Math worksheet for comparing and ordering fractions and decimals using a number line.

Let's solve each problem step by step by converting fractions and decimals to their decimal equivalents (where needed), comparing them, and placing them correctly on the number line.

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Problem 1:

Numbers:
$$
\frac{2}{3},\quad -\frac{3}{4},\quad \frac{2}{9},\quad -\frac{1}{3}
$$

#### Step 1: Convert to decimals:
- $\frac{2}{3} = 0.\overline{6} \approx 0.67$
- $-\frac{3}{4} = -0.75$
- $\frac{2}{9} \approx 0.222... \approx 0.22$
- $-\frac{1}{3} \approx -0.333... \approx -0.33$

#### Step 2: Order from smallest to largest:
- $-0.75$ → $-\frac{3}{4}$
- $-0.33$ → $-\frac{1}{3}$
- $0.22$ → $\frac{2}{9}$
- $0.67$ → $\frac{2}{3}$

So the order is:
$$
-\frac{3}{4} < -\frac{1}{3} < \frac{2}{9} < \frac{2}{3}
$$

#### Step 3: Place on number line:
From left to right:
1. $-\frac{3}{4}$ → between $-1$ and $0$, closer to $-1$
2. $-\frac{1}{3}$ → between $-1$ and $0$, closer to $0$
3. $\frac{2}{9}$ → just above $0$, near $0.2$
4. $\frac{2}{3}$ → between $0$ and $1$, near $0.7$

✔ So fill in the boxes from left to right:
- First box: $-\frac{3}{4}$
- Second box: $-\frac{1}{3}$
- Third box: $\frac{2}{9}$
- Fourth box: $\frac{2}{3}$

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Problem 2:

Numbers:
$$
-\frac{7}{2},\quad 0.6,\quad \frac{4}{3},\quad -1.25
$$

#### Step 1: Convert to decimals:
- $-\frac{7}{2} = -3.5$
- $0.6$ → already a decimal
- $\frac{4}{3} \approx 1.333... \approx 1.33$
- $-1.25$ → already a decimal

#### Step 2: Order from smallest to largest:
- $-3.5$ → $-\frac{7}{2}$
- $-1.25$
- $0.6$
- $1.33$ → $\frac{4}{3}$

So:
$$
-\frac{7}{2} < -1.25 < 0.6 < \frac{4}{3}
$$

#### Step 3: Place on number line:
- $-\frac{7}{2} = -3.5$: between $-4$ and $-3$, halfway
- $-1.25$: between $-2$ and $-1$, closer to $-1$
- $0.6$: between $0$ and $1$, closer to $1$
- $\frac{4}{3} \approx 1.33$: between $1$ and $2$, closer to $1$

✔ Fill in boxes from left to right:
1. $-\frac{7}{2}$
2. $-1.25$
3. $0.6$
4. $\frac{4}{3}$

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Problem 3:

Numbers:
$$
-\frac{6}{3},\quad -\frac{3}{5},\quad -\frac{8}{3},\quad -\frac{2}{3}
$$

#### Step 1: Simplify and convert to decimals:
- $-\frac{6}{3} = -2$
- $-\frac{3}{5} = -0.6$
- $-\frac{8}{3} \approx -2.666... \approx -2.67$
- $-\frac{2}{3} \approx -0.666... \approx -0.67$

#### Step 2: Order from smallest to largest:
- $-2.67$ → $-\frac{8}{3}$
- $-2$ → $-\frac{6}{3}$
- $-0.67$ → $-\frac{2}{3}$
- $-0.6$ → $-\frac{3}{5}$

Note: On the number line, more negative numbers are further left.

So:
$$
-\frac{8}{3} < -\frac{6}{3} < -\frac{2}{3} < -\frac{3}{5}
$$

Wait! Let’s double-check:
- $-2.67 < -2 < -0.67 < -0.6$ → Yes, correct.

But note: $-0.6 > -0.67$, so $-\frac{3}{5} > -\frac{2}{3}$

So final order:
$$
-\frac{8}{3} < -\frac{6}{3} < -\frac{2}{3} < -\frac{3}{5}
$$

#### Step 3: Place on number line:
- $-\frac{8}{3} \approx -2.67$: between $-3$ and $-2$, closer to $-3$
- $-\frac{6}{3} = -2$: exactly at $-2$
- $-\frac{2}{3} \approx -0.67$: between $-1$ and $0$, closer to $-1$
- $-\frac{3}{5} = -0.6$: between $-1$ and $0$, closer to $0$

✔ Fill in boxes from left to right:
1. $-\frac{8}{3}$
2. $-\frac{6}{3}$
3. $-\frac{2}{3}$
4. $-\frac{3}{5}$

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✔ Final Answers:

#### 1) From left to right:
- $-\frac{3}{4}$
- $-\frac{1}{3}$
- $\frac{2}{9}$
- $\frac{2}{3}$

#### 2) From left to right:
- $-\frac{7}{2}$
- $-1.25$
- $0.6$
- $\frac{4}{3}$

#### 3) From left to right:
- $-\frac{8}{3}$
- $-\frac{6}{3}$
- $-\frac{2}{3}$
- $-\frac{3}{5}$

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🔍 Summary:

To solve these problems:
1. Convert all numbers to decimals for easier comparison.
2. Order them from least to greatest (left to right on number line).
3. Place them accordingly, noting that negatives go left of zero, and larger magnitude negatives are further left.

Let me know if you'd like this as a printable answer sheet!