how to multiplly without using calculator

Multiplying numbers without a calculator involves understanding and applying basic multiplication principles and methods. Here are a few steps and techniques to help you multiply numbers manually:

### Basic Multiplication Steps:

1. **Multiplication Table**:
   - Familiarize yourself with the multiplication table (up to 12×12) as it helps in quick reference for small numbers.

2. **Long Multiplication**:
   - For larger numbers, use the long multiplication method.

#### Example: Multiply 34 by 56

- **Step 1: Write the numbers** one below the other, aligning the digits by place value.

```
    34
  × 56
```

- **Step 2: Multiply each digit of the bottom number (56) by each digit of the top number (34)**, starting from the rightmost digit of the bottom number.

1. Multiply 6 by 34:
```
     34
  ×   6
  ------
    204   (6*4=24, write 4, carry 2; 6*3=18, add carry 2, result 20)
```

2. Multiply 5 by 34 and shift one place to the left (because it's actually 50):
```
     34
  ×  50
  ------
   1700  (5*4=20, write 0, carry 2; 5*3=15, add carry 2, result 17; place zero to the right)
```

- **Step 3: Add the results together**:

```
    204
  1700
  ------
   1904
```

So, \(34 \times 56 = 1904\).

### Techniques for Faster Multiplication:

1. **Distributive Property**:
   - Break the numbers into smaller parts that are easier to multiply and then add the results.
   - Example: \( 34 \times 56 \)
     \[
     34 \times (50 + 6) = (34 \times 50) + (34 \times 6)
     \]
     \[
     34 \times 50 = 1700
     \]
     \[
     34 \times 6 = 204
     \]
     \[
     1700 + 204 = 1904
     \]

2. **Lattice Multiplication**:
   - A grid-based method that can make multiplication more visual and systematic.

3. **Mental Math Tricks**:
   - For multiplying by 10, just add a zero to the number.
   - For multiplying by 5, halve the number and multiply by 10.
   - For squaring numbers ending in 5, use the formula: \( n^2 = (n-1) \times (n+1) + 25 \).

### Practice Problems:

1. Multiply 23 by 45.
2. Multiply 67 by 89.
3. Multiply 123 by 456.
4. Multiply 78 by 34.
5. Multiply 99 by 99.
6. Multiply 245 by 123.
7. Multiply 56 by 78.
8. Multiply 37 by 49.

### Tip:

When multiplying larger numbers, it helps to write out all intermediate steps clearly and check each part of the calculation to avoid errors.

Do you want details or have any questions about any specific method or example?

Learn how to multiply numbers without using a calculator with manual multiplication techniques. Understand basic multiplication steps, long multiplication, distributive property, lattice multiplication, and mental math tricks. Practice problems included. Suitable for students in Grades 4-6.

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