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 only 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 (it is).

2. Test divisibility by small prime numbers (2, 3, 5, 7, etc.).

3. If you find a divisor other than 1 and 182, the number is composite.

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:

• 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.

2. After each division, write down the prime factor and continue factoring the quotient.

3. Repeat until all factors are prime numbers.

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 given numbers.

Key Terms and Formulas:

• 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, take the highest power that appears in any factorization.

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 Formulas:

• Equivalent Fractions: Fractions that represent the same value.

• 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 and denominator of 5/6 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: Simplifying Fractions

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

Key Terms and Formulas:

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

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

Step-by-Step Guidance

1. Find the GCF of 10 and 14.

2. Divide both numerator and denominator by the GCF.

3. Write the simplified fraction.

Try solving on your own before revealing the answer!