1. Solve For \[$ F \$\]: \[$\frac{f}{2} = \frac{5}{8}\$\]2. Calculate: \[$\frac{1}{2} - \frac{5}{8}\$\]3. Solve For \[$ T \$\]: \[$13.27 = T - 24.45\$\]4. Perform The Following Calculations:

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Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields, including science, engineering, economics, and finance. In this article, we will focus on solving equations and calculating expressions, which are essential skills in mathematics.

Solving for f

Problem 1: Solve for f

We are given the equation f2=58\frac{f}{2} = \frac{5}{8}. To solve for ff, we need to isolate the variable ff on one side of the equation.

To do this, we can multiply both sides of the equation by 2, which is the denominator of the fraction on the left-hand side. This will cancel out the fraction and leave us with the value of ff.

\frac{f}{2} = \frac{5}{8}
\Rightarrow f = 2 \times \frac{5}{8}
\Rightarrow f = \frac{10}{8}
\Rightarrow f = \frac{5}{4}

Therefore, the value of ff is 54\frac{5}{4}.

Calculating Expressions

Problem 2: Calculate 12−58\frac{1}{2} - \frac{5}{8}

To calculate this expression, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 2 and 8 is 8.

\frac{1}{2} - \frac{5}{8} = \frac{4}{8} - \frac{5}{8}
= \frac{4-5}{8}
= \frac{-1}{8}

Therefore, the value of the expression is −18-\frac{1}{8}.

Solving for t

Problem 3: Solve for t

We are given the equation 13.27=t−24.4513.27 = t - 24.45. To solve for tt, we need to isolate the variable tt on one side of the equation.

To do this, we can add 24.45 to both sides of the equation, which will cancel out the negative term and leave us with the value of tt.

13.27 = t - 24.45
\Rightarrow 13.27 + 24.45 = t - 24.45 + 24.45
\Rightarrow 37.72 = t

Therefore, the value of tt is 37.72.

Performing Calculations

Problem 4: Perform the following calculations

We are given the following calculations:

  • 34×2\frac{3}{4} \times 2
  • 56+16\frac{5}{6} + \frac{1}{6}
  • 23−13\frac{2}{3} - \frac{1}{3}

To perform these calculations, we need to follow the order of operations (PEMDAS):

  1. Parentheses: None
  2. Exponents: None
  3. Multiplication and Division: From left to right
  4. Addition and Subtraction: From left to right

Calculation 1: 34×2\frac{3}{4} \times 2

To perform this calculation, we need to multiply the fraction by 2.

\frac{3}{4} \times 2 = \frac{3}{4} \times \frac{2}{1}
= \frac{6}{4}
= \frac{3}{2}

Therefore, the value of the expression is 32\frac{3}{2}.

Calculation 2: 56+16\frac{5}{6} + \frac{1}{6}

To perform this calculation, we need to add the two fractions.

\frac{5}{6} + \frac{1}{6} = \frac{5+1}{6}
= \frac{6}{6}
= 1

Therefore, the value of the expression is 1.

Calculation 3: 23−13\frac{2}{3} - \frac{1}{3}

To perform this calculation, we need to subtract the two fractions.

\frac{2}{3} - \frac{1}{3} = \frac{2-1}{3}
= \frac{1}{3}

Therefore, the value of the expression is 13\frac{1}{3}.

Conclusion

In this article, we have solved equations and calculated expressions using various mathematical operations. We have also followed the order of operations (PEMDAS) to perform calculations. By practicing these skills, you will become proficient in solving equations and calculating expressions, which are essential skills in mathematics.

References

Further Reading

  • Algebra: A Comprehensive Introduction by Michael Artin
  • Calculus: Early Transcendentals by James Stewart
  • Discrete Mathematics and Its Applications by Kenneth H. Rosen

Introduction

In our previous article, we covered the basics of solving equations and calculating expressions. However, we understand that you may still have some questions. In this article, we will address some of the most frequently asked questions related to solving equations and calculating expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify fractions?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. We can then divide both the numerator and denominator by the GCD to simplify the fraction.

For example, let's simplify the fraction 1216\frac{12}{16}:

\frac{12}{16} = \frac{12 \div 4}{16 \div 4}
= \frac{3}{4}

Q: How do I add and subtract fractions?

A: To add or subtract fractions, we need to have a common denominator. We can then add or subtract the numerators while keeping the denominator the same.

For example, let's add the fractions 14\frac{1}{4} and 14\frac{1}{4}:

\frac{1}{4} + \frac{1}{4} = \frac{1+1}{4}
= \frac{2}{4}
= \frac{1}{2}

Q: How do I multiply and divide fractions?

A: To multiply fractions, we can simply multiply the numerators and denominators separately.

For example, let's multiply the fractions 12\frac{1}{2} and 34\frac{3}{4}:

\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4}
= \frac{3}{8}

To divide fractions, we can invert the second fraction and then multiply.

For example, let's divide the fractions 12\frac{1}{2} and 34\frac{3}{4}:

\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3}
= \frac{4}{6}
= \frac{2}{3}

Q: How do I solve linear equations?

A: To solve a linear equation, we need to isolate the variable on one side of the equation. We can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

For example, let's solve the equation x+2=5x + 2 = 5:

x + 2 = 5
\Rightarrow x + 2 - 2 = 5 - 2
\Rightarrow x = 3

Q: How do I solve quadratic equations?

A: To solve a quadratic equation, we need to find the values of the variable that satisfy the equation. We can do this by factoring the equation, using the quadratic formula, or graphing the equation.

For example, let's solve the quadratic equation x2+4x+4=0x^2 + 4x + 4 = 0:

x^2 + 4x + 4 = 0
\Rightarrow (x + 2)^2 = 0
\Rightarrow x + 2 = 0
\Rightarrow x = -2

Conclusion

In this article, we have addressed some of the most frequently asked questions related to solving equations and calculating expressions. We hope that this article has been helpful in clarifying any doubts you may have had. If you have any further questions, please don't hesitate to ask.

References

Further Reading

  • Algebra: A Comprehensive Introduction by Michael Artin
  • Calculus: Early Transcendentals by James Stewart
  • Discrete Mathematics and Its Applications by Kenneth H. Rosen

Note: The references and further reading section are for additional resources and are not required for the article.