1. Reciprocity of multiplication and division: For fractions a/b and c/d, there is (a/b)×(c/d)=(a×c)/(b×d). This property can be used to simplify the fractional division operation. For example, when calculating 3/4÷5/6, you can multiply two fractions to get (3/4)×(6/5)=9/ 10, and then divide the numerator and denominator to get 9/ 10=0.9.
2. Dividing a number is equal to multiplying the reciprocal of this number: for fractions a/b and c/d, there is (a/b)÷(c/d)=(a/b)×(d/c). This property can be used to convert division into multiplication, thus simplifying calculation. For example, when calculating 3/4÷5/6, you can first convert division into multiplication to get (3/4)×(6/5)=9/ 10, and then divide the numerator and denominator to get 9/ 10=0.9.
3. Mixed operation of fractions: When calculating fractional division, different operation sequences can be combined to simplify the calculation. For example, when calculating (3+4)/5÷(6-2)/6, you can add and subtract the fractions in brackets first, and then divide them evenly.
Common mistakes in fractional division:
1, numerator divided by numerator, denominator divided by denominator: This is wrong, because it will cause the result to become decimal or integer instead of fraction. The correct way is to multiply the numerator by the reciprocal of the divisor and the denominator by the reciprocal of the dividend.
2. Wrong operation sequence: When calculating fractional division, the inner side of brackets should be calculated first, and then the outer side of brackets should be calculated. If the order is not correct, the calculation result will be incorrect.
3. Ignore integer multiples: When calculating fractional division, if the numerator and denominator have integer multiples, they will be divided. If integer multiples are ignored, the calculation result will be incorrect.
4. Error of magnification or reduction: When magnification or reduction, the numerator and denominator should simultaneously magnify or reduce the same magnification, instead of just magnifying or reducing the numerator or denominator. If only one number is enlarged or reduced, the calculation result will be incorrect.
5. Sign error: When calculating fractional division, the divisor should be changed to its reciprocal, not its reciprocal. If it becomes the opposite number, it will lead to incorrect calculation results.