Example

Example of Dividing 25.65÷(0.06)-25.65 \div (-0.06)

To divide 25.65÷(0.06)-25.65 \div (-0.06), apply the five-step decimal division procedure:

  1. Determine the sign: Both 25.65-25.65 and 0.06-0.06 are negative (they have the same sign), so the quotient is positive.
  2. Make the divisor a whole number: The divisor 0.06-0.06 has two decimal places. As justified by the Equivalent Fractions Property, move its decimal point two places to the right to obtain 6-6.
  3. Shift the dividend's decimal point: Move the decimal point in 25.65-25.65 two places to the right as well, giving 2565.0-2565.0.
  4. Divide by long division: The problem is now equivalent to 2565.0÷62565.0 \div 6. Performing the long division:
    • 6 into 25 is 4, remainder 1.
    • Bring down 6 to make 16. 6 into 16 is 2, remainder 4.
    • Bring down 5 to make 45. 6 into 45 is 7, remainder 3.
    • Bring down 0 to make 30. 6 into 30 is 5, remainder 0. The quotient is 427.5427.5, with the decimal point placed directly above its new position in the dividend.
  5. Apply the sign: As determined in step 1, the result is positive.

Therefore, 25.65÷(0.06)=427.5-25.65 \div (-0.06) = 427.5.

Image 0

0

1

Updated 2026-04-21

Tags

OpenStax

Elementary Algebra @ OpenStax

Ch.1 Foundations - Elementary Algebra @ OpenStax

Algebra

Math

Prealgebra

Intermediate Algebra @ OpenStax

Ch.1 Foundations - Intermediate Algebra @ OpenStax

Related
Learn After