Mentally compute the number to fill in the blank in each of the following equations. Complete parts (a) through (d) below. a. $$ 25.2 \cdot 6.0=12.6 \cdot 12 $$ (Type an integer or a decimal.) b. $$ 25.2 \div 0.4=12.6 \div 0.2 $$ (Type an integer or a decimal.) c. $$ a b=\left(a \cdot 10^{-5}\right) \cdot \square $$ (Simplify your answer.)

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Let's solve each part step by step:

### **a. $$ 25.2 \cdot 6.0 = 12.6 \cdot \square $$**

We need to find the value of the blank ($$\square$$).

$$
25.2 \times 6.0 = 12.6 \times \square
$$

First, compute $$25.2 \times 6.0$$:

$$
25.2 \times 6 = 151.2
$$

Now, set up the equation to solve for $$\square$$:

$$
151.2 = 12.6 \times \square
$$

$$
\square = \frac{151.2}{12.6} = 12
$$

**Answer:** $$12$$

---

### **b. $$ 25.2 \div 0.4 = 12.6 \div \square $$**

We need to find the value of the blank ($$\square$$).

$$
\frac{25.2}{0.4} = \frac{12.6}{\square}
$$

First, compute $$\frac{25.2}{0.4}$$:

$$
\frac{25.2}{0.4} = 63
$$

Now, set up the equation to solve for $$\square$$:

$$
63 = \frac{12.6}{\square}
$$

$$
\square = \frac{12.6}{63} = 0.2
$$

**Answer:** $$0.2$$

---

### **c. $$ a b = \left(a \cdot 10^{-5}\right) \cdot \square $$**

We need to express $$\square$$ in terms of $$b$$.

Starting with:

$$
a b = \left(a \cdot 10^{-5}\right) \cdot \square
$$

Divide both sides by $$\left(a \cdot 10^{-5}\right)$$:

$$
\square = \frac{a b}{a \cdot 10^{-5}} = b \cdot 10^{5}
$$

**Answer:** $$b \times 10^{5}$$
a. 12 b. 0.2 c. $$ b \times 10^{5} $$

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