Revision1. Simplify: A) $15 + 4 \times 2$ B) $0 \times 50 + 0 \div 18$ C) $125 \div 1 + 32 \times 1$ 2. The Radius Of The Earth Is About $6 \frac{1}{2}$ Million Meters. Write This Number In Figures.3.

Feb 28, 2025 by ADMIN 212 views

Introduction

In mathematics, simplifying algebraic expressions and converting mixed numbers to figures are essential skills that help us solve problems efficiently. In this article, we will focus on simplifying three algebraic expressions and converting a mixed number to figures.

Simplifying Algebraic Expressions

1. Simplify: $15 + 4 \times 2$

To simplify the expression $15 + 4 \times 2$ , we need to follow the order of operations (PEMDAS):

Multiply 4 and 2: $4 \times 2 = 8$
Add 15 and 8: $15 + 8 = 23$

Therefore, the simplified expression is $23$ .

2. Simplify: $0 \times 50 + 0 \div 18$

To simplify the expression $0 \times 50 + 0 \div 18$ , we need to follow the order of operations (PEMDAS):

Multiply 0 and 50: $0 \times 50 = 0$
Divide 0 by 18: $0 \div 18 = 0$
Add 0 and 0: $0 + 0 = 0$

Therefore, the simplified expression is $0$ .

3. Simplify: $125 \div 1 + 32 \times 1$

To simplify the expression $125 \div 1 + 32 \times 1$ , we need to follow the order of operations (PEMDAS):

Divide 125 by 1: $125 \div 1 = 125$
Multiply 32 and 1: $32 \times 1 = 32$
Add 125 and 32: $125 + 32 = 157$

Therefore, the simplified expression is $157$ .

Converting Mixed Numbers to Figures

1. The radius of the Earth is about $6 \frac{1}{2}$ million meters. Write this number in figures.

To convert the mixed number $6 \frac{1}{2}$ to figures, we need to multiply the whole number part by the denominator and add the numerator:

$6 \times 2 = 12$ $12 + 1 = 13$

Therefore, the mixed number $6 \frac{1}{2}$ is equal to $13$ million meters.

Conclusion

In conclusion, simplifying algebraic expressions and converting mixed numbers to figures are essential skills that help us solve problems efficiently. By following the order of operations (PEMDAS) and converting mixed numbers to figures, we can simplify complex expressions and convert them to a more manageable form.

Discussion

What are some common algebraic expressions that can be simplified using the order of operations (PEMDAS)?
How do you convert mixed numbers to figures?
Can you think of any real-world applications of simplifying algebraic expressions and converting mixed numbers to figures?

References

[1] Khan Academy. (n.d.). Order of Operations. Retrieved from https://www.khanacademy.org/math/algebra/x2f6b7d/x2f6b7d/x2f6b7d
[2] Math Open Reference. (n.d.). Mixed Numbers. Retrieved from https://www.mathopenref.com/mixednumbers.html

Additional Resources

Khan Academy: Algebra
Math Open Reference: Mixed Numbers
Wolfram Alpha: Algebraic Expressions
Simplifying Algebraic Expressions and Converting Mixed Numbers to Figures: Q&A ====================================================================

Introduction

In our previous article, we discussed simplifying algebraic expressions and converting mixed numbers to figures. In this article, we will provide a Q&A section to help you better understand these concepts.

Q&A

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:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
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):

Evaluate any expressions inside parentheses.
Evaluate any exponential expressions.
Evaluate any multiplication and division operations from left to right.
Finally, evaluate any addition and subtraction operations from left to right.

Q: What is a mixed number?

A: A mixed number is a number that consists of a whole number part and a fractional part. For example, $3 \frac{1}{2}$ is a mixed number.

Q: How do I convert a mixed number to figures?

A: To convert a mixed number to figures, multiply the whole number part by the denominator and add the numerator:

$3 \times 2 = 6$ $6 + 1 = 7$

Therefore, the mixed number $3 \frac{1}{2}$ is equal to $7$ .

Q: Can I simplify an expression with a zero in it?

A: Yes, you can simplify an expression with a zero in it. When you multiply or divide a number by zero, the result is always zero.

Q: How do I simplify an expression with a negative number?

A: To simplify an expression with a negative number, follow the same rules as you would for a positive number. When you multiply or divide a negative number by another number, the result is always negative.

Q: Can I simplify an expression with a variable in it?

A: Yes, you can simplify an expression with a variable in it. When you have an expression with a variable, you can simplify it by following the order of operations (PEMDAS) and combining like terms.

Examples

Example 1: Simplify the expression $2 \times 3 + 5$

To simplify the expression $2 \times 3 + 5$ , follow the order of operations (PEMDAS):

Multiply 2 and 3: $2 \times 3 = 6$
Add 6 and 5: $6 + 5 = 11$

Therefore, the simplified expression is $11$ .

Example 2: Convert the mixed number $4 \frac{1}{3}$ to figures

To convert the mixed number $4 \frac{1}{3}$ to figures, multiply the whole number part by the denominator and add the numerator:

$4 \times 3 = 12$ $12 + 1 = 13$

Therefore, the mixed number $4 \frac{1}{3}$ is equal to $13$ .

Conclusion

Discussion

What are some common algebraic expressions that can be simplified using the order of operations (PEMDAS)?
How do you convert mixed numbers to figures?
Can you think of any real-world applications of simplifying algebraic expressions and converting mixed numbers to figures?

References

[1] Khan Academy. (n.d.). Order of Operations. Retrieved from https://www.khanacademy.org/math/algebra/x2f6b7d/x2f6b7d/x2f6b7d
[2] Math Open Reference. (n.d.). Mixed Numbers. Retrieved from https://www.mathopenref.com/mixednumbers.html

Additional Resources

Khan Academy: Algebra
Math Open Reference: Mixed Numbers
Wolfram Alpha: Algebraic Expressions

Introduction

Simplifying Algebraic Expressions

1. Simplify: 15+4×215 + 4 \times 215+4×2

2. Simplify: 0×50+0÷180 \times 50 + 0 \div 180×50+0÷18

3. Simplify: 125÷1+32×1125 \div 1 + 32 \times 1125÷1+32×1

Converting Mixed Numbers to Figures

1. The radius of the Earth is about 6126 \frac{1}{2}621​ million meters. Write this number in figures.

Conclusion

Discussion

References

Additional Resources

Introduction

Q&A

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

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

Q: What is a mixed number?

Q: How do I convert a mixed number to figures?

Q: Can I simplify an expression with a zero in it?

Q: How do I simplify an expression with a negative number?

Q: Can I simplify an expression with a variable in it?

Examples

Example 1: Simplify the expression 2×3+52 \times 3 + 52×3+5

Example 2: Convert the mixed number 4134 \frac{1}{3}431​ to figures

Conclusion

Discussion

References

Additional Resources

1. Simplify: $15 + 4 \times 2$

2. Simplify: $0 \times 50 + 0 \div 18$

3. Simplify: $125 \div 1 + 32 \times 1$

1. The radius of the Earth is about $6 \frac{1}{2}$ million meters. Write this number in figures.

Example 1: Simplify the expression $2 \times 3 + 5$

Example 2: Convert the mixed number $4 \frac{1}{3}$ to figures