What is place value?  Write the number 2,348 in expanded form (break down the value of each digit).

What is commutative property of multiplication? Give me one example. If you multiply 18 × 6, then add 12, what’s the result?
a) 24 cookies are shared equally among 6 children. How many cookies does each child get?

b) If the time is 3:30 PM now, what will the time be 2 hours later?
a) Define what a fraction is and what the numerator and denominator represent.

b) A square has 4 equal sides. If one side is 5 cm, what is the total length of all the sides (perimeter) of the square?

a) If you go to bed at 8:00 PM and wake up at 6:30 AM, how many hours did you sleep?

b) Subtract 12 from the product of 4 × 5. What do you get?
make another 3 sets of question like above

### Explanation of Place Value
Place value refers to the value of each digit in a number based on its position. In the number 2,348:

- The digit 2 is in the **thousands** place, so its value is 2,000.
- The digit 3 is in the **hundreds** place, so its value is 300.
- The digit 4 is in the **tens** place, so its value is 40.
- The digit 8 is in the **ones** place, so its value is 8.

### Expanded Form of 2,348
The number 2,348 can be written in expanded form as:
\[
2,348 = 2,000 + 300 + 40 + 8
\]

### Commutative Property of Multiplication
The commutative property of multiplication states that changing the order of the factors does not change the product. In other words, for any two numbers \( a \) and \( b \):
\[
a \times b = b \times a
\]
**Example**: 
\[
4 \times 5 = 5 \times 4 = 20
\]

### Multiplication and Addition
If you multiply \( 18 \times 6 \) and then add 12:
\[
18 \times 6 = 108
\]
\[
108 + 12 = 120
\]

### Questions:
1. a) **Division Problem**: 24 cookies are shared equally among 6 children. How many cookies does each child get?
\[
\frac{24}{6} = 4 \text{ cookies per child}
\]

b) **Time Addition**: If the time is 3:30 PM now, what will the time be 2 hours later?
\[
3:30 \, \text{PM} + 2 \, \text{hours} = 5:30 \, \text{PM}
\]

### Fraction Definition
A **fraction** represents a part of a whole. It has two parts:
- The **numerator** (top number) represents how many parts we have.
- The **denominator** (bottom number) represents the total number of equal parts the whole is divided into.

### Square and Perimeter
A square has 4 equal sides. If one side is 5 cm, the total length of all sides (perimeter) is:
\[
\text{Perimeter} = 4 \times 5 = 20 \, \text{cm}
\]

### Sleeping Hours Calculation
If you go to bed at 8:00 PM and wake up at 6:30 AM, the number of hours slept is:
\[
8:00 \, \text{PM} \, \text{to} \, 6:30 \, \text{AM} = 10 \, \text{hours and} \, 30 \, \text{minutes}
\]

### Subtraction and Multiplication Problem
Subtract 12 from the product of \( 4 \times 5 \):
\[
4 \times 5 = 20
\]
\[
20 - 12 = 8
\]

### Additional Problem Sets

1. a) A pizza is cut into 8 equal slices. If you eat 3 slices, what fraction of the pizza did you eat?

b) You have 5 dimes. How much money do you have in total?

2. a) If a rectangle has a length of 7 cm and a width of 3 cm, what is its area?

b) What is the result of subtracting 15 from the sum of \( 9 + 12 \)?

3. a) If you walk at a speed of 4 km/h for 3 hours, how far will you have walked?

b) What is 25% of 80?

### Tip:
When working with fractions, always remember that the denominator represents the number of equal parts the whole is divided into, while the numerator tells you how many of those parts you're focusing on. 

Would you like more details or have any questions?

What is place value? Write the number 2,348 in expanded form (break down the value of each digit). What is commutative property of multiplication? Give me one example. If you multiply 18 × 6, then add 12, what’s the result? a) 24 cookies are shared equally among 6 children. How many cookies does each child get? b) If the time is 3:30 PM now, what will the time be 2 hours later? a) Define what a fraction is and what the numerator and denominator represent. b) A square has 4 equal sides. If one side is 5 cm, what is the total length of all the sides (perimeter) of the square? a) If you go to bed at 8:00 PM and wake up at 6:30 AM, how many hours did you sleep? b) Subtract 12 from the product of 4 × 5. What do you get?

Solve a variety of math problems involving place value, fractions, time calculations, and the commutative property of multiplication. Learn the expanded form of the number 2,348, and explore concepts like division, perimeter, and time. Suitable for students in Grades 4-6.

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