Select All That Are True.A. 6 × 3 5 = 1 10 6 \times \frac{3}{5} = \frac{1}{10} 6 × 5 3 = 10 1 B. 7 8 × 13 = 7 104 \frac{7}{8} \times 13 = \frac{7}{104} 8 7 × 13 = 104 7 C. 7 8 × 28 = 24 1 2 \frac{7}{8} \times 28 = 24 \frac{1}{2} 8 7 × 28 = 24 2 1 D. 56 × 5 9 = 31 1 9 56 \times \frac{5}{9} = 31 \frac{1}{9} 56 × 9 5 = 31 9 1

Mar 13, 2025 by ADMIN 341 views

**Select All That Are True: Evaluating Mathematical Statements**

In mathematics, evaluating expressions and statements is a crucial skill that requires attention to detail and a solid understanding of mathematical concepts. In this article, we will examine four mathematical statements and determine which ones are true.

Understanding the Statements

Before we dive into the evaluation process, let's take a closer look at each statement:

A. $6 \times \frac{3}{5} = \frac{1}{10}$
B. $\frac{7}{8} \times 13 = \frac{7}{104}$
C. $\frac{7}{8} \times 28 = 24 \frac{1}{2}$
D. $56 \times \frac{5}{9} = 31 \frac{1}{9}$

Evaluating Statement A

To evaluate statement A, we need to multiply 6 by $\frac{3}{5}$ .

$\begin{aligned} 6 \times \frac{3}{5} &= \frac{6 \times 3}{5} \\ &= \frac{18}{5} \\ &= 3 \frac{3}{5} \end{aligned}$

As we can see, statement A is false because the result is $3 \frac{3}{5}$ , not $\frac{1}{10}$ .

Evaluating Statement B

Next, let's evaluate statement B by multiplying $\frac{7}{8}$ by 13.

$\begin{aligned} \frac{7}{8} \times 13 &= \frac{7 \times 13}{8} \\ &= \frac{91}{8} \\ &= 11 \frac{3}{8} \end{aligned}$

Statement B is also false because the result is $11 \frac{3}{8}$ , not $\frac{7}{104}$ .

Evaluating Statement C

Now, let's evaluate statement C by multiplying $\frac{7}{8}$ by 28.

$\begin{aligned} \frac{7}{8} \times 28 &= \frac{7 \times 28}{8} \\ &= \frac{196}{8} \\ &= 24 \frac{4}{8} \\ &= 24 \frac{1}{2} \end{aligned}$

Interestingly, statement C is true because the result is indeed $24 \frac{1}{2}$ .

Evaluating Statement D

Finally, let's evaluate statement D by multiplying 56 by $\frac{5}{9}$ .

$\begin{aligned} 56 \times \frac{5}{9} &= \frac{56 \times 5}{9} \\ &= \frac{280}{9} \\ &= 31 \frac{1}{9} \end{aligned}$

Statement D is also true because the result is indeed $31 \frac{1}{9}$ .

Conclusion

In conclusion, out of the four mathematical statements, only two are true: statement C and statement D. Statement A and statement B are false because their results do not match the given values. It's essential to carefully evaluate mathematical expressions and statements to ensure accuracy and avoid errors.

Key Takeaways

When evaluating mathematical expressions, it's crucial to follow the order of operations (PEMDAS/BODMAS).
Multiplying fractions involves multiplying the numerators and denominators separately.
To check if a statement is true or false, calculate the result and compare it with the given value.

Additional Resources

For more information on mathematical concepts and techniques, consider exploring the following resources:

Khan Academy: A free online platform offering video lessons and practice exercises on various math topics.
Mathway: An online math problem solver that can help you evaluate expressions and solve equations.
Wolfram Alpha: A powerful computational engine that can perform mathematical calculations and provide step-by-step solutions.

In our previous article, we explored four mathematical statements and determined which ones are true. In this article, we'll address some common questions and concerns related to evaluating mathematical expressions and statements.

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

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) and BODMAS (Brackets, Orders, Division and Multiplication, and Addition and Subtraction) are two common notations used to remember the order of operations.

Q: How do I multiply fractions?

A: To multiply fractions, you multiply the numerators (the numbers on top) and denominators (the numbers on the bottom) separately. For example, to multiply $\frac{2}{3}$ by $\frac{4}{5}$ , you would multiply the numerators (2 and 4) to get 8, and multiply the denominators (3 and 5) to get 15, resulting in $\frac{8}{15}$ .

Q: What is the difference between a true statement and a false statement?

A: A true statement is one that accurately reflects the result of a mathematical operation or expression. A false statement, on the other hand, is one that does not accurately reflect the result of a mathematical operation or expression.

Q: How can I check if a statement is true or false?

A: To check if a statement is true or false, you can calculate the result of the mathematical operation or expression and compare it with the given value. If the result matches the given value, the statement is true. If the result does not match the given value, the statement is false.

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

A: Some common mistakes to avoid when evaluating mathematical expressions include:

Not following the order of operations (PEMDAS/BODMAS)
Not multiplying fractions correctly
Not checking the result against the given value
Not using the correct notation or symbols

Q: How can I practice evaluating mathematical expressions and statements?

A: You can practice evaluating mathematical expressions and statements by:

Working through practice problems and exercises
Using online resources such as Khan Academy, Mathway, or Wolfram Alpha
Asking a teacher or tutor for help
Joining a study group or math club

Q: What are some real-world applications of evaluating mathematical expressions and statements?

A: Evaluating mathematical expressions and statements has many real-world applications, including:

Science and engineering: mathematical models and equations are used to describe and predict natural phenomena
Finance: mathematical calculations are used to determine interest rates, investments, and financial risks
Computer programming: mathematical algorithms and expressions are used to solve problems and make decisions
Data analysis: mathematical calculations are used to analyze and interpret data

Conclusion

Evaluating mathematical expressions and statements is a crucial skill that requires attention to detail and a solid understanding of mathematical concepts. By following the order of operations, multiplying fractions correctly, and checking the result against the given value, you can ensure accuracy and avoid errors. Practice evaluating mathematical expressions and statements to become more confident in your ability to assess mathematical statements and make accurate calculations.

Additional Resources

For more information on mathematical concepts and techniques, consider exploring the following resources:

Khan Academy: A free online platform offering video lessons and practice exercises on various math topics.
Mathway: An online math problem solver that can help you evaluate expressions and solve equations.
Wolfram Alpha: A powerful computational engine that can perform mathematical calculations and provide step-by-step solutions.

By following these resources and practicing mathematical evaluation, you'll become more confident in your ability to assess mathematical statements and make accurate calculations.