Question

Chứng minh rằng là : 7/9 = 77/99 = 777/999 = 7777/9999

Answer 1

\(\dfrac{7}{9}=\dfrac{7}{9}\)

\(\dfrac{77}{99}=\dfrac{77\div11}{99\div11}=\dfrac{7}{9}\)

\(\dfrac{777}{999}=\dfrac{777\div111}{999\div111}=\dfrac{7}{9}\)

\(\dfrac{7777}{9999}=\dfrac{7777\div1111}{9999\div1111}=\dfrac{7}{9}\)

\(\Rightarrow\dfrac{7}{9}=\dfrac{77}{99}=\dfrac{777}{999}=\dfrac{7777}{9999}\)

Answer 2

\(\dfrac{77}{99}\) = \(\dfrac{77:11}{99:11}\) = \(\dfrac{7}{9}\)

\(\dfrac{777}{999}\) = \(\dfrac{777:111}{999:111}\) = \(\dfrac{7}{9}\)

\(\dfrac{7777}{9999}\) = \(\dfrac{7777:1111}{9999:1111}\) = \(\dfrac{7}{9}\)

Từ những lập luận luận trên ta có:

\(\dfrac{7}{9}\) = \(\dfrac{77}{99}\) = \(\dfrac{777}{999}\) = \(\dfrac{7777}{9999}\) (đpcm)