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I really need help with these problems please, if you help I’m going to be so thankful with you


For each of the sections below, you need to design 3 questions. Be sure to include instructions.

show the answers for each of your questions step by step please
- worked out!

4.1 Divisibility Rules

4.2 Prime and Composite Numbers

4.3 GCD and LCM

5.1 Addition and Subtraction of Integers

5.2
Multiplication and Division of Integers

6.1 Rational Numbers

6.2 Addition and Subtraction of Rational Numbers

6.3 Multiplication and Division of Rational Numbers

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4.1 Divisibility Rules:

Question:

Determine whether 987 is divisible by 3. Show each step of your solution.

Worked-out Answer:

  • Add the digits of 987: 9 + 8 + 7 = 24.
  • Check if the sum (24) is divisible by 3.
  • Since 24 is divisible by 3, the original number 987 is also divisible by 3.

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4.2 Prime and Composite Numbers:

Question:

Identify whether 67 is a prime or composite number. Show your reasoning step by step.

Worked-out Answer:

  • Check for factors of 67.
  • Since 67 has no factors other than 1 and 67, it is a prime number.

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4.3 GCD and LCM:

Question:

Find the Greatest Common Divisor (GCD) of 36 and 48. Show your work step by step.

Worked-out Answer:

  • List the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
  • List the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
  • Identify the common factors: 1, 2, 3, 4, 6.
  • The GCD is 6.

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5.1 Addition and Subtraction of Integers:

Question:

Perform the following calculation: (-15) + 8 - 20. Show each step.

Worked-out Answer:

  • Combine like terms: (-15) + 8 - 20 = -7 - 20.
  • Perform the subtraction: -7 - 20 = -27.

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5.2 Multiplication and Division of Integers:

Question:

Evaluate the expression: [tex]\frac{-18*3}{6}[/tex]. Show your work step by step.

Worked-out Answer:

  • Perform the multiplication: -18 × 3 = -54.
  • Perform the division: [tex]\frac{-54}{6}[/tex] = -9.

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6.1 Rational Numbers:

Question:

Determine whether [tex]\frac{5}{2}[/tex] is a rational number. Explain your reasoning.

Worked-out Answer:

  • A rational number is any number that can be expressed as a fraction.
  • Since [tex]\frac{5}{2}[/tex] can be expressed as a fraction, it is a rational number.

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6.2 Addition and Subtraction of Rational Numbers:

Question:

Calculate [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}[/tex]. Show each step of your solution.

Worked-out Answer:

  • Find a common denominator: [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{9}{12}[/tex] + [tex]\frac{4}{12}[/tex].
  • Add the numerators:  [tex]\frac{9}{12}[/tex] + [tex]\frac{4}{12}[/tex]. = [tex]\frac{13}{12}[/tex].

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6.3 Multiplication and Division of Rational Numbers:

Question:

Divide [tex]\frac{5}{6}[/tex] by [tex]\frac{2}{3}[/tex]. Show your work step by step.

Worked-out Answer:

  • Invert the divisor:  [tex]\frac{5}{6}[/tex] ÷ [tex]\frac{2}{3}[/tex]. = [tex]\frac{5}{6}[/tex] × [tex]\frac{3}{2}[/tex].
  • Multiply the numerators and denominators: [tex]\frac{5*3}{6*2}[/tex] = [tex]\frac{15}{12}[/tex].
  • Simplify the fraction if necessary.

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