Simplify The Following Expression:${ \frac{1 \frac{5}{5} \text{ Of } \left(\frac{3}{4} + \frac{5}{5}\right)}{1 \frac{1}{2} - \frac{2}{5}} }$

by ADMIN 142 views

=====================================================

Introduction

Mathematical expressions can be complex and challenging to simplify. In this article, we will focus on simplifying a given mathematical expression that involves fractions and mixed numbers. The expression is as follows:

{ \frac{1 \frac{5}{5} \text{ of } \left(\frac{3}{4} + \frac{5}{5}\right)}{1 \frac{1}{2} - \frac{2}{5}} \}

Understanding the Expression

To simplify the given expression, we need to understand its components. The expression involves two main parts: the numerator and the denominator. The numerator is 1551 \frac{5}{5} of (34+55)\left(\frac{3}{4} + \frac{5}{5}\right), and the denominator is 112−251 \frac{1}{2} - \frac{2}{5}.

Simplifying the Numerator

The numerator can be simplified by first evaluating the expression inside the parentheses. We have 34+55\frac{3}{4} + \frac{5}{5}. To add these fractions, we need to find a common denominator, which is 20. So, we can rewrite the fractions as follows:

{ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \}

{ \frac{5}{5} = \frac{5 \times 4}{5 \times 4} = \frac{20}{20} \}

Now, we can add the fractions:

{ \frac{15}{20} + \frac{20}{20} = \frac{35}{20} \}

Converting the Mixed Number to an Improper Fraction

The mixed number 1551 \frac{5}{5} can be converted to an improper fraction. To do this, we multiply the whole number part by the denominator and add the numerator:

{ 1 \times 5 + 5 = 10 \}

So, the mixed number 1551 \frac{5}{5} is equal to the improper fraction 105\frac{10}{5}.

Simplifying the Numerator Further

Now, we can simplify the numerator by multiplying the improper fraction 105\frac{10}{5} by the fraction 3520\frac{35}{20}:

{ \frac{10}{5} \times \frac{35}{20} = \frac{10 \times 35}{5 \times 20} = \frac{350}{100} \}

Simplifying the Denominator

The denominator is 112−251 \frac{1}{2} - \frac{2}{5}. We can simplify the mixed number 1121 \frac{1}{2} by converting it to an improper fraction:

{ 1 \times 2 + 1 = 3 \}

So, the mixed number 1121 \frac{1}{2} is equal to the improper fraction 32\frac{3}{2}.

Converting the Mixed Number to an Improper Fraction

The mixed number 1121 \frac{1}{2} can be converted to an improper fraction. To do this, we multiply the whole number part by the denominator and add the numerator:

{ 1 \times 2 + 1 = 3 \}

So, the mixed number 1121 \frac{1}{2} is equal to the improper fraction 32\frac{3}{2}.

Simplifying the Denominator Further

Now, we can simplify the denominator by subtracting the fraction 25\frac{2}{5} from the improper fraction 32\frac{3}{2}:

{ \frac{3}{2} - \frac{2}{5} = \frac{3 \times 5}{2 \times 5} - \frac{2 \times 2}{5 \times 2} = \frac{15}{10} - \frac{4}{10} = \frac{11}{10} \}

Simplifying the Expression

Now that we have simplified the numerator and the denominator, we can simplify the expression by dividing the numerator by the denominator:

{ \frac{\frac{350}{100}}{\frac{11}{10}} = \frac{350}{100} \times \frac{10}{11} = \frac{350 \times 10}{100 \times 11} = \frac{3500}{1100} \}

Canceling Common Factors

We can simplify the expression further by canceling common factors:

{ \frac{3500}{1100} = \frac{350 \times 10}{110 \times 10} = \frac{350}{110} \}

Simplifying the Expression Further

We can simplify the expression further by dividing both the numerator and the denominator by their greatest common factor, which is 10:

{ \frac{350}{110} = \frac{35 \times 10}{11 \times 10} = \frac{35}{11} \}

The final answer is 3511\boxed{\frac{35}{11}}.

Conclusion

In this article, we simplified a given mathematical expression that involved fractions and mixed numbers. We started by simplifying the numerator and the denominator separately, and then we simplified the expression by dividing the numerator by the denominator. We canceled common factors and simplified the expression further to obtain the final answer.

=====================================================

Introduction

In our previous article, we simplified a given mathematical expression that involved fractions and mixed numbers. In this article, we will answer some frequently asked questions (FAQs) related to the simplification of the expression.

Q: What is the first step in simplifying the given expression?

A: The first step in simplifying the given expression is to evaluate the expression inside the parentheses in the numerator.

Q: How do I evaluate the expression inside the parentheses in the numerator?

A: To evaluate the expression inside the parentheses in the numerator, you need to find a common denominator for the two fractions. In this case, the common denominator is 20. You can then rewrite the fractions with the common denominator and add them.

Q: What is the common denominator for the two fractions in the numerator?

A: The common denominator for the two fractions in the numerator is 20.

Q: How do I add the fractions in the numerator?

A: To add the fractions in the numerator, you need to add the numerators and keep the common denominator. In this case, the sum of the numerators is 35, and the common denominator is 20.

Q: What is the result of adding the fractions in the numerator?

A: The result of adding the fractions in the numerator is 3520\frac{35}{20}.

Q: How do I convert the mixed number in the numerator to an improper fraction?

A: To convert the mixed number in the numerator to an improper fraction, you need to multiply the whole number part by the denominator and add the numerator. In this case, the mixed number is 1551 \frac{5}{5}, and the result of multiplying the whole number part by the denominator and adding the numerator is 10.

Q: What is the result of converting the mixed number in the numerator to an improper fraction?

A: The result of converting the mixed number in the numerator to an improper fraction is 105\frac{10}{5}.

Q: How do I simplify the numerator further?

A: To simplify the numerator further, you need to multiply the improper fraction 105\frac{10}{5} by the fraction 3520\frac{35}{20}. The result of multiplying the two fractions is 350100\frac{350}{100}.

Q: What is the result of simplifying the numerator further?

A: The result of simplifying the numerator further is 350100\frac{350}{100}.

Q: How do I simplify the denominator?

A: To simplify the denominator, you need to convert the mixed number 1121 \frac{1}{2} to an improper fraction. The result of converting the mixed number to an improper fraction is 32\frac{3}{2}.

Q: What is the result of simplifying the denominator?

A: The result of simplifying the denominator is 32\frac{3}{2}.

Q: How do I subtract the fraction 25\frac{2}{5} from the improper fraction 32\frac{3}{2}?

A: To subtract the fraction 25\frac{2}{5} from the improper fraction 32\frac{3}{2}, you need to find a common denominator for the two fractions. In this case, the common denominator is 10. You can then rewrite the fractions with the common denominator and subtract them.

Q: What is the result of subtracting the fraction 25\frac{2}{5} from the improper fraction 32\frac{3}{2}?

A: The result of subtracting the fraction 25\frac{2}{5} from the improper fraction 32\frac{3}{2} is 1110\frac{11}{10}.

Q: How do I simplify the expression?

A: To simplify the expression, you need to divide the numerator by the denominator. The result of dividing the numerator by the denominator is 35001100\frac{3500}{1100}.

Q: What is the result of simplifying the expression?

A: The result of simplifying the expression is 35001100\frac{3500}{1100}.

Q: How do I cancel common factors in the expression?

A: To cancel common factors in the expression, you need to find the greatest common factor of the numerator and the denominator. In this case, the greatest common factor is 10. You can then divide both the numerator and the denominator by the greatest common factor.

Q: What is the result of canceling common factors in the expression?

A: The result of canceling common factors in the expression is 350110\frac{350}{110}.

Q: How do I simplify the expression further?

A: To simplify the expression further, you need to divide both the numerator and the denominator by their greatest common factor, which is 10.

Q: What is the result of simplifying the expression further?

A: The result of simplifying the expression further is 3511\frac{35}{11}.

Conclusion

In this article, we answered some frequently asked questions related to the simplification of the given mathematical expression. We hope that this article has been helpful in clarifying any doubts you may have had about the simplification of the expression.