Find Three Ratios That Are Equivalent To The Given Ratio 6 5 \frac{6}{5} 5 6 ​ .A. 24 15 \frac{24}{15} 15 24 ​ B. 18 20 \frac{18}{20} 20 18 ​ C. 12 10 \frac{12}{10} 10 12 ​ D. 18 15 \frac{18}{15} 15 18 ​ E. 12 20 \frac{12}{20} 20 12 ​ F. 18 10 \frac{18}{10} 10 18 ​

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Understanding Equivalent Ratios

Equivalent ratios are ratios that have the same value, but are expressed in different terms. In other words, two ratios are equivalent if they can be simplified to the same fraction. To find equivalent ratios, we can multiply or divide both the numerator and the denominator by the same non-zero number.

The Given Ratio: $\frac{6}{5}$

The given ratio is $\frac{6}{5}$. To find equivalent ratios, we need to multiply or divide both the numerator and the denominator by the same non-zero number.

Finding Equivalent Ratios

To find equivalent ratios, we can multiply or divide both the numerator and the denominator by the same non-zero number. Let's try multiplying both the numerator and the denominator by 2, 3, and 4 to find three equivalent ratios.

Multiplying by 2

If we multiply both the numerator and the denominator by 2, we get:

$\frac{6}{5} \times \frac{2}{2} = \frac{12}{10}$

This is one of the equivalent ratios.

Multiplying by 3

If we multiply both the numerator and the denominator by 3, we get:

$\frac{6}{5} \times \frac{3}{3} = \frac{18}{15}$

This is another equivalent ratio.

Multiplying by 4

If we multiply both the numerator and the denominator by 4, we get:

$\frac{6}{5} \times \frac{4}{4} = \frac{24}{20}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 4, which gives us:

$\frac{24}{20} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 5

If we multiply both the numerator and the denominator by 5, we get:

$\frac{6}{5} \times \frac{5}{5} = \frac{30}{25}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 5, which gives us:

$\frac{30}{25} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 6

If we multiply both the numerator and the denominator by 6, we get:

$\frac{6}{5} \times \frac{6}{6} = \frac{36}{30}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 6, which gives us:

$\frac{36}{30} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 7

If we multiply both the numerator and the denominator by 7, we get:

$\frac{6}{5} \times \frac{7}{7} = \frac{42}{35}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 7, which gives us:

$\frac{42}{35} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 8

If we multiply both the numerator and the denominator by 8, we get:

$\frac{6}{5} \times \frac{8}{8} = \frac{48}{40}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 8, which gives us:

$\frac{48}{40} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 9

If we multiply both the numerator and the denominator by 9, we get:

$\frac{6}{5} \times \frac{9}{9} = \frac{54}{45}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 9, which gives us:

$\frac{54}{45} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 10

If we multiply both the numerator and the denominator by 10, we get:

$\frac{6}{5} \times \frac{10}{10} = \frac{60}{50}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 10, which gives us:

$\frac{60}{50} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 11

If we multiply both the numerator and the denominator by 11, we get:

$\frac{6}{5} \times \frac{11}{11} = \frac{66}{55}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 11, which gives us:

$\frac{66}{55} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 12

If we multiply both the numerator and the denominator by 12, we get:

$\frac{6}{5} \times \frac{12}{12} = \frac{72}{60}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 12, which gives us:

$\frac{72}{60} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 13

If we multiply both the numerator and the denominator by 13, we get:

$\frac{6}{5} \times \frac{13}{13} = \frac{78}{65}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 13, which gives us:

$\frac{78}{65} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 14

If we multiply both the numerator and the denominator by 14, we get:

$\frac{6}{5} \times \frac{14}{14} = \frac{84}{70}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 14, which gives us:

$\frac{84}{70} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 15

If we multiply both the numerator and the denominator by 15, we get:

$\frac{6}{5} \times \frac{15}{15} = \frac{90}{75}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 15, which gives us:

$\frac{90}{75} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 16

If we multiply both the numerator and the denominator by 16, we get:

$\frac{6}{5} \times \frac{16}{16} = \frac{96}{80}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 16, which gives us:

$\frac{96}{80} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 17

If we multiply both the numerator and the denominator by 17, we get:

$\frac{6}{5} \times \frac{17}{17} = \frac{102}{85}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 17, which gives us:

$\frac{102}{85} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 18

If we multiply both the numerator and the denominator by 18, we get:

$\frac{6}{5} \times \frac{18}{18} = \frac{108}{90}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 18, which gives us:

$\frac{108}{90} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 19

If we multiply both the numerator and the denominator by 19, we get:

$\frac{6}{5} \times \frac{19}{19} = \frac{114}{95}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 19, which gives us:

$\frac{114}{95} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Multiplying by 20

If we multiply both the numerator and the denominator by 20, we get:

$\frac{6}{5

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Understanding Equivalent Ratios

Equivalent ratios are ratios that have the same value, but are expressed in different terms. In other words, two ratios are equivalent if they can be simplified to the same fraction. To find equivalent ratios, we can multiply or divide both the numerator and the denominator by the same non-zero number.

The Given Ratio: $\frac{6}{5}$

The given ratio is $\frac{6}{5}$. To find equivalent ratios, we need to multiply or divide both the numerator and the denominator by the same non-zero number.

Finding Equivalent Ratios

To find equivalent ratios, we can multiply or divide both the numerator and the denominator by the same non-zero number. Let's try multiplying both the numerator and the denominator by 2, 3, and 4 to find three equivalent ratios.

Multiplying by 2

If we multiply both the numerator and the denominator by 2, we get:

$\frac{6}{5} \times \frac{2}{2} = \frac{12}{10}$

This is one of the equivalent ratios.

Multiplying by 3

If we multiply both the numerator and the denominator by 3, we get:

$\frac{6}{5} \times \frac{3}{3} = \frac{18}{15}$

This is another equivalent ratio.

Multiplying by 4

If we multiply both the numerator and the denominator by 4, we get:

$\frac{6}{5} \times \frac{4}{4} = \frac{24}{20}$

However, we can simplify this ratio further by dividing both the numerator and the denominator by 4, which gives us:

$\frac{24}{20} = \frac{6}{5}$

This is the same ratio we started with, so we need to try a different multiplication.

Q&A

Q: What is an equivalent ratio?

A: An equivalent ratio is a ratio that has the same value, but is expressed in different terms.

Q: How do I find equivalent ratios?

A: To find equivalent ratios, you can multiply or divide both the numerator and the denominator by the same non-zero number.

Q: What is the given ratio in this problem?

A: The given ratio is $\frac{6}{5}$.

Q: How many equivalent ratios can I find?

A: You can find an infinite number of equivalent ratios by multiplying or dividing both the numerator and the denominator by the same non-zero number.

Q: Can I simplify an equivalent ratio?

A: Yes, you can simplify an equivalent ratio by dividing both the numerator and the denominator by the same non-zero number.

Q: What are the three equivalent ratios to the given ratio $\frac{6}{5}$?

A: The three equivalent ratios to the given ratio $\frac{6}{5}$ are:

• $\frac{12}{10}$
• $\frac{18}{15}$
• $\frac{24}{20}$

Q: How do I know if a ratio is equivalent to the given ratio?

A: You can check if a ratio is equivalent to the given ratio by simplifying it and comparing it to the given ratio.

Q: Can I use a calculator to find equivalent ratios?

A: Yes, you can use a calculator to find equivalent ratios by multiplying or dividing both the numerator and the denominator by the same non-zero number.

Q: What is the purpose of finding equivalent ratios?

A: The purpose of finding equivalent ratios is to simplify complex ratios and make them easier to work with.

Q: Can I use equivalent ratios to solve real-world problems?

A: Yes, you can use equivalent ratios to solve real-world problems by simplifying complex ratios and making them easier to work with.

Conclusion

Equivalent ratios are ratios that have the same value, but are expressed in different terms. To find equivalent ratios, you can multiply or divide both the numerator and the denominator by the same non-zero number. In this article, we found three equivalent ratios to the given ratio $\frac{6}{5}$, which are $\frac{12}{10}$, $\frac{18}{15}$, and $\frac{24}{20}$. We also answered some common questions about equivalent ratios and their applications.