Math worksheet featuring multiplication and division exercises for students.

Problem Overview:

The task involves solving multiplication and division problems. Let's break it down into two sections:

1. Multiplication Problems (Problems ① to ⑥)
2. Division Problems (Problems ① to ⑥)

We will solve each problem step by step.

---

Section 1: Multiplication

#### Problem ①: \( 827 \times 3 \)
\[
827 \times 3 = (800 \times 3) + (20 \times 3) + (7 \times 3)
\]
\[
= 2400 + 60 + 21 = 2481
\]

#### Problem ②: \( 489 \times 6 \)
\[
489 \times 6 = (400 \times 6) + (80 \times 6) + (9 \times 6)
\]
\[
= 2400 + 480 + 54 = 2934
\]

#### Problem ③: \( 748 \times 9 \)
\[
748 \times 9 = (700 \times 9) + (40 \times 9) + (8 \times 9)
\]
\[
= 6300 + 360 + 72 = 6732
\]

#### Problem ④: \( 675 \times 4 \)
\[
675 \times 4 = (600 \times 4) + (70 \times 4) + (5 \times 4)
\]
\[
= 2400 + 280 + 20 = 2700
\]

#### Problem ⑤: \( 383 \times 4 \)
\[
383 \times 4 = (300 \times 4) + (80 \times 4) + (3 \times 4)
\]
\[
= 1200 + 320 + 12 = 1532
\]

#### Problem ⑥: \( 465 \times 7 \)
\[
465 \times 7 = (400 \times 7) + (60 \times 7) + (5 \times 7)
\]
\[
= 2800 + 420 + 35 = 3255
\]

---

Section 2: Division

#### Problem ①: \( 596 \div 4 \)
Perform long division:
\[
596 \div 4 = 149
\]
- \( 4 \) goes into \( 5 \) once, so write \( 1 \) and subtract \( 4 \) from \( 5 \) to get \( 1 \).
- Bring down the next digit \( 9 \), making it \( 19 \). \( 4 \) goes into \( 19 \) four times, so write \( 4 \) and subtract \( 16 \) from \( 19 \) to get \( 3 \).
- Bring down the next digit \( 6 \), making it \( 36 \). \( 4 \) goes into \( 36 \) nine times, so write \( 9 \) and subtract \( 36 \) from \( 36 \) to get \( 0 \).

#### Problem ②: \( 615 \div 5 \)
Perform long division:
\[
615 \div 5 = 123
\]
- \( 5 \) goes into \( 6 \) once, so write \( 1 \) and subtract \( 5 \) from \( 6 \) to get \( 1 \).
- Bring down the next digit \( 1 \), making it \( 11 \). \( 5 \) goes into \( 11 \) twice, so write \( 2 \) and subtract \( 10 \) from \( 11 \) to get \( 1 \).
- Bring down the next digit \( 5 \), making it \( 15 \). \( 5 \) goes into \( 15 \) three times, so write \( 3 \) and subtract \( 15 \) from \( 15 \) to get \( 0 \).

#### Problem ③: \( 860 \div 4 \)
Perform long division:
\[
860 \div 4 = 215
\]
- \( 4 \) goes into \( 8 \) twice, so write \( 2 \) and subtract \( 8 \) from \( 8 \) to get \( 0 \).
- Bring down the next digit \( 6 \), making it \( 6 \). \( 4 \) goes into \( 6 \) once, so write \( 1 \) and subtract \( 4 \) from \( 6 \) to get \( 2 \).
- Bring down the next digit \( 0 \), making it \( 20 \). \( 4 \) goes into \( 20 \) five times, so write \( 5 \) and subtract \( 20 \) from \( 20 \) to get \( 0 \).

#### Problem ④: \( 654 \div 3 \)
Perform long division:
\[
654 \div 3 = 218
\]
- \( 3 \) goes into \( 6 \) twice, so write \( 2 \) and subtract \( 6 \) from \( 6 \) to get \( 0 \).
- Bring down the next digit \( 5 \), making it \( 5 \). \( 3 \) goes into \( 5 \) once, so write \( 1 \) and subtract \( 3 \) from \( 5 \) to get \( 2 \).
- Bring down the next digit \( 4 \), making it \( 24 \). \( 3 \) goes into \( 24 \) eight times, so write \( 8 \) and subtract \( 24 \) from \( 24 \) to get \( 0 \).

#### Problem ⑤: \( 456 \div 4 \)
Perform long division:
\[
456 \div 4 = 114
\]
- \( 4 \) goes into \( 4 \) once, so write \( 1 \) and subtract \( 4 \) from \( 4 \) to get \( 0 \).
- Bring down the next digit \( 5 \), making it \( 5 \). \( 4 \) goes into \( 5 \) once, so write \( 1 \) and subtract \( 4 \) from \( 5 \) to get \( 1 \).
- Bring down the next digit \( 6 \), making it \( 16 \). \( 4 \) goes into \( 16 \) four times, so write \( 4 \) and subtract \( 16 \) from \( 16 \) to get \( 0 \).

#### Problem ⑥: \( 632 \div 4 \)
Perform long division:
\[
632 \div 4 = 158
\]
- \( 4 \) goes into \( 6 \) once, so write \( 1 \) and subtract \( 4 \) from \( 6 \) to get \( 2 \).
- Bring down the next digit \( 3 \), making it \( 23 \). \( 4 \) goes into \( 23 \) five times, so write \( 5 \) and subtract \( 20 \) from \( 23 \) to get \( 3 \).
- Bring down the next digit \( 2 \), making it \( 32 \). \( 4 \) goes into \( 32 \) eight times, so write \( 8 \) and subtract \( 32 \) from \( 32 \) to get \( 0 \).

---

Final Answers:

#### Multiplication:
1. \( 827 \times 3 = 2481 \)
2. \( 489 \times 6 = 2934 \)
3. \( 748 \times 9 = 6732 \)
4. \( 675 \times 4 = 2700 \)
5. \( 383 \times 4 = 1532 \)
6. \( 465 \times 7 = 3255 \)

#### Division:
1. \( 596 \div 4 = 149 \)
2. \( 615 \div 5 = 123 \)
3. \( 860 \div 4 = 215 \)
4. \( 654 \div 3 = 218 \)
5. \( 456 \div 4 = 114 \)
6. \( 632 \div 4 = 158 \)

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Multiplication:} & 2481, 2934, 6732, 2700, 1532, 3255 \\
\text{Division:} & 149, 123, 215, 218, 114, 158
\end{array}
}
\]