Solve For \[$ M \$\]:$\[ \frac{m}{28} = \frac{7}{8} \\]

Feb 26, 2025 by ADMIN 56 views

$Solve for $m$: $\frac{m}{28} = \frac{7}{8}$$

Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields such as science, engineering, economics, and finance. In mathematics, solving equations is a vital skill that helps us to understand and analyze complex problems. In this article, we will focus on solving a simple equation involving fractions, specifically the equation $\frac{m}{28} = \frac{7}{8}$ .

Understanding the Equation

The given equation is a simple proportionality equation, where the ratio of two quantities is equal to a given ratio. In this case, the ratio of $m$ to $28$ is equal to the ratio of $7$ to $8$ . To solve for $m$ , we need to isolate the variable $m$ on one side of the equation.

Cross-Multiplication

One of the most common methods to solve proportionality equations is cross-multiplication. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. In this case, we can cross-multiply as follows:

\frac{m}{28} = \frac{7}{8}

m \times 8 = 28 \times 7

Simplifying the Equation

After cross-multiplying, we get the equation $8m = 196$ . To solve for $m$ , we need to isolate the variable $m$ on one side of the equation. We can do this by dividing both sides of the equation by $8$ .

8m = 196

m = \frac{196}{8}

Simplifying the Fraction

The fraction $\frac{196}{8}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $4$ .

m = \frac{196}{8}

m = \frac{49}{2}

Conclusion

In this article, we solved the equation $\frac{m}{28} = \frac{7}{8}$ using cross-multiplication and simplification. We found that the value of $m$ is $\frac{49}{2}$ . This equation is a simple example of a proportionality equation, and solving it requires a basic understanding of fractions and algebraic manipulations.

Real-World Applications

Solving proportionality equations like the one above has many real-world applications. For example, in finance, the ratio of the price of a stock to its earnings per share is often used to determine the stock's value. In engineering, the ratio of the length of a beam to its height is used to determine the beam's strength. In science, the ratio of the volume of a gas to its pressure is used to determine the gas's behavior.

Tips and Tricks

Here are some tips and tricks to help you solve proportionality equations like the one above:

Always read the equation carefully and understand what is being asked.
Use cross-multiplication to solve proportionality equations.
Simplify fractions by dividing both the numerator and the denominator by their greatest common divisor.
Check your answer by plugging it back into the original equation.

Common Mistakes

Here are some common mistakes to avoid when solving proportionality equations like the one above:

Not reading the equation carefully and understanding what is being asked.
Not using cross-multiplication to solve proportionality equations.
Not simplifying fractions by dividing both the numerator and the denominator by their greatest common divisor.
Not checking your answer by plugging it back into the original equation.

Final Thoughts

Solving proportionality equations like the one above is a fundamental skill that is used in many real-world applications. By following the tips and tricks outlined above and avoiding common mistakes, you can become proficient in solving these types of equations. Remember to always read the equation carefully and understand what is being asked, and to use cross-multiplication and simplification to solve the equation.

Introduction

In our previous article, we solved the equation $\frac{m}{28} = \frac{7}{8}$ using cross-multiplication and simplification. We found that the value of $m$ is $\frac{49}{2}$ . In this article, we will answer some frequently asked questions about solving proportionality equations like the one above.

Q&A

Q: What is a proportionality equation?

A: A proportionality equation is an equation that states that two ratios are equal. It is often written in the form $\frac{a}{b} = \frac{c}{d}$ , where $a$ , $b$ , $c$ , and $d$ are numbers.

Q: How do I solve a proportionality equation?

A: To solve a proportionality equation, you can use cross-multiplication. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. You can then simplify the resulting equation to find the value of the variable.

Q: What is cross-multiplication?

A: Cross-multiplication is a method of solving proportionality equations. It involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. This can be written as:

\frac{a}{b} = \frac{c}{d}

a \times d = b \times c

Q: How do I simplify a fraction?

A: To simplify a fraction, you can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

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

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. It can be found using the Euclidean algorithm.

Q: How do I check my answer?

A: To check your answer, you can plug it back into the original equation. If the equation is true, then your answer is correct.

Q: What are some common mistakes to avoid when solving proportionality equations?

A: Some common mistakes to avoid when solving proportionality equations include:

Not reading the equation carefully and understanding what is being asked.
Not using cross-multiplication to solve proportionality equations.
Not simplifying fractions by dividing both the numerator and the denominator by their greatest common divisor.
Not checking your answer by plugging it back into the original equation.