Ⲁⲛ⳽ⲱⲉⲅ:
The ratios which are equivalent to [tex] \sf{\dfrac{6}{7}}[/tex] are :
[tex] \qquad\leadsto \quad\sf{ B) \: \dfrac{12}{14}}[/tex]
[tex] \qquad\leadsto \quad\sf{C)\:\dfrac{18}{21} }[/tex]
[tex]\quad\rule{300pt}{1.5pt}\quad [/tex]
Ⲋⲟⳑⳙⲧⳕⲟⲛ :
Here, we have to find the ratios which are equivalent to the given fraction [tex] \sf{\dfrac{6}{7}}[/tex] i.e, we have to check all the given ratios by multiplying a same number on both numerator and denominator. Let's check all the 4 given options :
[tex]\quad\bull \quad \sf{ A)\: \dfrac{12}{21}} [/tex]
[tex] \qquad\dashrightarrow \quad\sf{\dfrac{12}{21} = \dfrac{6\times 2}{7\times 3} }[/tex]
[tex] \qquad\dashrightarrow \quad\sf{\dfrac{12}{21}= \dfrac{6}{7}\times \dfrac{2}{3} }[/tex]
As, in [tex]\sf{ \dfrac{2}{3}} [/tex] the denominator and the numerator are not same , therefore [tex]\sf{\dfrac{12}{21}} [/tex] is not equivalent to [tex]\sf{\dfrac{6}{7}} [/tex]
[tex]\quad\bull \quad \sf{ A)\: \dfrac{12}{14}} [/tex]
[tex] \qquad\dashrightarrow \quad\sf{\dfrac{12}{14} = \dfrac{6\times 2}{7\times 2} }[/tex]
[tex] \qquad\dashrightarrow \quad\sf{\dfrac{12}{21}= \dfrac{6}{7}\times \dfrac{2}{2} }[/tex]
As, in [tex]\sf{ \dfrac{2}{2}} [/tex] the denominator and the numerator are same , therefore [tex]\sf{\dfrac{12}{14}} [/tex] is equivalent to [tex]\sf{\dfrac{6}{7}} [/tex]
[tex]\quad\bull \quad \sf{ A)\: \dfrac{18}{21}} [/tex]
[tex] \qquad\dashrightarrow \quad\sf{\dfrac{18}{21} = \dfrac{6\times 3}{7\times 3} }[/tex]
[tex] \qquad\dashrightarrow \quad\sf{\dfrac{18}{21}= \dfrac{6}{7}\times \dfrac{3}{3} }[/tex]
As, in [tex]\sf{ \dfrac{3}{3}} [/tex] the denominator and the numerator are same , therefore [tex]\sf{\dfrac{18}{21}} [/tex] is equivalent to [tex]\sf{\dfrac{6}{7}} [/tex]
[tex]\quad\bull \quad \sf{ A)\: \dfrac{18}{28}} [/tex]
[tex] \qquad\dashrightarrow \quad\sf{\dfrac{18}{28} = \dfrac{6\times 3}{7\times 4} }[/tex]
[tex] \qquad\dashrightarrow \quad\sf{\dfrac{18}{28}= \dfrac{6}{7}\times \dfrac{3}{4} }[/tex]
As, in [tex]\sf{ \dfrac{3}{4}} [/tex] the denominator and the numerator are not same , therefore [tex]\sf{\dfrac{18}{28}} [/tex] is not equivalent to [tex]\sf{\dfrac{6}{7}} [/tex]
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