Solve For $b$ In The Proportion:$\frac{33}{b} = \frac{21}{28}$b =$

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Introduction

In mathematics, proportions are used to describe the relationship between two or more quantities. A proportion is a statement that two ratios are equal. In this article, we will focus on solving for $b$ in the proportion $\frac{33}{b} = \frac{21}{28}$. We will break down the solution step by step and provide a clear explanation of each step.

Understanding the Proportion

A proportion is a statement that two ratios are equal. In this case, we have the proportion $\frac{33}{b} = \frac{21}{28}$. This means that the ratio of 33 to $b$ is equal to the ratio of 21 to 28.

Step 1: Cross-Multiplication

To solve for $b$, we can use the method of cross-multiplication. This involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. In this case, we multiply 33 by 28 and 21 by $b$.

$\frac{33}{b} = \frac{21}{28}$

$33 \times 28 = 21 \times b$

Step 2: Simplifying the Equation

Now we have the equation $33 \times 28 = 21 \times b$. We can simplify this equation by multiplying 33 by 28.

$924 = 21 \times b$

Step 3: Solving for $b$

To solve for $b$, we need to isolate $b$ on one side of the equation. We can do this by dividing both sides of the equation by 21.

$\frac{924}{21} = b$

Step 4: Simplifying the Fraction

Now we have the fraction $\frac{924}{21}$. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

$\frac{924}{21} = \frac{308}{7}$

Step 5: Simplifying the Fraction Further

We can simplify the fraction $\frac{308}{7}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 7.

$\frac{308}{7} = \frac{44}{1}$

Step 6: Simplifying the Fraction to a Whole Number

We can simplify the fraction $\frac{44}{1}$ to a whole number by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

$\frac{44}{1} = 44$

Conclusion

In this article, we solved for $b$ in the proportion $\frac{33}{b} = \frac{21}{28}$. We used the method of cross-multiplication to solve for $b$, and then simplified the equation to isolate $b$ on one side. We also simplified the fraction to a whole number. The final answer is $b = 44$.

Example Use Case

Solving for $b$ in a proportion can be useful in a variety of real-world applications, such as:

• Calculating the cost of goods sold in a business
• Determining the amount of material needed for a construction project
• Finding the ratio of two quantities in a scientific experiment

Tips and Tricks

When solving for $b$ in a proportion, make sure to:

• Use the method of cross-multiplication to solve for $b$
• Simplify the equation to isolate $b$ on one side
• Simplify the fraction to a whole number if possible

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Introduction

In our previous article, we solved for $b$ in the proportion $\frac{33}{b} = \frac{21}{28}$. We used the method of cross-multiplication to solve for $b$, and then simplified the equation to isolate $b$ on one side. In this article, we will answer some common questions related to solving for $b$ in a proportion.

Q: What is a proportion?

A proportion is a statement that two ratios are equal. It is a way of expressing the relationship between two or more quantities.

A: How do I know if a proportion is true or false?

To determine if a proportion is true or false, you can use the method of cross-multiplication. If the product of the numerators is equal to the product of the denominators, then the proportion is true. Otherwise, it is false.

Q: What is the method of cross-multiplication?

The method of cross-multiplication involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. This is a way of solving for $b$ in a proportion.

A: How do I simplify a fraction?

To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, you divide both the numerator and the denominator by the GCD.

Q: What is the greatest common divisor (GCD)?

The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder.

A: How do I find the GCD of two numbers?

There are several ways to find the GCD of two numbers. One way is to list the factors of each number and find the largest common factor. Another way is to use the Euclidean algorithm.

Q: What is the Euclidean algorithm?

The Euclidean algorithm is a method for finding the greatest common divisor (GCD) of two numbers. It involves repeatedly dividing the larger number by the smaller number and taking the remainder.

A: How do I use the Euclidean algorithm to find the GCD?

To use the Euclidean algorithm, you need to follow these steps:

1. Divide the larger number by the smaller number.
2. Take the remainder.
3. Divide the smaller number by the remainder.
4. Take the remainder.
5. Repeat steps 3 and 4 until the remainder is 0.
6. The last non-zero remainder is the GCD.

Q: What are some common applications of proportions?

Proportions are used in a variety of real-world applications, such as:

• Calculating the cost of goods sold in a business
• Determining the amount of material needed for a construction project
• Finding the ratio of two quantities in a scientific experiment

Q: What are some common mistakes to avoid when solving for $b$ in a proportion?

Some common mistakes to avoid when solving for $b$ in a proportion include:

• Not using the method of cross-multiplication
• Not simplifying the equation to isolate $b$ on one side
• Not simplifying the fraction to a whole number if possible

Conclusion

In this article, we answered some common questions related to solving for $b$ in a proportion. We covered topics such as what a proportion is, how to use the method of cross-multiplication, and how to simplify a fraction. We also discussed some common applications of proportions and some common mistakes to avoid when solving for $b$ in a proportion.

Example Use Case

Solving for $b$ in a proportion can be useful in a variety of real-world applications, such as:

• Calculating the cost of goods sold in a business
• Determining the amount of material needed for a construction project
• Finding the ratio of two quantities in a scientific experiment

Tips and Tricks

When solving for $b$ in a proportion, make sure to:

• Use the method of cross-multiplication to solve for $b$
• Simplify the equation to isolate $b$ on one side
• Simplify the fraction to a whole number if possible

By following these steps and tips, you can solve for $b$ in a proportion with ease.