تمارين في الرياضيات

تصحيح التمرين رقم 1:

بما أن $ xy = \frac{5}{6} $

A:

$$ A = [ y \times (-\frac{1}{4}) ] \times x $$

$$ A = -\frac{1}{4} \times y \times x $$

$$ A = -\frac{1}{4} \times (xy) $$

$$ A = -\frac{1}{4} \times \frac{5}{6} $$

$$ A = -\frac{5}{24} $$

B:

$$ B = (-6x) \times [ y \times (-\frac{1}{5}) ] $$

$$ B = (-6) \times x \times y \times (-\frac{1}{5}) $$

$$ B = (-6) \times (xy) \times (-\frac{1}{5}) $$

$$ B = (-6) \times \frac{5}{6} \times (-\frac{1}{5}) $$

$$ B = -5 \times (-\frac{1}{5}) $$

$$ B = 1 $$

C:

$$ C = -x \times [ -\frac{6}{5} \times (-y) ] $$

$$ C = -x \times \frac{6}{5}y $$

$$ C = -\frac{6}{5} \times x \times y $$

$$ C = -\frac{6}{5} \times (xy) $$

$$ C = -\frac{6}{5} \times \frac{5}{6} $$

$$ C = -1 $$

تصحيح العبارات:

I:

$$ I = -\frac{3}{4} \times (-\frac{5}{7}) \times (-1) \times \frac{4}{3} \times 9 $$

$$ I = (\frac{3}{4} \times \frac{4}{3}) \times (\frac{5}{7} \times 1 \times 9) \times (-1) $$

$$ I = 1 \times \frac{45}{7} \times (-1) $$

$$ I = -\frac{45}{7} $$

J:

$$ J = 1 - \frac{9}{2} - \frac{15}{2} \times \frac{10}{6} - 7.5 $$

$$ J = 1 - 4.5 - \frac{150}{12} - 7.5 $$

$$ J = 1 - 4.5 - 12.5 - 7.5 $$

$$ J = 1 - (4.5 + 12.5 + 7.5) $$

$$ J = 1 - 24.5 $$

$$ J = -23.5 $$

K:

$$ K = (\frac{3}{5}+2) \div (\frac{2}{7}-1) $$

$$ K = (\frac{3}{5}+\frac{10}{5}) \div (\frac{2}{7}-\frac{7}{7}) $$

$$ K = (\frac{13}{5}) \div (-\frac{5}{7}) $$

$$ K = \frac{13}{5} \times (-\frac{7}{5}) $$

$$ K = -\frac{91}{25} $$

L:

$$ L = (-\frac{3}{2}) \times \frac{7}{4} + (\frac{7}{4}) \times (-\frac{3}{5}) - (-\frac{3}{5} \times -\frac{2}{2}) $$

$$ L = \frac{7}{4} \times (-\frac{3}{2} - \frac{3}{5}) - (+\frac{3}{5}) $$

$$ L = \frac{7}{4} \times (-\frac{15}{10} - \frac{6}{10}) - \frac{3}{5} $$

$$ L = \frac{7}{4} \times (-\frac{21}{10}) - \frac{3}{5} $$

$$ L = -\frac{147}{40} - \frac{3}{5} $$

$$ L = -\frac{147}{40} - \frac{24}{40} $$

$$ L = -\frac{171}{40} $$

تصحيح العمليات:

M:

$$ M = \frac{\frac{11}{55} \times \frac{-1}{7}}{\frac{6}{2}} $$

$$ \text{Numerator: } \frac{11}{55} \times \frac{-1}{7} = \frac{1}{5} \times \frac{-1}{7} = -\frac{1}{35} $$

$$ \text{Denominator: } \frac{6}{2} = 3 $$

$$ M = \frac{-\frac{1}{35}}{3} = -\frac{1}{35} \times \frac{1}{3} = -\frac{1}{105} $$

N:

$$ N = \frac{\frac{11}{3}}{\frac{6}{3}} - \frac{\frac{3}{11}}{\frac{7}{11}} $$

$$ \text{First term: } \frac{\frac{11}{3}}{\frac{6}{3}} = \frac{11}{3} \times \frac{3}{6} = \frac{11}{6} $$

$$ \text{Second term: } \frac{\frac{3}{11}}{\frac{7}{11}} = \frac{3}{11} \times \frac{11}{7} = \frac{3}{7} $$

$$ N = \frac{11}{6} - \frac{3}{7} = \frac{77 - 18}{42} = \frac{59}{42} $$

تصحيح إيجاد x:

1)

$$ \frac{1}{0.25}x = -\frac{1}{4} $$

$$ \frac{1}{\frac{1}{4}}x = -\frac{1}{4} $$

$$ 4x = -\frac{1}{4} $$

$$ x = -\frac{1}{4} \div 4 = -\frac{1}{4} \times \frac{1}{4} = -\frac{1}{16} $$

2)

$$ -7x = -\frac{35}{3} $$

$$ x = -\frac{35}{3} \div (-7) = -\frac{35}{3} \times (-\frac{1}{7}) $$

$$ x = \frac{35}{21} = \frac{5}{3} $$

3)

$$ -\frac{9}{2}x+2 = \frac{12}{5} $$

$$ -\frac{9}{2}x = \frac{12}{5} - 2 $$

$$ -\frac{9}{2}x = \frac{12}{5} - \frac{10}{5} = \frac{2}{5} $$

$$ x = \frac{2}{5} \div (-\frac{9}{2}) = \frac{2}{5} \times (-\frac{2}{9}) $$

$$ x = -\frac{4}{45} $$