13 x 17 using breakdown method

1 answer

To multiply 13 by 17 using the breakdown method, you can break down the numbers into easier parts.

Here’s how it can be done:

  1. Break down the numbers:

    \( 13 = 10 + 3 \)
    \( 17 = 10 + 7 \)

  2. Use the distributive property:

    Now, you can use the distributive property to multiply:

    \[ 13 \times 17 = (10 + 3)(10 + 7) \]

  3. Apply the distributive property:

    This can be expanded using FOIL (First, Outside, Inside, Last):

    \[ = 10 \times 10 + 10 \times 7 + 3 \times 10 + 3 \times 7 \]

    Now, calculating each part:

    \[ 10 \times 10 = 100 \] \[ 10 \times 7 = 70 \] \[ 3 \times 10 = 30 \] \[ 3 \times 7 = 21 \]

  4. Add all the parts together:

    \[ 100 + 70 + 30 + 21 = 221 \]

So, \( 13 \times 17 = 221 \).