Question

Select all the ratios that are equivalent to the ratio 12:3. explain how you know( show multiplication or division)

A 6:1
B1:4
C4:1
D24:6
E15:6
F1200:300
G112:13​

Answer 1

C 4:1

D 24:6

F 1200:300

Explanation:

The given ratio is
`(12)/(3)`

Simplify

Divide by 3 both numerator and denominator

`(4)/(1)`

Verify each case

case A) we have

`(6)/(1)`

Compare with the given ratio

`(6)/(1) \\eq (4)/(1)`

therefore

The ratio is not equivalent

case B) we have

`(1)/(4)`

Compare with the given ratio

`(1)/(4) \\eq (4)/(1)`

therefore

The ratio is not equivalent

case C) we have

`(4)/(1)`

Compare with the given ratio

`(4)/(1)=(4)/(1)`

therefore

The ratio is equivalent

case D) we have

`(24)/(6)`

Simplify

Divide by 6 both numerator and denominator

`(4)/(1)`

Compare with the given ratio

`(4)/(1)=(4)/(1)`

therefore

The ratio is equivalent

case E) we have

`(15)/(6)`

Simplify

Divide by 3 both numerator and denominator

`(5)/(2)`

Compare with the given ratio

`(5)/(2) \\eq (4)/(1)`

therefore

The ratio is not equivalent

case F) we have

`(1,200)/(300)`

Simplify

Divide by 300 both numerator and denominator

`(4)/(1)`

Compare with the given ratio

`(4)/(1)=(4)/(1)`

therefore

The ratio is equivalent

case G) we have

`(112)/(13)` ----> irreducible

Compare with the given ratio

`(112)/(13) \\eq (4)/(1)`

therefore

The ratio is not equivalent