Students can sharpen their arithmetic skills by solving these 18 double-digit multiplication problems on scratch paper.

Problem Description:

The task involves solving a series of double-digit multiplication problems. The goal is to multiply the given pairs of two-digit numbers and provide the correct products.

Solution Approach:

We will solve each multiplication problem step by step using the standard algorithm for multiplication. Here's how we proceed:

1. Write down the two numbers to be multiplied.
2. Multiply the second number (the multiplier) by each digit of the first number (the multiplicand), starting from the rightmost digit.
3. Shift the result one place to the left for each new row as you move to the next digit in the multiplier.
4. Add up all the resulting rows to get the final product.

Let's solve each problem systematically.

---

Problem 1: \( 52 \times 16 \)

\[
\begin{array}{r}
52 \\
\times 16 \\
\hline
312 \quad \text{(52 × 6)} \\
+ 520 \quad \text{(52 × 1, shifted one place to the left)} \\
\hline
832 \\
\end{array}
\]
Answer: \( 832 \)

---

Problem 2: \( 83 \times 47 \)

\[
\begin{array}{r}
83 \\
\times 47 \\
\hline
581 \quad \text{(83 × 7)} \\
+ 3320 \quad \text{(83 × 4, shifted one place to the left)} \\
\hline
3901 \\
\end{array}
\]
Answer: \( 3901 \)

---

Problem 3: \( 46 \times 14 \)

\[
\begin{array}{r}
46 \\
\times 14 \\
\hline
184 \quad \text{(46 × 4)} \\
+ 460 \quad \text{(46 × 1, shifted one place to the left)} \\
\hline
644 \\
\end{array}
\]
Answer: \( 644 \)

---

Problem 4: \( 96 \times 23 \)

\[
\begin{array}{r}
96 \\
\times 23 \\
\hline
288 \quad \text{(96 × 3)} \\
+ 1920 \quad \text{(96 × 2, shifted one place to the left)} \\
\hline
2208 \\
\end{array}
\]
Answer: \( 2208 \)

---

Problem 5: \( 73 \times 71 \)

\[
\begin{array}{r}
73 \\
\times 71 \\
\hline
73 \quad \text{(73 × 1)} \\
+ 5110 \quad \text{(73 × 7, shifted one place to the left)} \\
\hline
5183 \\
\end{array}
\]
Answer: \( 5183 \)

---

Problem 6: \( 49 \times 49 \)

\[
\begin{array}{r}
49 \\
\times 49 \\
\hline
441 \quad \text{(49 × 9)} \\
+ 1960 \quad \text{(49 × 4, shifted one place to the left)} \\
\hline
2401 \\
\end{array}
\]
Answer: \( 2401 \)

---

Problem 7: \( 63 \times 93 \)

\[
\begin{array}{r}
63 \\
\times 93 \\
\hline
189 \quad \text{(63 × 3)} \\
+ 5670 \quad \text{(63 × 9, shifted one place to the left)} \\
\hline
5859 \\
\end{array}
\]
Answer: \( 5859 \)

---

Problem 8: \( 32 \times 34 \)

\[
\begin{array}{r}
32 \\
\times 34 \\
\hline
128 \quad \text{(32 × 4)} \\
+ 960 \quad \text{(32 × 3, shifted one place to the left)} \\
\hline
1088 \\
\end{array}
\]
Answer: \( 1088 \)

---

Problem 9: \( 11 \times 11 \)

\[
\begin{array}{r}
11 \\
\times 11 \\
\hline
11 \quad \text{(11 × 1)} \\
+ 110 \quad \text{(11 × 1, shifted one place to the left)} \\
\hline
121 \\
\end{array}
\]
Answer: \( 121 \)

---

Problem 10: \( 90 \times 10 \)

\[
\begin{array}{r}
90 \\
\times 10 \\
\hline
900 \quad \text{(90 × 10)} \\
\end{array}
\]
Answer: \( 900 \)

---

Problem 11: \( 23 \times 79 \)

\[
\begin{array}{r}
23 \\
\times 79 \\
\hline
207 \quad \text{(23 × 9)} \\
+ 1610 \quad \text{(23 × 7, shifted one place to the left)} \\
\hline
1817 \\
\end{array}
\]
Answer: \( 1817 \)

---

Problem 12: \( 64 \times 55 \)

\[
\begin{array}{r}
64 \\
\times 55 \\
\hline
320 \quad \text{(64 × 5)} \\
+ 3200 \quad \text{(64 × 5, shifted one place to the left)} \\
\hline
3520 \\
\end{array}
\]
Answer: \( 3520 \)

---

Problem 13: \( 83 \times 61 \)

\[
\begin{array}{r}
83 \\
\times 61 \\
\hline
83 \quad \text{(83 × 1)} \\
+ 4980 \quad \text{(83 × 6, shifted one place to the left)} \\
\hline
5063 \\
\end{array}
\]
Answer: \( 5063 \)

---

Problem 14: \( 12 \times 73 \)

\[
\begin{array}{r}
12 \\
\times 73 \\
\hline
36 \quad \text{(12 × 3)} \\
+ 840 \quad \text{(12 × 7, shifted one place to the left)} \\
\hline
876 \\
\end{array}
\]
Answer: \( 876 \)

---

Problem 15: \( 44 \times 16 \)

\[
\begin{array}{r}
44 \\
\times 16 \\
\hline
264 \quad \text{(44 × 6)} \\
+ 440 \quad \text{(44 × 1, shifted one place to the left)} \\
\hline
704 \\
\end{array}
\]
Answer: \( 704 \)

---

Problem 16: \( 53 \times 39 \)

\[
\begin{array}{r}
53 \\
\times 39 \\
\hline
477 \quad \text{(53 × 9)} \\
+ 1590 \quad \text{(53 × 3, shifted one place to the left)} \\
\hline
2067 \\
\end{array}
\]
Answer: \( 2067 \)

---

Problem 17: \( 47 \times 23 \)

\[
\begin{array}{r}
47 \\
\times 23 \\
\hline
141 \quad \text{(47 × 3)} \\
+ 940 \quad \text{(47 × 2, shifted one place to the left)} \\
\hline
1081 \\
\end{array}
\]
Answer: \( 1081 \)

---

Problem 18: \( 91 \times 16 \)

\[
\begin{array}{r}
91 \\
\times 16 \\
\hline
546 \quad \text{(91 × 6)} \\
+ 910 \quad \text{(91 × 1, shifted one place to the left)} \\
\hline
1456 \\
\end{array}
\]
Answer: \( 1456 \)

---

Final Answers:

\[
\boxed{
\begin{array}{cccccccc}
832 & 3901 & 644 & 2208 & 5183 & 2401 \\
5859 & 1088 & 121 & 900 & 1817 & 3520 \\
5063 & 876 & 704 & 2067 & 1081 & 1456 \\
\end{array}
}
\]