Comprehensive Step-by-Step Guidance for Beginning-Intermediate Algebra Review

Q1. Is 182 a prime or composite number?

Background

Topic: Prime and Composite Numbers

This question tests your understanding of the definitions of prime and composite numbers and your ability to determine which category a given number falls into.

Key Terms:

• Prime Number: A number greater than 1 that has exactly two positive divisors: 1 and itself.

• Composite Number: A number greater than 1 that has more than two positive divisors.

Step-by-Step Guidance

1. Check if 182 is greater than 1 (since only numbers greater than 1 can be prime or composite).

2. Test if 182 can be divided evenly by any integer other than 1 and itself (for example, try dividing by 2, 3, 5, etc.).

3. If you find a divisor other than 1 and 182, then 182 is composite. If not, it is prime.

Try solving on your own before revealing the answer!

Q2. Find the prime factorization of 294.

Background

Topic: Prime Factorization

This question tests your ability to break down a composite number into a product of prime numbers.

Key Terms and Process:

• Prime Factorization: Expressing a number as a product of its prime factors.

Step-by-Step Guidance

1. Start by dividing 294 by the smallest prime number (2) and continue dividing by prime numbers (3, 5, 7, etc.) until you reach all prime factors.

2. Write 294 as a product of these prime numbers.

3. Double-check that all factors are prime and their product equals 294.

Try solving on your own before revealing the answer!

Q3. Find the least common multiple (LCM) of 8, 18, and 24.

Background

Topic: Least Common Multiple (LCM)

This question tests your ability to find the smallest number that is a multiple of all the given numbers.

Key Terms and Formula:

• LCM: The smallest positive integer that is a multiple of two or more numbers.

• Prime factorize each number to help find the LCM.

Step-by-Step Guidance

1. Prime factorize each number: 8, 18, and 24.

2. For each prime factor, take the highest power that appears in any of the numbers.

3. Multiply these highest powers together to get the LCM.

Try solving on your own before revealing the answer!

Q4. Write the fraction 5/6 with a denominator of 18.

Background

Topic: Equivalent Fractions

This question tests your ability to write an equivalent fraction with a specified denominator.

Key Terms and Formula:

• Equivalent Fractions: Fractions that represent the same value but have different numerators and denominators.

• To find an equivalent fraction, multiply the numerator and denominator by the same number.

Step-by-Step Guidance

1. Determine what number you need to multiply 6 by to get 18.

2. Multiply both the numerator (5) and the denominator (6) by this number.

3. Write the new fraction with denominator 18.

Try solving on your own before revealing the answer!

Q5. Reduce the fraction 10/14, if possible.

Background

Topic: Reducing Fractions

This question tests your ability to simplify fractions by dividing the numerator and denominator by their greatest common factor (GCF).

Key Terms and Formula:

• Greatest Common Factor (GCF): The largest integer that divides both the numerator and denominator.

• To reduce a fraction, divide both the numerator and denominator by their GCF.

Step-by-Step Guidance

1. Find the GCF of 10 and 14.

2. Divide both the numerator and denominator by the GCF.

3. Write the simplified fraction.

Try solving on your own before revealing the answer!