Evaluate each of the following, giving your answer as a...

Evaluate each of the following, giving your answer as a fraction: (a) $\frac{1}{3}+\frac{3}{5}$ (b) $\frac{2}{7}-\frac{1}{9}$ (c) $\frac{8}{3} \times \frac{6}{5}$ (d) $\frac{4}{5}$ of $\frac{2}{15}$ (e) $\frac{9}{2} \div \frac{3}{2}$ (f) $\frac{6}{7}-\frac{4}{5} \times \frac{3}{2} \div \frac{7}{5}+\frac{9}{4}$

Evaluate each of the following, giving your answer as a fraction:
(a) $\frac{1}{3}+\frac{3}{5}$
(b) $\frac{2}{7}-\frac{1}{9}$
(c) $\frac{8}{3} \times \frac{6}{5}$
(d) $\frac{4}{5}$ of $\frac{2}{15}$
(e) $\frac{9}{2} \div \frac{3}{2}$
(f) $\frac{6}{7}-\frac{4}{5} \times \frac{3}{2} \div \frac{7}{5}+\frac{9}{4}$

Key Concepts

Order of Operations

When evaluating expressions containing multiple fractional operations, the order of operations (parentheses, multiplication, division, addition, and subtraction) dictates the correct sequence of computations to ensure accurate results.

Fraction Division

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. This method, which converts the division operation into a multiplication one, is essential for handling complex fractional operations.

Simplification of Fractions

After performing operations with fractions, simplifying the resulting fraction by finding the greatest common divisor of the numerator and denominator is crucial to express the result in its simplest form. This step is important for clarity and correctness in mathematical expressions.

Fraction Subtraction

Subtracting fractions also necessitates finding a common denominator so that the difference is calculated correctly between the numerators. This concept emphasizes the importance of aligning denominators to accurately reflect the parts of the whole being compared.

Fraction Addition

Fraction addition requires finding a common denominator to combine two fractions. This involves converting the fractions so that they have the same bottom number before adding the numerators, which is a foundational concept in working with rational numbers.

Fraction Multiplication

To multiply fractions, you directly multiply the numerators together and the denominators together. This straightforward procedure simplifies the process of combining fractions multiplicatively without needing a common denominator.

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