Completing the Table with the Basic Ratio

Oct 13, 2025 by windailys.com 53 views

Introduction

In mathematics, ratios are used to compare the relationship between two or more quantities. A basic ratio is a simple comparison of two numbers, often expressed as a fraction. In this article, we will explore how to complete a table with a basic ratio and understand the underlying mathematical concepts.

What is a Basic Ratio?

A basic ratio is a simple comparison of two numbers, often expressed as a fraction. For example, the ratio of 4 to 6 can be written as 4:6 or 4/6. Basic ratios are used in various mathematical operations, such as addition, subtraction, multiplication, and division.

Completing the Table with the Basic Ratio

The table below contains some missing values and requires us to complete it with a basic ratio.

{ \begin{tabular}{|c|c|} \hline & \\ \hline 4 & 6 \\ \hline & 12 \\ \hline 12 & \\ \hline 16 & \\ \hline & 30 \\ \hline \end{tabular} \}

To complete the table, we need to find the missing values and express them as a basic ratio.

Step 1: Find the Missing Value in the First Row

The first row contains the numbers 4 and 6. We can express this as a basic ratio: 4:6 or 4/6.

Step 2: Find the Missing Value in the Second Row

The second row contains the number 12. We need to find the missing value that, when multiplied by the first row's ratio, gives us 12. Let's call the missing value x.

{ \frac{4}{6} \times x = 12 \}

To solve for x, we can multiply both sides of the equation by 6/4, which is the reciprocal of 4/6.

{ x = 12 \times \frac{6}{4} \}

Simplifying the equation, we get:

{ x = 18 \}

So, the missing value in the second row is 18.

Step 3: Find the Missing Value in the Third Row

The third row contains the number 12. We need to find the missing value that, when multiplied by the first row's ratio, gives us 12. Let's call the missing value y.

{ \frac{4}{6} \times y = 12 \}

To solve for y, we can multiply both sides of the equation by 6/4, which is the reciprocal of 4/6.

{ y = 12 \times \frac{6}{4} \}

Simplifying the equation, we get:

{ y = 18 \}

So, the missing value in the third row is also 18.

Step 4: Find the Missing Value in the Fourth Row

The fourth row contains the number 16. We need to find the missing value that, when multiplied by the first row's ratio, gives us 16. Let's call the missing value z.

{ \frac{4}{6} \times z = 16 \}

To solve for z, we can multiply both sides of the equation by 6/4, which is the reciprocal of 4/6.

{ z = 16 \times \frac{6}{4} \}

Simplifying the equation, we get:

{ z = 24 \}

So, the missing value in the fourth row is 24.

Step 5: Find the Missing Value in the Fifth Row

The fifth row contains the number 30. We need to find the missing value that, when multiplied by the first row's ratio, gives us 30. Let's call the missing value w.

{ \frac{4}{6} \times w = 30 \}

To solve for w, we can multiply both sides of the equation by 6/4, which is the reciprocal of 4/6.

{ w = 30 \times \frac{6}{4} \}

Simplifying the equation, we get:

{ w = 45 \}

So, the missing value in the fifth row is 45.

Conclusion

In this article, we have completed the table with a basic ratio by finding the missing values and expressing them as a fraction. We have also understood the underlying mathematical concepts and operations involved in completing the table.

Basic Ratio: 4:6 or 4/6

The basic ratio is 4:6 or 4/6.

Final Table

The completed table is:

{ \begin{tabular}{|c|c|} \hline & \\ \hline 4 & 6 \\ \hline 18 & 12 \\ \hline 12 & 18 \\ \hline 16 & 24 \\ \hline 45 & 30 \\ \hline \end{tabular} \}

Q1: What is a basic ratio?

A basic ratio is a simple comparison of two numbers, often expressed as a fraction. For example, the ratio of 4 to 6 can be written as 4:6 or 4/6.

Q2: How do I find the missing value in a table with a basic ratio?

To find the missing value in a table with a basic ratio, you need to multiply the first row's ratio by the missing value to get the second row's value. For example, if the first row is 4:6 and the second row is x:12, you can multiply 4/6 by x to get 12.

Q3: What is the difference between a basic ratio and a proportion?

A basic ratio is a simple comparison of two numbers, while a proportion is a statement that two ratios are equal. For example, the ratio of 4 to 6 is a basic ratio, while the proportion 4/6 = 2/3 is a proportion.

Q4: How do I simplify a basic ratio?

To simplify a basic ratio, you need to find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD. For example, the ratio 12:18 can be simplified by dividing both numbers by 6 to get 2:3.

Q5: Can I add or subtract basic ratios?

No, you cannot add or subtract basic ratios. However, you can multiply or divide basic ratios to get a new ratio.

Q6: How do I convert a basic ratio to a decimal?

To convert a basic ratio to a decimal, you need to divide the first number by the second number. For example, the ratio 4:6 can be converted to a decimal by dividing 4 by 6, which gives 0.67.

Q7: Can I use basic ratios in real-life situations?

Yes, basic ratios are used in many real-life situations, such as cooking, building, and finance. For example, a recipe may require a ratio of 2:3 of flour to sugar, while a builder may use a ratio of 3:4 of concrete to sand.

Q8: How do I find the missing value in a table with multiple basic ratios?

To find the missing value in a table with multiple basic ratios, you need to use the same method as finding the missing value in a table with a single basic ratio. However, you may need to use multiple equations to solve for the missing value.

Q9: Can I use basic ratios with fractions?

Yes, you can use basic ratios with fractions. For example, the ratio 1/2:3/4 can be simplified by multiplying both fractions by 4 to get 2:3.

Q10: How do I check if a basic ratio is true?

To check if a basic ratio is true, you need to multiply the first row's ratio by the second row's value to get the third row's value. If the result is equal to the third row's value, then the basic ratio is true.

Conclusion

We hope this article has provided a clear understanding of basic ratios and has helped you to develop your mathematical skills. If you have any further questions or need help with a specific problem, please don't hesitate to ask.