Question

1 întreg 1 pe 4-2 pe 7+3 întreg 1 pe 2- 3 pe 14​

Answer 1

Răspuns:

$\dfrac{7}{4}$

Explicație pas cu pas:

$\displaystyle{ 1\frac{1}{4} - \frac{2}{7} + 3\frac{1}{2} - \frac{3}{14} = }$

$\displaystyle{ = \frac{1 \cdot 4 + 1}{4} - \frac{2}{7} + \frac{3 \cdot 2 + 1}{2} - \frac{3}{14} }$

$\displaystyle{ = \frac{5}{4} - \frac{2}{7} + \frac{7}{2} - \frac{3}{14} }$

Numitorul comun este 28 deci amplificam prima fractie cu 7, a doua cu 4, a treia cu 14 si ultima cu 2.

$\displaystyle{ = \frac{5 \cdot 7 - 2 \cdot 4 + 7 \cdot 14 - 3 \cdot 2}{28} }$

$\displaystyle{ = \frac{35-8+28-6}{28} }$

$\displaystyle{ = \frac{27 + 28 - 6}{28} }$

$\displaystyle{ = \frac{55-6}{28} }$

$\displaystyle{ = \frac{49}{28}^{(7} }$

$\displaystyle{ = \frac{7}{4} }$

Answer 2

$\it 1\dfrac{1}{4}-\dfrac{2}{7}+3\dfrac{1}{2}-\dfrac{3}{14}=\dfrac{^{7)}5}{4}-\dfrac{^{4)}2}{7}+\dfrac{^{14)}7}{2}-\dfrac{^{2)}3}{14}=\dfrac{35-8+98-6}{28}=\\ \\ \\ =\dfrac{119^{(7}}{28}=\dfrac{17}{4}=4\dfrac{1}{4}$