can you give me a step by step Long division and multiplication decimal problem 

Sure! Let's walk through **long division** and **multiplication with decimals** step by step using examples.

### **1. Long Division Example with Decimals**
**Problem**: Divide \( 7.48 \div 2.5 \).

**Step 1: Make the divisor a whole number.**
We are dividing by \( 2.5 \), a decimal. To simplify, multiply both the divisor and dividend by 10 to make the divisor a whole number.

\[
7.48 \div 2.5 \quad \text{becomes} \quad 74.8 \div 25
\]

**Step 2: Perform long division.**
Now, divide \( 74.8 \) by \( 25 \).

- **25 into 74**: 25 goes into 74 two times because \( 25 \times 2 = 50 \). Subtract \( 74 - 50 = 24 \).
- **Bring down the 8** (the decimal part): Now, divide \( 248 \div 25 \).
- **25 into 248**: 25 goes into 248 nine times because \( 25 \times 9 = 225 \). Subtract \( 248 - 225 = 23 \).

Now, we get a remainder of 23. We can continue by adding a zero to the remainder and dividing again to get a more precise decimal.

- **Bring down a 0**: Now, divide \( 230 \div 25 \). 25 goes into 230 nine times (because \( 25 \times 9 = 225 \)).

The final quotient is approximately \( 2.992 \).

**Answer**: \( 7.48 \div 2.5 = 2.992 \).

---

### **2. Multiplication Example with Decimals**
**Problem**: Multiply \( 3.46 \times 2.1 \).

**Step 1: Ignore the decimals and multiply as whole numbers.**
Treat \( 3.46 \) and \( 2.1 \) as \( 346 \) and \( 21 \).

\[
346 \times 21 = 346 \times (20 + 1) = 346 \times 20 + 346 \times 1
\]

- \( 346 \times 1 = 346 \)
- \( 346 \times 20 = 6920 \)

Add the two products together:

\[
346 + 6920 = 7266
\]

**Step 2: Place the decimal point.**
Count the total number of decimal places in the original numbers. \( 3.46 \) has 2 decimal places and \( 2.1 \) has 1 decimal place, so the product will have \( 2 + 1 = 3 \) decimal places.

Starting from the right, place the decimal point three digits to the left.

\[
7266 \rightarrow 7.266
\]

**Answer**: \( 3.46 \times 2.1 = 7.266 \).

---

Would you like more details or have any questions?

Here are 5 questions to expand your understanding:
1. How do you handle remainders when dividing with decimals?
2. What if both numbers have multiple decimal places in division?
3. How do you multiply two decimal numbers mentally?
4. How can you estimate a decimal division problem before calculating?
5. What happens when multiplying by powers of 10?

**Tip**: When dividing decimals, always remember to multiply both numbers by the same power of 10 to make the divisor a whole number!

Can you give me a step by step Long division and multiplication decimal problem?

Explore a detailed step-by-step guide to solving long division and multiplication with decimal problems, using examples like 7.48 ÷ 2.5 and 3.46 × 2.1. Learn key concepts such as adjusting decimal places and performing long division with remainders. Perfect for Grades 5-7 students looking to understand these core math skills.

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