Calculate The Following:1. $4 \frac{5}{8} - 3 \frac{1}{4} \times 1 \frac{2}{5}$2. $7 + [8 - 3 \times (\sqrt{4} + 2)]$

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Introduction

Mathematics is a vast and complex subject that requires a deep understanding of various concepts and formulas. In this article, we will delve into two complex math calculations and provide a step-by-step guide on how to solve them. These calculations involve mixed numbers, fractions, and square roots, making them challenging for even the most skilled mathematicians.

Calculation 1: Mixed Numbers and Fractions

The first calculation involves mixed numbers and fractions. We need to calculate the following expression:

458−314×1254 \frac{5}{8} - 3 \frac{1}{4} \times 1 \frac{2}{5}

To solve this expression, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expressions inside the parentheses: In this case, there are no expressions inside the parentheses, so we can move on to the next step.
  2. Multiply the fractions: We need to multiply the fractions 3143 \frac{1}{4} and 1251 \frac{2}{5}. To do this, we need to convert the mixed numbers to improper fractions:

314=1343 \frac{1}{4} = \frac{13}{4}

125=751 \frac{2}{5} = \frac{7}{5}

Now, we can multiply the fractions:

134×75=9120\frac{13}{4} \times \frac{7}{5} = \frac{91}{20}

  1. Subtract the fractions: Now, we need to subtract the fraction 9120\frac{91}{20} from the mixed number 4584 \frac{5}{8}. To do this, we need to convert the mixed number to an improper fraction:

458=3784 \frac{5}{8} = \frac{37}{8}

Now, we can subtract the fractions:

378−9120=18540−18240=340\frac{37}{8} - \frac{91}{20} = \frac{185}{40} - \frac{182}{40} = \frac{3}{40}

Therefore, the final answer to the first calculation is:

340\boxed{\frac{3}{40}}

Calculation 2: Square Roots and Fractions

The second calculation involves square roots and fractions. We need to calculate the following expression:

7+[8−3×(4+2)]7 + [8 - 3 \times (\sqrt{4} + 2)]

To solve this expression, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expressions inside the parentheses: We need to evaluate the expression inside the parentheses:

4+2=2+2=4\sqrt{4} + 2 = 2 + 2 = 4

  1. Multiply the fraction: We need to multiply the fraction 33 by the result of the expression inside the parentheses:

3×4=123 \times 4 = 12

  1. Subtract the result from 8: We need to subtract the result of the multiplication from 8:

8−12=−48 - 12 = -4

  1. Add 7 to the result: Finally, we need to add 7 to the result:

7+(−4)=37 + (-4) = 3

Therefore, the final answer to the second calculation is:

3\boxed{3}

Conclusion

In this article, we have solved two complex math calculations involving mixed numbers, fractions, and square roots. By following the order of operations (PEMDAS) and converting mixed numbers to improper fractions, we were able to simplify the expressions and arrive at the final answers. These calculations demonstrate the importance of understanding various math concepts and formulas in order to solve complex problems.

Tips and Tricks

  • When working with mixed numbers, it's often easier to convert them to improper fractions.
  • When working with fractions, it's often easier to find a common denominator before adding or subtracting.
  • When working with square roots, it's often easier to simplify the expression before evaluating it.

Practice Problems

  • Calculate the following expression: $2 \frac{3}{4} - 1 \frac{1}{2} \times 3 \frac{1}{3}$
  • Calculate the following expression: $9 + [6 - 2 \times (\sqrt{9} + 1)]$

Introduction

In our previous article, we delved into two complex math calculations involving mixed numbers, fractions, and square roots. We provided a step-by-step guide on how to solve these calculations and offered tips and tricks for simplifying the expressions. In this article, we will continue to explore complex math calculations and provide answers to frequently asked questions.

Q&A: Mixed Numbers and Fractions

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a numerator that is greater than or equal to the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the denominator.

Q: How do I add or subtract mixed numbers?

A: To add or subtract mixed numbers, convert them to improper fractions first. Then, find a common denominator and add or subtract the fractions.

Q: How do I multiply mixed numbers?

A: To multiply mixed numbers, convert them to improper fractions first. Then, multiply the fractions and simplify the result.

Q&A: Square Roots and Fractions

Q: What is the difference between a square root and a fraction?

A: A square root is a mathematical operation that finds the number that, when multiplied by itself, gives a specified value. A fraction is a way of expressing a part of a whole.

Q: How do I simplify a square root expression?

A: To simplify a square root expression, look for perfect squares that can be factored out of the expression.

Q: How do I add or subtract square roots?

A: To add or subtract square roots, combine the numbers inside the square roots and simplify the result.

Q&A: Complex Math Calculations

Q: How do I evaluate complex math expressions?

A: To evaluate complex math expressions, follow the order of operations (PEMDAS): parentheses, exponents, multiplication and division, and addition and subtraction.

Q: How do I simplify complex math expressions?

A: To simplify complex math expressions, look for opportunities to combine like terms, factor out common factors, and simplify fractions.

Q: How do I practice complex math calculations?

A: To practice complex math calculations, try solving problems on your own, use online resources, and work with a tutor or mentor.

Conclusion

In this article, we have provided answers to frequently asked questions about complex math calculations involving mixed numbers, fractions, and square roots. By following the tips and tricks outlined in this article, you will become more confident and proficient in solving complex math problems.

Practice Problems

  • Calculate the following expression: $3 \frac{1}{3} - 2 \frac{2}{5} \times 1 \frac{3}{4}$
  • Calculate the following expression: $8 + [6 - 2 \times (\sqrt{16} + 1)]$

By practicing these calculations and following the tips and tricks outlined in this article, you will become more confident and proficient in solving complex math problems.

Additional Resources

  • Khan Academy: Math
  • Mathway: Math Problem Solver
  • Wolfram Alpha: Math Calculator

These resources provide additional support and practice for complex math calculations.