AMP Units 4-5 Review FY25

Front

What is the process for simplifying the expression \(\frac{2}{3}(2x + 6) - 4\)?

Back

To simplify the expression, distribute \(\frac{2}{3}\) to both terms inside the parentheses: \(\frac{2}{3} \cdot 2x + \frac{2}{3} \cdot 6 - 4 = \frac{4x}{3} + 4 - 4 = \frac{4x}{3}\).

Front

How do you determine if two fractions are equivalent?

Back

Two fractions are equivalent if their cross products are equal, or if they simplify to the same lowest terms.

Front

What is the least common multiple (LCM) of two numbers, and how is it calculated?

Back

The least common multiple of two numbers is the smallest multiple that is evenly divisible by both numbers. It can be calculated by listing the multiples of each number and finding the smallest common one, or by using the formula: \(\text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)}\).

Front

What is prime factorization, and how is it performed?

Back

Prime factorization is the process of expressing a number as the product of its prime factors. It is performed by dividing the number by the smallest prime number until the result is 1.

Front

What is the formula for finding the total cost of multiple items?

Back

The total cost can be found using the formula: \(\text{Total Cost} = \text{Number of Items} \times \text{Cost per Item}\).

Front

How do you simplify the expression \(\frac{6}{4}(-6x + 6) + 3x\)?

Back

First, distribute \(\frac{6}{4}\) to both terms: \(\frac{6}{4} \cdot -6x + \frac{6}{4} \cdot 6 + 3x = -\frac{36x}{4} + \frac{36}{4} + 3x = -9x + 9 + 3x = -6x + 9\).

Front

What is the significance of the greatest common divisor (GCD) in simplifying fractions?

Back

The greatest common divisor is used to simplify fractions by dividing both the numerator and the denominator by the GCD, resulting in the simplest form of the fraction.

Front

How can you find the number of days until two events coincide if they occur at different intervals?

Back

To find the number of days until two events coincide, calculate the least common multiple (LCM) of the two intervals.

Front

What is the relationship between factors and multiples?

Back

A factor is a number that divides another number without leaving a remainder, while a multiple is the result of multiplying a number by an integer.

Front

What is the distributive property, and how is it applied in algebra?

Back

The distributive property states that \(a(b + c) = ab + ac\). It is applied by distributing the multiplier to each term inside the parentheses.