rite the following ratios in its simplest form. (a) $$ 9: 15 $$ (b) $$ 21: 35 $$ (c) $$ 12: 24: 48 $$ (d) $$ 18: 54: 81 $$

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UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{21}{35}=x$$
- step1: Reduce the fraction:
  $$\frac{3}{5}=x$$
- step2: Swap the sides:
  $$x=\frac{3}{5}$$
Solve the equation $$ 9/15=x $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{9}{15}=x$$
- step1: Reduce the fraction:
  $$\frac{3}{5}=x$$
- step2: Swap the sides:
  $$x=\frac{3}{5}$$
Solve the equation $$ 18/54=x $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{18}{54}=x$$
- step1: Reduce the fraction:
  $$\frac{1}{3}=x$$
- step2: Swap the sides:
  $$x=\frac{1}{3}$$
Solve the equation $$ 12/24=x $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{12}{24}=x$$
- step1: Reduce the fraction:
  $$\frac{1}{2}=x$$
- step2: Swap the sides:
  $$x=\frac{1}{2}$$
Let's simplify each of the given ratios step by step.

### (a) $$ 9: 15 $$

To simplify the ratio $$ 9:15 $$, we divide both numbers by their greatest common divisor (GCD), which is 3.

$$
\frac{9 \div 3}{15 \div 3} = \frac{3}{5}
$$

So, the simplest form of $$ 9:15 $$ is $$ 3:5 $$.

### (b) $$ 21: 35 $$

For the ratio $$ 21:35 $$, we also divide both numbers by their GCD, which is 7.

$$
\frac{21 \div 7}{35 \div 7} = \frac{3}{5}
$$

Thus, the simplest form of $$ 21:35 $$ is $$ 3:5 $$.

### (c) $$ 12: 24: 48 $$

For the ratio $$ 12:24:48 $$, we find the GCD of all three numbers, which is 12.

$$
\frac{12 \div 12}{24 \div 12}{48 \div 12} = \frac{1}{2}{4}
$$

Therefore, the simplest form of $$ 12:24:48 $$ is $$ 1:2:4 $$.

### (d) $$ 18: 54: 81 $$

For the ratio $$ 18:54:81 $$, the GCD is 9.

$$
\frac{18 \div 9}{54 \div 9}{81 \div 9} = \frac{2}{6}{9}
$$

Thus, the simplest form of $$ 18:54:81 $$ is $$ 2:6:9 $$.

### Summary of Simplified Ratios:
- (a) $$ 9:15 $$ simplifies to $$ 3:5 $$
- (b) $$ 21:35 $$ simplifies to $$ 3:5 $$
- (c) $$ 12:24:48 $$ simplifies to $$ 1:2:4 $$
- (d) $$ 18:54:81 $$ simplifies to $$ 2:6:9 $$
The simplified ratios are: - (a) $$ 3:5 $$ - (b) $$ 3:5 $$ - (c) $$ 1:2:4 $$ - (d) $$ 2:6:9 $$

rite the following ratios in its simplest form. (a) \( 9: 15 \) (b) \( 21: 35 \) (c) \( 12: 24: 48 \) (d) \( 18: 54: 81 \)

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