Add or subtract as indicated. Write answers in lowest terms as needed. 8(2/9)-4(2/3)

Verified step by step guidance

1. Distribute the 8 in the expression $8\left(\frac{2}{9}\right)$ to get $\frac{16}{9}$.
2. Distribute the 4 in the expression $4\left(\frac{2}{3}\right)$ to get $\frac{8}{3}$.
3. Find a common denominator for the fractions $\frac{16}{9}$ and $\frac{8}{3}$. The least common denominator is 9.
4. Convert $\frac{8}{3}$ to a fraction with a denominator of 9 by multiplying both the numerator and the denominator by 3, resulting in $\frac{24}{9}$.
5. Subtract $\frac{24}{9}$ from $\frac{16}{9}$ to get the final result.

Key Concepts

Fraction Operations

Understanding how to add and subtract fractions is essential in algebra. This involves finding a common denominator, which allows fractions to be combined or compared. For example, to subtract 4(2/3) from 8(2/9), one must first convert both fractions to have the same denominator before performing the operation.

Multiplication of Fractions

Multiplying a whole number by a fraction requires converting the whole number into a fraction. For instance, 8 can be expressed as 8/1, allowing for straightforward multiplication with the fraction. This concept is crucial for simplifying expressions like 8(2/9) and 4(2/3) before performing addition or subtraction.

Simplifying Fractions

After performing operations on fractions, it is important to simplify the result to its lowest terms. This involves dividing the numerator and denominator by their greatest common divisor (GCD). Simplifying ensures that the answer is presented in the most concise and understandable form, which is a key aspect of working with fractions in algebra.