Question

a) \(\dfrac{2}{3}\) + \(\dfrac{-2}{18}\) 

b) (-12,5) + 3,4 + 12,5 + (-3,4) 

c) \(\dfrac{-6}{11}\): \(\dfrac{7}{4}\)+ \(\dfrac{-6}{11}\): \(\dfrac{7}{3}\)+ \(1\dfrac{1}{11}\)

Answer 1

a) \(\dfrac{2}{3}+\dfrac{-2}{18}=\dfrac{12}{18}+\dfrac{-2}{18}=\dfrac{10}{18}=\dfrac{5}{9}\)

b) \(\left(-12,5\right)+3,4+12,5+\left(-3,4\right)=\left(12,5-12,5\right)+\left(3,4-3,4\right)=0\)

c) 

\(\dfrac{-6}{11}:\dfrac{7}{4}+\dfrac{-6}{11}:\dfrac{7}{3}+1\dfrac{1}{11}\\ =\dfrac{-6}{11}\cdot\dfrac{4}{7}+\dfrac{-6}{11}\cdot\dfrac{3}{7}+\dfrac{12}{11}\\ =-\dfrac{6}{11}\cdot\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+\dfrac{12}{11}\\ =\dfrac{-6}{11}+\dfrac{12}{11}\\ =\dfrac{6}{11}\)

Answer 2

a) \(\dfrac{2}{3}+\dfrac{-2}{18}=\dfrac{2}{3}-\dfrac{1}{9}\\ =\dfrac{6}{9}-\dfrac{1}{9}=\dfrac{5}{9}\)

b) \(\left(-12,5\right)+3,4+12,5+\left(-3,4\right)\\ =\left(12,5-12,5\right)+\left(3,4-3,4\right)\\ =0\)

c) \(\dfrac{-6}{11}:\dfrac{7}{4}+\dfrac{-6}{11}:\dfrac{7}{3}+1\dfrac{1}{11}\\ =-\dfrac{6}{11}\times\dfrac{4}{7}+\dfrac{-6}{11}\times\dfrac{3}{7}+\dfrac{12}{11}\\ =-\dfrac{6}{11}\times\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+\dfrac{12}{11}\\ =-\dfrac{6}{11}\times1+\dfrac{12}{11}\\ =-\dfrac{6}{11}+\dfrac{12}{11}=\dfrac{6}{11}\)

Answer 3

\(a,\dfrac{2}{3}+\dfrac{-2}{18}\)

\(=\dfrac{2}{3}+\dfrac{-1}{9}\)

\(=\dfrac{6}{9}+\dfrac{-1}{9}\)

\(=\dfrac{5}{9}\)

\(b,\left(-12,5\right)+3,4+12,5+\left(-3,4\right)\)

\(=\left[\left(-12,5\right)+12,5\right]+\left[3,4+\left(-3,4\right)\right]\)

\(=0+0\)

\(=0\)

\(c,\dfrac{-6}{11}:\dfrac{7}{4}+\dfrac{-6}{11}:\dfrac{7}{3}+1\dfrac{1}{11}\)

\(=\dfrac{-6}{11}\times\dfrac{4}{7}+\dfrac{-6}{11}\times\dfrac{3}{7}+\dfrac{12}{11}\)

\(=\dfrac{-6}{11}\times\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+\dfrac{12}{11}\)

\(=\dfrac{-6}{11}\times1+\dfrac{12}{11}\)

\(=\dfrac{-6}{11}+\dfrac{12}{11}\)

\(=\dfrac{6}{11}\)