MATHEMATICS GRADE 9 ASSIGNMENT 1Question 4 Simplify The Following Without Using A Calculator:4.1. \[$ 1 \frac{2}{3} : 2 \frac{2}{3} \$\]4.2. \[$ 2(\sqrt[3]{64} + \sqrt{25}) \$\]4.3. \[$ (3.6 \times 10^6) - (5.2 \times 10^5)

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Introduction

In this article, we will focus on simplifying expressions in Mathematics Grade 9 Assignment 1, Question 4. We will break down each expression into manageable steps, making it easier to understand and solve. Our goal is to provide a clear and concise guide on how to simplify these expressions without using a calculator.

Simplifying the First Expression: 1 2/3 : 2 2/3

To simplify the first expression, we need to follow the order of operations (PEMDAS):

  1. Convert mixed numbers to improper fractions: We will convert 1 2/3 and 2 2/3 to improper fractions.

    • 1 2/3 = (3 + 2)/3 = 5/3
    • 2 2/3 = (8 + 2)/3 = 10/3

  2. Divide the two fractions: To divide fractions, we will multiply the first fraction by the reciprocal of the second fraction.

    • (5/3) ÷ (10/3) = (5/3) × (3/10) = 5/10 = 1/2

Therefore, the simplified expression is 1/2.

Simplifying the Second Expression: 2(√[3]64 + √25)

To simplify the second expression, we need to follow the order of operations (PEMDAS):

  1. Evaluate the cube root: We will evaluate the cube root of 64.

    • ∛64 = ∛(4^3) = 4

  2. Evaluate the square root: We will evaluate the square root of 25.

    • √25 = √(5^2) = 5

  3. Multiply 2 by the sum of the cube root and square root: We will multiply 2 by the sum of the cube root and square root.

    • 2(4 + 5) = 2(9) = 18

Therefore, the simplified expression is 18.

Simplifying the Third Expression: (3.6 × 10^6) - (5.2 × 10^5)

To simplify the third expression, we need to follow the order of operations (PEMDAS):

  1. Evaluate the exponents: We will evaluate the exponents of 10.

    • 3.6 × 10^6 = 3.6 × (10^6)
    • 5.2 × 10^5 = 5.2 × (10^5)

  2. Subtract the two expressions: We will subtract the two expressions.

    • (3.6 × 10^6) - (5.2 × 10^5) = (3.6 × 10^6) - (0.052 × 10^6)
    • = (3.6 - 0.052) × 10^6
    • = 3.548 × 10^6

Therefore, the simplified expression is 3.548 × 10^6.

Conclusion

In this article, we have simplified three expressions in Mathematics Grade 9 Assignment 1, Question 4. We have followed the order of operations (PEMDAS) and broken down each expression into manageable steps. Our goal is to provide a clear and concise guide on how to simplify these expressions without using a calculator. By following these steps, students can confidently simplify expressions and solve problems in mathematics.

Discussion

  • What are some common mistakes students make when simplifying expressions?
  • How can students apply the order of operations (PEMDAS) to simplify expressions?
  • What are some real-world applications of simplifying expressions in mathematics?

References

Introduction

In our previous article, we provided a step-by-step guide on simplifying expressions in Mathematics Grade 9 Assignment 1, Question 4. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions. Our goal is to provide a clear and concise guide on how to simplify expressions and address common questions and concerns.

Q&A

Q: What are some common mistakes students make when simplifying expressions?

A: Some common mistakes students make when simplifying expressions include:

  • Not following the order of operations (PEMDAS)
  • Not converting mixed numbers to improper fractions
  • Not evaluating exponents correctly
  • Not simplifying fractions correctly

Q: How can students apply the order of operations (PEMDAS) to simplify expressions?

A: Students can apply the order of operations (PEMDAS) by following these steps:

  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: What are some real-world applications of simplifying expressions in mathematics?

A: Simplifying expressions has many real-world applications, including:

  • Science and Engineering: Simplifying expressions is essential in science and engineering to solve complex problems and make predictions.
  • Finance: Simplifying expressions is used in finance to calculate interest rates, investments, and other financial calculations.
  • Computer Programming: Simplifying expressions is used in computer programming to write efficient and effective code.

Q: How can students practice simplifying expressions?

A: Students can practice simplifying expressions by:

  • Solving problems: Practice solving problems that involve simplifying expressions.
  • Using online resources: Use online resources, such as math websites and apps, to practice simplifying expressions.
  • Working with a tutor: Work with a tutor or teacher to practice simplifying expressions.

Q: What are some tips for simplifying expressions?

A: Here are some tips for simplifying expressions:

  • Read the problem carefully: Read the problem carefully to understand what is being asked.
  • Break down the problem: Break down the problem into smaller, manageable steps.
  • Use the order of operations: Use the order of operations (PEMDAS) to simplify expressions.
  • Check your work: Check your work to ensure that it is correct.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) related to simplifying expressions. We have provided tips and resources for students to practice simplifying expressions and address common questions and concerns. Our goal is to provide a clear and concise guide on how to simplify expressions and make mathematics more accessible and enjoyable.

Discussion

  • What are some other real-world applications of simplifying expressions in mathematics?
  • How can students apply the order of operations (PEMDAS) to simplify expressions in different contexts?
  • What are some common mistakes students make when simplifying expressions, and how can they avoid them?

References