Operations on rational fractions: subtraction, opposite bottoms, powers, identities
Subtract rational fractions with the sign change, find extra factors, handle opposite bottoms, raise a fraction to a power and prove identities, as the Grade 8 Ukrainian book does.
- أوكرانيا: الصف ٨
- روسيا: الصف ٨
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الدليل
In the Ukrainian programme this is Grade 8 algebra, §1 "Rational expressions", items 3-6: adding, subtracting, multiplying and dividing rational fractions, raising a fraction to a power, and identical transformations.
Fractions with the same bottom: AC + BC = A + BC and AC − BC = A − BC. If a minus stands in front of a fraction, every term of its top changes sign, so put the top in brackets.
For different bottoms, find a common bottom that every bottom divides, and multiply the top and bottom of each fraction by its extra factor. The expressions a − b and b − a are opposites: b − a = −(a − b).
A fraction to the power n has top an and bottom bn. To prove an identity, transform one side (or both) until the same expression appears.
On the board tap a fraction's chip and then the × button to multiply its top and bottom by the extra factor. Type the answer on the keypad; the fraction key puts what follows under the bar.