Dodawanie i odejmowanie ułamków zwykłych – Zadanie 2

Wykonaj odejmowanie ułamków:

a) \( \dfrac{2}{3}-\dfrac{2}{5}\)

b) \( \dfrac{5}{6}-\dfrac{4}{9}\)

c) \( \dfrac{1}{2}-\dfrac{7}{15}\)

d) \( \dfrac{5}{7}-\dfrac{4}{14}\)

e) \( \dfrac{3}{4}-\dfrac{16}{25}\)

Rozwiązanie
a)
\(\dfrac{2}{3}-\dfrac{2}{5}=
\dfrac{2}{3}_{\: / \: \cdot 5}-\dfrac{2}{5}_{\: / \: \cdot 3}=
\dfrac{10}{15}-\dfrac{6}{15}=\dfrac{4}{15}\)

b)
\(\dfrac{5}{6}-\dfrac{4}{9}=
\dfrac{5}{6}_{\: / \: \cdot 3}-\dfrac{4}{9}_{\: / \: \cdot 2}=
\dfrac{15}{18}-\dfrac{8}{18}=\dfrac{7}{18}\)

c)
\(\dfrac{1}{2}-\dfrac{7}{15}=
\dfrac{1}{2}_{\: / \: \cdot 15}-\dfrac{7}{15}_{\: / \: \cdot 2}=
\dfrac{15}{30}-\dfrac{14}{30}=\dfrac{1}{30}\)

d)
\(\dfrac{5}{7}-\dfrac{4}{14}=
\dfrac{5}{7}_{\: / \: \cdot 2}-\dfrac{4}{14}=
\dfrac{10}{14}-\dfrac{4}{14}=\dfrac{6}{14}\)

e)
\(\dfrac{3}{4}-\dfrac{16}{25}=
\dfrac{3}{4}_{\: / \: \cdot 25}-\dfrac{16}{25}_{\: / \: \cdot 4}=
\dfrac{75}{100}-\dfrac{64}{100}=\dfrac{11}{100}\)