Question

Select all the ratios that are equivalent to 6/7

A 12/21
B 12/14
C 18/21
D 18/28

Answer 1

B, and C

6/7 x 2/2 = 12/14, B

6/7 x 3/3 = 18/21, C

Answer 2

Ⲁⲛ⳽ⲱⲉⲅ:

The ratios which are equivalent to
`\sf{(6)/(7)}` are :

`\qquad\leadsto \quad\sf{ B) \: (12)/(14)}`

`\qquad\leadsto \quad\sf{C)\:(18)/(21) }`

`\quad\rule{300pt}{1.5pt}\quad`

Ⲋⲟⳑⳙⲧⳕⲟⲛ :

Here, we have to find the ratios which are equivalent to the given fraction
`\sf{(6)/(7)}` 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 :

`\quad\bull \quad \sf{ A)\: (12)/(21)}`

`\qquad\dashrightarrow \quad\sf{(12)/(21) = (6* 2)/(7* 3) }`

`\qquad\dashrightarrow \quad\sf{(12)/(21)= (6)/(7)* (2)/(3) }`

As, in
`\sf{ (2)/(3)}` the denominator and the numerator are not same , therefore
`\sf{(12)/(21)}` is not equivalent to
`\sf{(6)/(7)}`

`\quad\bull \quad \sf{ A)\: (12)/(14)}`

`\qquad\dashrightarrow \quad\sf{(12)/(14) = (6* 2)/(7* 2) }`

`\qquad\dashrightarrow \quad\sf{(12)/(21)= (6)/(7)* (2)/(2) }`

As, in
`\sf{ (2)/(2)}` the denominator and the numerator are same , therefore
`\sf{(12)/(14)}` is equivalent to
`\sf{(6)/(7)}`

`\quad\bull \quad \sf{ A)\: (18)/(21)}`

`\qquad\dashrightarrow \quad\sf{(18)/(21) = (6* 3)/(7* 3) }`

`\qquad\dashrightarrow \quad\sf{(18)/(21)= (6)/(7)* (3)/(3) }`

As, in
`\sf{ (3)/(3)}` the denominator and the numerator are same , therefore
`\sf{(18)/(21)}` is equivalent to
`\sf{(6)/(7)}`

`\quad\bull \quad \sf{ A)\: (18)/(28)}`

`\qquad\dashrightarrow \quad\sf{(18)/(28) = (6* 3)/(7* 4) }`

`\qquad\dashrightarrow \quad\sf{(18)/(28)= (6)/(7)* (3)/(4) }`

As, in
`\sf{ (3)/(4)}` the denominator and the numerator are not same , therefore
`\sf{(18)/(28)}` is not equivalent to
`\sf{(6)/(7)}`

`\rule{300pt}{2pt}`