Question Find the ratio equivalent to 9:180.

Studdy Solution

STEP 1

Assumptions1. The given ratio is $9180$ . We need to find an equivalent ratio from the given options

STEP 2

To find an equivalent ratio, we need to simplify the given ratio to its simplest form. We can do this by dividing both terms of the ratio by their greatest common divisor (GCD).
$implified\, ratio = \frac{First\, term}{GCD} \frac{Second\, term}{GCD}$

STEP 3

Now, plug in the given values for the first term and the second term to calculate the simplified ratio.
$implified\, ratio = \frac{9}{GCD(9,180)} \frac{180}{GCD(9,180)}$

STEP 4

Calculate the GCD of9 and180.
The GCD of9 and180 is9.

STEP 5

Plug in the value of the GCD to calculate the simplified ratio.
$implified\, ratio = \frac{9}{9} \frac{180}{9}$

STEP 6

Calculate the simplified ratio.
$implified\, ratio =120$

STEP 7

Now, we need to compare this simplified ratio with the simplified form of each of the given options. The one that matches is the equivalent ratio.
For option A, simplify the ratio $5200$ by dividing both terms by their GCD.
$implified\, ratio\, A = \frac{5}{GCD(5,200)} \frac{200}{GCD(5,200)}$

STEP 8

Calculate the GCD of5 and200.
The GCD of5 and200 is5.

STEP 9

Plug in the value of the GCD to calculate the simplified ratio for option A.
$implified\, ratio\, A = \frac{5}{5} \frac{200}{5}$

STEP 10

Calculate the simplified ratio for option A.
$implified\, ratio\, A =40$

STEP 11

The simplified ratio for option A does not match the simplified ratio of the given ratio. So, option A is not equivalent to the given ratio.
Repeat the same process for options B, C, and D.

STEP 12

For option B, simplify the ratio $12240$ by dividing both terms by their GCD.
$implified\, ratio\, B = \frac{12}{GCD(12,240)} \frac{240}{GCD(12,240)}$

STEP 13

Calculate the GCD of12 and240.
The GCD of12 and240 is12.

STEP 14

Plug in the value of the GCD to calculate the simplified ratio for option B.
$implified\, ratio\, B = \frac{12}{12} \frac{240}{12}$

STEP 15

Calculate the simplified ratio for option B.
$implified\, ratio\, B =20$

STEP 16

The simplified ratio for option B matches the simplified ratio of the given ratio. So, option B is equivalent to the given ratio.
Therefore, the ratio equivalent to $9180$ is $12240$ .

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