d) $$ 18532-6732 $$ 7. Use long multiplication to multiply the following and check the answers on your calculator: a) $$ 2189 imes 21 $$

Question

d) $$ 18532-6732 $$ 7. Use long multiplication to multiply the following and check the answers on your calculator: a) $$ 2189 	imes 21 $$

UpStudy AI · Accepted Answer

Certainly! Let's solve each problem step by step.

---

**Problem d)**  
$$ 18,\!532 - 6,\!732 $$

**Solution:**  
Subtract the smaller number from the larger number.

$$
\begin{align*}
18,\!532 \
- \ 6,\!732 \
\hline
\end{align*}
$$

Subtract digit by digit from right to left:

1. **Units place:** $$2 - 2 = 0$$
2. **Tens place:** $$3 - 3 = 0$$
3. **Hundreds place:** $$5 - 7$$  
   Since 5 is less than 7, borrow 1 from the thousands place:
   $$
   15 - 7 = 8
   $$
4. **Thousands place:** $$ (8 - 1) - 6 = 1 $$  
   (We borrowed 1 in the previous step)

So, the result is:

$$
18,\!532 - 6,\!732 = 11,\!800
$$

---

**Problem 7.a)**  
**Use long multiplication to multiply the following and check the answer on your calculator:**
$$ 2,\!189 \times 21 $$

**Solution:**

**Step 1: Set Up the Multiplication**

$$
\begin{array}{r}
\phantom{0}2,\!189 \
\times \phantom{0}21 \
\hline
\end{array}
$$

**Step 2: Multiply by the Units Digit (1) of the Second Number**

$$
2,\!189 \times 1 = 2,\!189
$$

Write this down:

$$
\begin{array}{r}
\phantom{0}2,\!189 \
\times \phantom{0}21 \
\hline
\phantom{0}2,\!189 \quad \text{(This is } 2,\!189 \times 1\text{)} \
\end{array}
$$

**Step 3: Multiply by the Tens Digit (2) of the Second Number**

Since the digit is in the tens place, multiply by 10:

$$
2,\!189 \times 20 = 43,\!780
$$

Write this down, shifted one place to the left:

$$
\begin{array}{r}
\phantom{0}2,\!189 \
\times \phantom{0}21 \
\hline
\phantom{00}2,\!189 \
+43,\!780 \quad \text{(This is } 2,\!189 \times 20\text{)} \
\hline
\end{array}
$$

**Step 4: Add the Two Products Together**

$$
2,\!189 \
+43,\!780 \
\hline
45,\!969 \
\end{align*}
$$

**Final Result:**
$$
2,\!189 \times 21 = 45,\!969
$$

**Step 5: Verify with Calculator**

Using a calculator to multiply $$2,\!189 \times 21$$:

$$
2,\!189 \times 21 = 45,\!969
$$

The calculated result matches the long multiplication method.

---

Feel free to ask if you have any more questions or need further assistance!
**Problem d)** $$ 18,\!532 - 6,\!732 = 11,\!800 $$ **Problem 7.a)** $$ 2,\!189 \times 21 = 45,\!969 $$

d) \( 18532-6732 \) 7. Use long multiplication to multiply the following and check the answers on your calculator: a) \( 2189 \times 21 \)

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