Multiplication

Multiplying numbers with Scientific Notation

To multiply numbers in scientific notation,

1. multiply the decimal numbers.
   • of the result, if the number is greater than 1, move the decimal left until the number is 1 digit again. Record however many places the decimal had to be moved, and add it to the result in step 2.
2. add the exponents of the powers of 10.
3. Place the new power of 10 with the decimal in scientific notation form.

Cross multiplication

To cross multiply is to restate a division problem in terms of multiplication.

Therefore:

Can be restated as:

Mental Multiplication tricks

• multiply two 2-digit numbers (make sure to carry)

  • ex. $31 \times 24$
    • first multiply the ones digits together: $1 \times 4 = 4$
    • then 'cross-multiply: $(3 \times 4) + (1 \times 2) = 14$ (4, since we carry the one)
    • finally multiply the tens digits together: $3 \times 2 = 6$ (7, since we add the one)
    • answer: 744

• multiply by 5: divide the number by 2 and add a zero.

• multiply a 2-digit number by 11: sum the digits of the 2-digit number and insert it between the digits of the original number (carrying if necessary)

  • ex. $45 \times 11 = 495$
  • ex. $48 \times 11 = 528$

• multiply by 25: divide the number by 4 and add 2 zeros.

  • ex.

• multiply by number ending in 5: take digits before five and multiply them with their successors. Then add it to 25.