Collection of basic math problems displayed on a blackboard, covering topics like arithmetic, algebra, fractions, and square roots, ideal for educational purposes.

Let's solve each of the math problems shown in the image step by step.

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1. $-9 - (-4)$

Subtracting a negative is the same as adding:

$$
-9 - (-4) = -9 + 4 = -5
$$

✔ Answer: $-5$

---

2. $12 \times 6 - 5$

Follow order of operations (PEMDAS): multiplication first, then subtraction.

$$
12 \times 6 = 72 \\
72 - 5 = 67
$$

✔ Answer: $67$

---

3. $\frac{2}{3} + \frac{5}{4}$

Find a common denominator. The least common denominator of 3 and 4 is 12.

$$
\frac{2}{3} = \frac{8}{12}, \quad \frac{5}{4} = \frac{15}{12} \\
\frac{8}{12} + \frac{15}{12} = \frac{23}{12}
$$

✔ Answer: $\frac{23}{12}$ or $1\frac{11}{12}$

---

4. $-\sqrt{18}$

Simplify $\sqrt{18}$:

$$
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}
$$

So:
$$
-\sqrt{18} = -3\sqrt{2}
$$

✔ Answer: $-3\sqrt{2}$

---

5. $5x + 4 = 0$

Solve for $x$:

$$
5x = -4 \\
x = -\frac{4}{5}
$$

✔ Answer: $x = -\frac{4}{5}$

---

6. $81^{3/4}$

This means: take the 4th root of 81, then raise to the 3rd power.

First, note that:
$$
81 = 3^4
$$

So:
$$
81^{3/4} = (3^4)^{3/4} = 3^{4 \cdot (3/4)} = 3^3 = 27
$$

✔ Answer: $27$

---

7. $30\%$ of $200$?

Convert percent to decimal and multiply:

$$
30\% = 0.30 \\
0.30 \times 200 = 60
$$

✔ Answer: $60$

---

8. Long division: $6 \div 39$

Wait — this is written as $6 \overline{)39}$, which means "39 divided by 6".

So:
$$
39 \div 6 = 6 \text{ remainder } 3
$$

Because:
$$
6 \times 6 = 36 \\
39 - 36 = 3
$$

So:
$$
39 \div 6 = 6 \text{ R } 3
$$

Or as a decimal: $6.5$

But since it shows the process with subtraction, we can write:

$$
\begin{array}{r}
6 \\
6 \overline{)39} \\
-36 \\
\hline
3 \\
\end{array}
$$

✔ Answer: $6$ remainder $3$, or $6.5$ if decimal.

---

9. $\sqrt{1.6 \times 10^{-7}}$

We want the square root of $1.6 \times 10^{-7}$.

Use:
$$
\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}
$$

So:
$$
\sqrt{1.6 \times 10^{-7}} = \sqrt{1.6} \times \sqrt{10^{-7}} = \sqrt{1.6} \times 10^{-3.5}
$$

But better to write $10^{-7}$ as $(10^{-7})$, so:
$$
\sqrt{10^{-7}} = 10^{-7/2} = 10^{-3.5} = 10^{-3} \times 10^{-0.5} = 0.001 \times \frac{1}{\sqrt{10}} \approx 0.001 \times 0.3162 = 3.162 \times 10^{-4}
$$

Now $\sqrt{1.6} \approx 1.2649$

So:
$$
\sqrt{1.6 \times 10^{-7}} \approx 1.2649 \times 3.162 \times 10^{-4} \quad \text{Wait — no!}
$$

Actually:
$$
\sqrt{1.6 \times 10^{-7}} = \sqrt{1.6} \times \sqrt{10^{-7}} = \sqrt{1.6} \times 10^{-3.5}
$$

But $10^{-3.5} = 10^{-3} \times 10^{-0.5} = 0.001 \times \frac{1}{\sqrt{10}} \approx 0.001 \times 0.3162 = 3.162 \times 10^{-4}$

And $\sqrt{1.6} \approx 1.2649$

So total:
$$
\sqrt{1.6 \times 10^{-7}} \approx 1.2649 \times 3.162 \times 10^{-4}? \quad \text{No — wait!}
$$

Actually:
$$
\sqrt{1.6 \times 10^{-7}} = \sqrt{1.6} \times 10^{-3.5}
$$

But $10^{-3.5} = 10^{-3} \times 10^{-0.5} = 0.001 \times 0.3162 = 3.162 \times 10^{-4}$

So:
$$
\sqrt{1.6} \approx 1.2649 \\
1.2649 \times 3.162 \times 10^{-4} \quad \text{No — that's wrong.}
$$

Wait — let’s do it correctly:

$$
\sqrt{1.6 \times 10^{-7}} = \sqrt{1.6} \times \sqrt{10^{-7}} = \sqrt{1.6} \times 10^{-3.5}
$$

But $10^{-3.5} = 10^{-3} \times 10^{-0.5} = 0.001 \times \frac{1}{\sqrt{10}} \approx 0.001 \times 0.3162 = 3.162 \times 10^{-4}$

Then:
$$
\sqrt{1.6} \approx 1.2649 \\
\Rightarrow \text{Total} \approx 1.2649 \times 3.162 \times 10^{-4}? \quad \text{No — it's just } \sqrt{1.6} \times 10^{-3.5}
$$

Better to write:
$$
\sqrt{1.6 \times 10^{-7}} = \sqrt{1.6} \times 10^{-3.5} \approx 1.2649 \times 10^{-3.5}
$$

But $10^{-3.5} = 3.162 \times 10^{-4}$, so:

$$
1.2649 \times 3.162 \times 10^{-4} \approx ? \quad \text{No — actually:}
$$

Wait — simpler: write $1.6 \times 10^{-7} = 16 \times 10^{-8}$

Then:
$$
\sqrt{16 \times 10^{-8}} = \sqrt{16} \times \sqrt{10^{-8}} = 4 \times 10^{-4} = 0.0004
$$

That’s much cleaner!

Yes:
$$
1.6 \times 10^{-7} = 16 \times 10^{-8} \\
\sqrt{16 \times 10^{-8}} = \sqrt{16} \times \sqrt{10^{-8}} = 4 \times 10^{-4} = 0.0004
$$

✔ Answer: $0.0004$ or $4 \times 10^{-4}$

---

10. $x^2 + 5x + 6 = 0$

Factor the quadratic:

We need two numbers that multiply to 6 and add to 5 → 2 and 3.

$$
x^2 + 5x + 6 = (x + 2)(x + 3) = 0
$$

So:
$$
x = -2 \quad \text{or} \quad x = -3
$$

✔ Answer: $x = -2$ or $x = -3$

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## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| $-9 - (-4)$ | $-5$ |
| $12 \times 6 - 5$ | $67$ |
| $\frac{2}{3} + \frac{5}{4}$ | $\frac{23}{12}$ |
| $-\sqrt{18}$ | $-3\sqrt{2}$ |
| $5x + 4 = 0$ | $x = -\frac{4}{5}$ |
| $81^{3/4}$ | $27$ |
| $30\%$ of $200$ | $60$ |
| $39 \div 6$ | $6$ R $3$ or $6.5$ |
| $\sqrt{1.6 \times 10^{-7}}$ | $4 \times 10^{-4}$ or $0.0004$ |
| $x^2 + 5x + 6 = 0$ | $x = -2$ or $x = -3$ |

Let me know if you'd like a visual explanation or practice exercises! 😊