What Is The Value Of The Expression Below?${ \left(\frac{4}{5}+\frac{3}{5}\right)+3.5 \times 5 }$A. ${ 17 \frac{7}{10}\$} B. ${ 18 \frac{9}{10}\$} C. ${ 21 \frac{3}{4}\$} D. ${ 24 \frac{1}{2}\$}

by ADMIN 196 views

Understanding the Expression

The given expression is a combination of fractions and decimals, along with a multiplication operation. To evaluate this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: None in this case.
  3. Multiplication and Division: Evaluate the multiplication operation.
  4. Addition and Subtraction: Finally, evaluate the addition operation.

Evaluating the Expression Inside the Parentheses

The expression inside the parentheses is 45+35\frac{4}{5}+\frac{3}{5}. To add these fractions, we need to have the same denominator, which is 5 in this case. Therefore, we can directly add the numerators:

45+35=4+35=75\frac{4}{5}+\frac{3}{5} = \frac{4+3}{5} = \frac{7}{5}

Multiplying 3.5 by 5

Now, let's evaluate the multiplication operation: 3.5×53.5 \times 5. To multiply a decimal by an integer, we can simply multiply the decimal part by the integer and then add the result to the product of the integer part and the integer:

3.5×5=(3×5)+(0.5×5)=15+2.5=17.53.5 \times 5 = (3 \times 5) + (0.5 \times 5) = 15 + 2.5 = 17.5

Adding the Results

Now that we have evaluated the expression inside the parentheses and the multiplication operation, we can add the results:

75+17.5=75+17.5×55=75+87.55=7+87.55=94.55\frac{7}{5} + 17.5 = \frac{7}{5} + \frac{17.5 \times 5}{5} = \frac{7}{5} + \frac{87.5}{5} = \frac{7 + 87.5}{5} = \frac{94.5}{5}

Converting the Result to a Mixed Number

To convert the result to a mixed number, we need to divide the numerator by the denominator:

94.55=18.9\frac{94.5}{5} = 18.9

Since we want to express the result as a mixed number, we can write it as:

1891018 \frac{9}{10}

Conclusion

Therefore, the value of the expression is 1891018 \frac{9}{10}.

Comparison with the Options

Let's compare our result with the options:

A. 1771017 \frac{7}{10} B. 1891018 \frac{9}{10} C. 213421 \frac{3}{4} D. 241224 \frac{1}{2}

Our result matches option B: 1891018 \frac{9}{10}.

Final Answer

The final answer is B\boxed{B}

Q: What is the order of operations (PEMDAS) and why is it important?

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

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

It's essential to follow the order of operations to ensure that we evaluate expressions correctly and avoid errors.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, we need to have the same denominator. We can do this by finding the least common multiple (LCM) of the two denominators and then converting each fraction to have the LCM as the denominator.

For example, to add 12\frac{1}{2} and 13\frac{1}{3}, we need to find the LCM of 2 and 3, which is 6. We can then convert each fraction to have a denominator of 6:

12=1×32×3=36\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}

13=1×23×2=26\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}

Now we can add the fractions:

36+26=3+26=56\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, we can use the following steps:

  1. Write the decimal as a fraction with a denominator of 1.
  2. Multiply the numerator and denominator by a power of 10 to eliminate the decimal.

For example, to convert 0.5 to a fraction, we can write it as:

0.5=0.510.5 = \frac{0.5}{1}

We can then multiply the numerator and denominator by 10 to eliminate the decimal:

0.5=0.5×101×10=5100.5 = \frac{0.5 \times 10}{1 \times 10} = \frac{5}{10}

We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5:

510=12\frac{5}{10} = \frac{1}{2}

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 proper fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

For example, 3123 \frac{1}{2} is a mixed number, while 72\frac{7}{2} is an improper fraction.

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

A: To convert a mixed number to an improper fraction, we can follow these steps:

  1. Multiply the whole number by the denominator.
  2. Add the product to the numerator.
  3. Write the result as a fraction with the original denominator.

For example, to convert 3123 \frac{1}{2} to an improper fraction, we can follow these steps:

  1. Multiply the whole number by the denominator: 3×2=63 \times 2 = 6
  2. Add the product to the numerator: 6+1=76 + 1 = 7
  3. Write the result as a fraction with the original denominator: 72\frac{7}{2}

Q: What is the final answer to the original expression?

A: The final answer to the original expression is 1891018 \frac{9}{10}.