Add or subtract as indicated. Write answers in lowest terms as needed. 7(5/12)-4(5/6)

Verified step by step guidance

1. Distribute the 7 in the expression $7\times \frac{5}{12}$ to get $\frac{35}{12}$.
2. Distribute the 4 in the expression $4\times \frac{5}{6}$ to get $\frac{20}{6}$.
3. Find a common denominator for the fractions $\frac{35}{12}$ and $\frac{20}{6}$. The least common denominator is 12.
4. Convert $\frac{20}{6}$ to an equivalent fraction with a denominator of 12. Multiply both the numerator and the denominator by 2 to get $\frac{40}{12}$.
5. Subtract $\frac{40}{12}$ from $\frac{35}{12}$ 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 with different denominators to be combined. For example, to subtract 4(5/6) from 7(5/12), one must first convert both fractions to have the same denominator before performing the operation.

Mixed Numbers

Mixed numbers consist of a whole number and a fraction, such as 7(5/12). To perform operations on mixed numbers, it is often helpful to convert them into improper fractions. This simplifies calculations and makes it easier to add or subtract the values accurately.

Lowest Terms

Expressing a fraction in lowest terms means simplifying it to its simplest form, where the numerator and denominator have no common factors other than 1. This is important for clarity and precision in mathematical communication. After performing operations on fractions, one should always check if the result can be simplified further.