الصيغ على الكسور الموجبة

✅ التصحيح

بتطبيق: a+(b±c) = (a+b)±c حيث a+b=2 ∈ ℕ

\( \dfrac{4}{3}+\left(\dfrac{2}{3}+\dfrac{2}{3}\right) =\left(\dfrac{4}{3}+\dfrac{2}{3}\right)+\dfrac{2}{3} = 2+\dfrac{2}{3} = \dfrac{8}{3} \)

✅ التصحيح

بتطبيق: (a-c)+(b+c) = a+b [c يختصر]

\( \left(\dfrac{5}{8}-\dfrac{33}{586}\right)+\left(\dfrac{1}{4}+\dfrac{33}{586}\right) = \dfrac{5}{8}+\dfrac{1}{4} = \dfrac{7}{8} \)

✅ التصحيح

بتطبيق: a+(b±c) = (a+b)±c حيث a+b=2 ∈ ℕ

\( \dfrac{3}{2}+\left(\dfrac{1}{2}+\dfrac{3}{9}\right) =\left(\dfrac{3}{2}+\dfrac{1}{2}\right)+\dfrac{3}{9} = 2+\dfrac{3}{9} = \dfrac{7}{3} \)

✅ التصحيح

من x−a=b نستنتج x=b+a

\( x-\dfrac{2}{6}=\dfrac{5}{12} x=\dfrac{5}{12}+\dfrac{2}{6}=\dfrac{3}{4} \)

✅ التصحيح

بتطبيق: a+(b±c) = (a+b)±c حيث a+b=5 ∈ ℕ

\( \dfrac{43}{10}+\left(\dfrac{7}{10}+\dfrac{2}{4}\right) =\left(\dfrac{43}{10}+\dfrac{7}{10}\right)+\dfrac{2}{4} = 5+\dfrac{2}{4} = \dfrac{11}{2} \)

✅ التصحيح

بتطبيق: (a-c)−(b-c) = a−b [c يختصر]

\( \left(\dfrac{3}{4}-\dfrac{3}{881}\right)-\left(\dfrac{3}{10}-\dfrac{3}{881}\right) = \dfrac{3}{4}-\dfrac{3}{10} = \dfrac{9}{20} \)

✅ التصحيح

بتطبيق: (a+c)+(b-c) = a+b [c يختصر]

\( \left(\dfrac{7}{10}+\dfrac{39}{709}\right)+\left(\dfrac{3}{4}-\dfrac{39}{709}\right) = \dfrac{7}{10}+\dfrac{3}{4} = \dfrac{29}{20} \)

✅ التصحيح

بتطبيق: a+(b±c) = (a+b)±c حيث a+b=3 ∈ ℕ

\( \dfrac{17}{7}+\left(\dfrac{4}{7}+\dfrac{2}{5}\right) =\left(\dfrac{17}{7}+\dfrac{4}{7}\right)+\dfrac{2}{5} = 3+\dfrac{2}{5} = \dfrac{17}{5} \)

✅ التصحيح

من a−x=b نستنتج x=a−b

\( \dfrac{47}{40}-x=\dfrac{4}{5} x=\dfrac{47}{40}-\dfrac{4}{5}=\dfrac{3}{8} \)

✅ التصحيح

بتطبيق: (a-c)−(b-c) = a−b [c يختصر]

\( \left(\dfrac{5}{7}-\dfrac{3}{714}\right)-\left(\dfrac{4}{11}-\dfrac{3}{714}\right) = \dfrac{5}{7}-\dfrac{4}{11} = \dfrac{27}{77} \)