Simplify The Following Expressions:A. 1.114 ( 3 + 5 1.114(3+5 1.114 ( 3 + 5 ]B. 1.23 1 2 − 2 1 3 1.23 \frac{1}{2} - 2 \frac{1}{3} 1.23 2 1 ​ − 2 3 1 ​ C. 1.32 ÷ 1 2 3 1.32 \div 1 \frac{2}{3} 1.32 ÷ 1 3 2 ​

In mathematics, simplifying expressions is an essential skill that helps us to evaluate and solve problems more efficiently. In this article, we will simplify three different expressions involving decimals and fractions.

A. $1.114(3+5)$

To simplify the expression $1.114(3+5)$, we need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the parentheses: $3+5 = 8$
2. Multiply $1.114$ by the result: $1.114 \times 8 = 8.912$

Therefore, the simplified expression is $8.912$.

B. $1.23 \frac{1}{2} - 2 \frac{1}{3}$

To simplify the expression $1.23 \frac{1}{2} - 2 \frac{1}{3}$, we need to convert the mixed numbers to improper fractions:

1. Convert $1.23 \frac{1}{2}$ to an improper fraction: $1.23 \frac{1}{2} = \frac{249}{200}$
2. Convert $2 \frac{1}{3}$ to an improper fraction: $2 \frac{1}{3} = \frac{7}{3}$
3. Find a common denominator for the two fractions: $200$ and $3$ have a common denominator of $600$
4. Rewrite the fractions with the common denominator: $\frac{249}{200} = \frac{3744}{600}$ and $\frac{7}{3} = \frac{1400}{600}$
5. Subtract the two fractions: $\frac{3744}{600} - \frac{1400}{600} = \frac{2344}{600}$
6. Simplify the fraction: $\frac{2344}{600} = 3.907$

Therefore, the simplified expression is $3.907$.

C. $1.32 \div 1 \frac{2}{3}$

To simplify the expression $1.32 \div 1 \frac{2}{3}$, we need to convert the mixed number to an improper fraction:

1. Convert $1 \frac{2}{3}$ to an improper fraction: $1 \frac{2}{3} = \frac{5}{3}$
2. Divide $1.32$ by the improper fraction: $\frac{1.32}{\frac{5}{3}} = 1.32 \times \frac{3}{5} = \frac{3.96}{5} = 0.792$

Therefore, the simplified expression is $0.792$.

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us to evaluate and solve problems more efficiently. In this article, we simplified three different expressions involving decimals and fractions. By following the order of operations and converting mixed numbers to improper fractions, we were able to simplify the expressions and find their values.

Tips and Tricks

• When simplifying expressions, always follow the order of operations (PEMDAS).
• Convert mixed numbers to improper fractions to make it easier to simplify the expression.
• Find a common denominator for the fractions to make it easier to subtract or add them.
• Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.

Practice Problems

1. Simplify the expression $2.45(6+8)$.
2. Simplify the expression $3.21 \frac{1}{4} - 1 \frac{3}{4}$.
3. Simplify the expression $4.56 \div 2 \frac{1}{2}$.

Answer Key

1. $2.45(6+8) = 2.45 \times 14 = 34.3$
2. $3.21 \frac{1}{4} - 1 \frac{3}{4} = \frac{809}{250} - \frac{625}{250} = \frac{184}{250} = 0.736$
3. $4.56 \div 2 \frac{1}{2} = \frac{4.56}{\frac{5}{2}} = 4.56 \times \frac{2}{5} = \frac{9.12}{5} = 1.824$
   Simplify the Following Expressions: Q&A =====================================

In our previous article, we simplified three different expressions involving decimals and fractions. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q: What is the order of operations (PEMDAS)?

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. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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.

Q: How do I simplify an expression with multiple operations?

A: To simplify an expression with multiple operations, follow the order of operations (PEMDAS):

1. Evaluate any expressions inside parentheses first.
2. Evaluate any exponential expressions next.
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

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, such as $2 \frac{1}{3}$. An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as $\frac{7}{3}$.

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

A: To convert a mixed number to an improper fraction, 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 $2 \frac{1}{3}$ to an improper fraction, we would:

1. Multiply $2$ by $3$: $2 \times 3 = 6$
2. Add $6$ to $1$: $6 + 1 = 7$
3. Write the result as a fraction with the original denominator: $\frac{7}{3}$

Q: How do I simplify an expression with decimals and fractions?

A: To simplify an expression with decimals and fractions, follow these steps:

1. Convert the decimal to a fraction.
2. Convert the fraction to an improper fraction.
3. Simplify the expression using the order of operations (PEMDAS).

For example, to simplify the expression $1.23 \frac{1}{2} - 2 \frac{1}{3}$, we would:

1. Convert $1.23$ to a fraction: $1.23 = \frac{123}{100}$
2. Convert $2 \frac{1}{3}$ to an improper fraction: $2 \frac{1}{3} = \frac{7}{3}$
3. Simplify the expression using the order of operations (PEMDAS): $\frac{123}{100} - \frac{7}{3} = \frac{369}{300} - \frac{700}{300} = \frac{-331}{300} = -1.1033$

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not following the order of operations (PEMDAS)
• Not converting mixed numbers to improper fractions
• Not finding a common denominator for fractions
• Not simplifying fractions by dividing both the numerator and the denominator by their greatest common divisor

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us to evaluate and solve problems more efficiently. By following the order of operations (PEMDAS) and converting mixed numbers to improper fractions, we can simplify expressions and find their values. Remember to avoid common mistakes such as not following the order of operations and not simplifying fractions.

Practice Problems

1. Simplify the expression $2.45(6+8)$.
2. Simplify the expression $3.21 \frac{1}{4} - 1 \frac{3}{4}$.
3. Simplify the expression $4.56 \div 2 \frac{1}{2}$.

Answer Key

1. $2.45(6+8) = 2.45 \times 14 = 34.3$
2. $3.21 \frac{1}{4} - 1 \frac{3}{4} = \frac{809}{250} - \frac{625}{250} = \frac{184}{250} = 0.736$
3. $4.56 \div 2 \frac{1}{2} = \frac{4.56}{\frac{5}{2}} = 4.56 \times \frac{2}{5} = \frac{9.12}{5} = 1.824$