Math / Numbers & Operations

Questionjelect all ratios equivalent to $5: 4$ . $11: 2$ $60: 48$ 3:6

Studdy Solution

STEP 1

1. We are given the ratio $5:4$ .
2. We need to determine which of the given ratios are equivalent to $5:4$ .
3. Ratios are equivalent if they simplify to the same simplest form.

STEP 2

1. Simplify the given ratio $5:4$ .
2. Simplify each of the provided ratios.
3. Compare each simplified ratio to $5:4$ .

STEP 3

Simplify the given ratio $5:4$ .
Since $5$ and $4$ are coprime, the simplest form of the ratio $5:4$ is itself $5:4$ .

STEP 4

Simplify the ratio $11:2$ .
The numbers $11$ and $2$ are coprime, so the simplest form of the ratio $11:2$ is itself $11:2$ .

STEP 5

Simplify the ratio $60:48$ .
Find the greatest common divisor (GCD) of $60$ and $48$ .
The GCD of $60$ and $48$ is $12$ .
Divide both terms by $12$ :
$\frac{60}{12} : \frac{48}{12} = 5:4$

STEP 6

Simplify the ratio $3:6$ .
Find the greatest common divisor (GCD) of $3$ and $6$ .
The GCD of $3$ and $6$ is $3$ .
Divide both terms by $3$ :
$\frac{3}{3} : \frac{6}{3} = 1:2$

STEP 7

Compare each simplified ratio to $5:4$ .
- $11:2$ is not equivalent to $5:4$ . - $60:48$ simplifies to $5:4$ , so it is equivalent. - $3:6$ simplifies to $1:2$ , so it is not equivalent.
The ratio equivalent to $5:4$ is:
$\boxed{60:48}$

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Questionjelect all ratios equivalent to $5: 4$ . $11: 2$ $60: 48$ 3:6

Studdy Solution

STEP 1

1. We are given the ratio $5:4$ .
2. We need to determine which of the given ratios are equivalent to $5:4$ .
3. Ratios are equivalent if they simplify to the same simplest form.

STEP 2

1. Simplify the given ratio $5:4$ .
2. Simplify each of the provided ratios.
3. Compare each simplified ratio to $5:4$ .

STEP 3

Simplify the given ratio $5:4$ .
Since $5$ and $4$ are coprime, the simplest form of the ratio $5:4$ is itself $5:4$ .

STEP 4

Simplify the ratio $11:2$ .
The numbers $11$ and $2$ are coprime, so the simplest form of the ratio $11:2$ is itself $11:2$ .

STEP 5

Simplify the ratio $60:48$ .
Find the greatest common divisor (GCD) of $60$ and $48$ .
The GCD of $60$ and $48$ is $12$ .
Divide both terms by $12$ :
$\frac{60}{12} : \frac{48}{12} = 5:4$

STEP 6

Simplify the ratio $3:6$ .
Find the greatest common divisor (GCD) of $3$ and $6$ .
The GCD of $3$ and $6$ is $3$ .
Divide both terms by $3$ :
$\frac{3}{3} : \frac{6}{3} = 1:2$

STEP 7

Compare each simplified ratio to $5:4$ .
- $11:2$ is not equivalent to $5:4$ . - $60:48$ simplifies to $5:4$ , so it is equivalent. - $3:6$ simplifies to $1:2$ , so it is not equivalent.
The ratio equivalent to $5:4$ is:
$\boxed{60:48}$

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Questionjelect all ratios equivalent to 5:45: 45:4. 11:211: 211:2 60:4860: 4860:48 3:6

Studdy Solution

STEP 1

1. We are given the ratio 5:45:45:4.2. We need to determine which of the given ratios are equivalent to 5:45:45:4.3. Ratios are equivalent if they simplify to the same simplest form.

STEP 2

1. Simplify the given ratio 5:45:45:4.2. Simplify each of the provided ratios.3. Compare each simplified ratio to 5:45:45:4.

STEP 3

Simplify the given ratio 5:45:45:4.Since 555 and 444 are coprime, the simplest form of the ratio 5:45:45:4 is itself 5:45:45:4.

STEP 4

Simplify the ratio 11:211:211:2.The numbers 111111 and 222 are coprime, so the simplest form of the ratio 11:211:211:2 is itself 11:211:211:2.

STEP 5

Simplify the ratio 60:4860:4860:48.Find the greatest common divisor (GCD) of 606060 and 484848.The GCD of 606060 and 484848 is 121212.Divide both terms by 121212:6012:4812=5:4\frac{60}{12} : \frac{48}{12} = 5:41260​:1248​=5:4

STEP 6

Simplify the ratio 3:63:63:6.Find the greatest common divisor (GCD) of 333 and 666.The GCD of 333 and 666 is 333.Divide both terms by 333:33:63=1:2\frac{3}{3} : \frac{6}{3} = 1:233​:36​=1:2

STEP 7

Compare each simplified ratio to 5:45:45:4.- 11:211:211:2 is not equivalent to 5:45:45:4. - 60:4860:4860:48 simplifies to 5:45:45:4, so it is equivalent. - 3:63:63:6 simplifies to 1:21:21:2, so it is not equivalent. The ratio equivalent to 5:45:45:4 is:60:48\boxed{60:48}60:48​

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Questionjelect all ratios equivalent to $5: 4$ . $11: 2$ $60: 48$ 3:6

1. We are given the ratio $5:4$ .
2. We need to determine which of the given ratios are equivalent to $5:4$ .
3. Ratios are equivalent if they simplify to the same simplest form.

1. Simplify the given ratio $5:4$ .
2. Simplify each of the provided ratios.
3. Compare each simplified ratio to $5:4$ .

Simplify the given ratio $5:4$ .
Since $5$ and $4$ are coprime, the simplest form of the ratio $5:4$ is itself $5:4$ .

Simplify the ratio $11:2$ .
The numbers $11$ and $2$ are coprime, so the simplest form of the ratio $11:2$ is itself $11:2$ .

Simplify the ratio $60:48$ .
Find the greatest common divisor (GCD) of $60$ and $48$ .
The GCD of $60$ and $48$ is $12$ .
Divide both terms by $12$ :
$\frac{60}{12} : \frac{48}{12} = 5:4$

Simplify the ratio $3:6$ .
Find the greatest common divisor (GCD) of $3$ and $6$ .
The GCD of $3$ and $6$ is $3$ .
Divide both terms by $3$ :
$\frac{3}{3} : \frac{6}{3} = 1:2$

Compare each simplified ratio to $5:4$ .
- $11:2$ is not equivalent to $5:4$ . - $60:48$ simplifies to $5:4$ , so it is equivalent. - $3:6$ simplifies to $1:2$ , so it is not equivalent.
The ratio equivalent to $5:4$ is:
$\boxed{60:48}$