, -1 is -5/5, so -5/5 + 2/5 = -3/5? Wait, no, if 0 is 0, -1 is -5/5, so each part is 1/5. So B is at -5/5 + 2/5 = -3/5? Wait, no, maybe between -1 and 0, there are 4 parts? No, the number line: -2, A, then ticks, -1, B, ticks, 0, C, ticks, 1. Let's assume between -2 and -1: 5 intervals (each 1/5), so A is at -2 + 1/5 = -9/5.

B: Between -1 and 0: 2 intervals (each 1/5), so -1 + 2/5 = -3/5.

C: Between 0 and 1: 2 intervals (each 1/5), so 0 + 2/5 = 2/5? Wait, no, the number line shows C near 1, maybe 3/5? Wait, this is ambiguous. Alternatively, if between 0 and 1, there are 5 intervals, each 1/5, so C is at 3/5.

D: Not present in the number line (the original has D crossed out, maybe a typo). So:

A: $-\frac{9}{5}$ (or -1.8)

B: $-\frac{3}{5}$ (or -0.6)

C: $\frac{2}{5}$ (or 0.4) – but this depends on the number line.

But let's use standard:

If between -2 and -1, 5 parts (each 1/5), A is at -2 + 1/5 = -9/5.

Between -1 and 0, 5 parts, B is at -1 + 2/5 = -3/5.

Between 0 and 1, 5 parts, C is at 0 + 2/5 = 2/5.

# Answer:
A: $-\frac{9}{5}$
B: $-\frac{3}{5}$
C: $\frac{2}{5}$
D: (Not present, maybe a typo)

### Question 4
# Explanation:
## Step1: Convert all numbers to decimals for easier comparison
- $-2.25$: Already decimal.
- $\frac{5}{4} = 1.25$
- $-1.5$: Already decimal.
- $-\frac{1}{8} = -0.125$
- $0.9$: Already decimal.

## Step2: Order from greatest to least
Positive numbers: $1.25$ (5/4), $0.9$
Negative numbers: $-0.125$ (-1/8), $-1.5$, $-2.25$ (since closer to 0 is greater)

So order: $\frac{5}{4}$, $0.9$, $-\frac{1}{8}$, $-1.5$, $-2.25$

## Step3: Sketch number line
Draw a horizontal line, mark -3, -2, -1, 0, 1, 2.
Mark -2.25 (left of -2), -1.5 (midway -1 and -2), -0.125 (close to 0 left), 0.9 (close to 1 left), 1.25 (right of 1).

# Answer:
Number line: Mark -2.25, -1.5, -0.125, 0.9, 1.25.
Order (greatest to least): $\frac{5}{4}$, $0.9$, $-\frac{1}{8}$, $-1.5$, $-2.25$

### Question 5
#### Part a) -7.3, -7.2
# Explanation:
For negative numbers, the one closer to 0 is greater. -7.2 is closer to 0 than -7.3, so -7.2 is greater.

# Answer: Circle -7.2

#### Part b) $\frac{4}{5}$, $\frac{5}{4}$
# Explanation:
Convert to decimals: $\frac{4}{5} = 0.8$, $\frac{5}{4} = 1.25$. Since 1.25 > 0.8, $\frac{5}{4}$ is greater.

# Answer: Circle $\frac{5}{4}$

#### Part c) 1.2, -1.3
# Explanation:
Positive numbers are greater than negative numbers. 1.2 is positive, -1.3 is negative, so 1.2 is greater.

# Answer: Circle 1.2

#### Part d) $-\frac{10}{13}$, $-\frac{10}{11}$
# Explanation:
For negative fractions with same numerator, the one with larger denominator is closer to 0 (since $\frac{10}{13} \approx 0.769$, $\frac{10}{11} \approx 0.909$; so $-\frac{10}{13}$ is closer to 0, hence greater).

# Answer: Circle $-\frac{10}{13}$

### Question 6
#### Part a) Vertical number line
# Explanation:
Draw a vertical line, mark 0 (sea level) at the top, negative numbers below (depth). Mark -2.3 (Diver A), -1.7 (Diver B), -3.2 (Diver C) below 0.

#### Part b) Farthest from surface
# Explanation:
Depth is the absolute value. |-2.3| = 2.3, |-1.7| = 1.7, |-3.2| = 3.2. Since 3.2 is largest, Diver C is farthest.

# Answer:
a) Vertical number line: 0 at top, -1, -2, -3 below. Mark -1.7 (B), -2.3 (A), -3.2 (C) from top to bottom.
b) Diver C is farthest, as 3.2 m depth is greatest (largest absolute value).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Simplify each fraction

Step1: Find A

Step1: Find A

Answer:

Question 2 (Assuming each segment between integers is divided into 10 parts for simplicity, adjust based on actual number line divisions. Here, let's assume between -2 and -1, -1 and 0, 0 and 1, there are 10 small ticks each, so each tick is 0.1)