What are three distinct numeric approaches for calculating the product 24x32?
To calculate the product of 24 and 32, you can use one of three distinct numeric approaches:
1. **Direct multiplication**: Multiply the two numbers directly.
- Multiply 4 (the units digit of 24) by 2 (the units digit of 32). The result is 8 (product: 4x2=8).
- Multiply 4 (the tens digit of 24) by 3 (the tens digit of 32). The result is 12 (product: 4x3=12).
- Concatenate the two products: 12 and 8. The result is 128 (product: 24x32=128).
2. **Lattice multiplication**: Use a grid-like structure to break down the multiplication process.
- Draw a 2x2 grid and divide it into four quadrants.
- Write the digits of the first number (24) along the top row and the digits of the second number (32) along the side column.
- Multiply the corresponding digits in each quadrant: 2x3=6, 2x0=0, 4x3=12, 4x0=0.
- Add the products in each quadrant to get the final result: 6+0+12+0=18.
- Place the digits of the result in the appropriate positions on the grid. In this case, the result is 180.
3. **Repeated addition**: Add one number repeatedly to itself the number of times indicated by the other number.
- Take one number (24) and add it to itself as many times as the other number (32) indicates.
- Start with 0 and add 24 thirty-two times: 0+24=24, 24+24=48, 48+24=72, ..., 720+24=744.
- The final sum is 744 (product: 24x32=744).
These three distinct numeric approaches provide different ways to calculate the product of 24 and 32. You can choose the method that suits you best or try a combination of them for better understanding and verification.