Find each sum or difference. -7/3 + 3/4

Verified step by step guidance

1. Identify the problem as adding two fractions: \(-\frac{7}{3} + \frac{3}{4}\).
2. Find the least common denominator (LCD) of the fractions. Since the denominators are 3 and 4, the LCD is the least common multiple of 3 and 4.
3. Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator appropriately: \(-\frac{7}{3} = -\frac{7 \times 4}{3 \times 4}\) and \(\frac{3}{4} = \frac{3 \times 3}{4 \times 3}\).
4. Add the numerators of the rewritten fractions while keeping the common denominator: \(\frac{-7 \times 4 + 3 \times 3}{12}\).
5. Simplify the numerator by performing the multiplication and addition, then write the final fraction. If possible, reduce the fraction to its simplest form.

Key Concepts

Adding and Subtracting Fractions

To add or subtract fractions, they must have a common denominator. This allows you to combine the numerators directly while keeping the denominator the same.

Finding the Least Common Denominator (LCD)

The LCD is the smallest number that both denominators divide into evenly. Finding the LCD helps rewrite fractions with different denominators into equivalent fractions with a common denominator.

Simplifying Fractions

After performing addition or subtraction, the resulting fraction should be simplified by dividing the numerator and denominator by their greatest common divisor to express the fraction in simplest form.