Find each sum or difference. See Example 1. -7⁄3 + 3⁄4

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Identify the problem as adding two fractions: \(-\frac{7}{3} + \frac{3}{4}\).

Find the least common denominator (LCD) of the two fractions. Since the denominators are 3 and 4, the LCD is the least common multiple of 3 and 4, which is 12.

Convert each fraction to an equivalent fraction with the denominator 12 by multiplying numerator and denominator appropriately: \(-\frac{7}{3} = -\frac{7 \times 4}{3 \times 4} = -\frac{28}{12}\) and \(\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}\).

Add the two fractions with the common denominator: \(-\frac{28}{12} + \frac{9}{12} = \frac{-28 + 9}{12} = \frac{-19}{12}\).

Simplify the fraction if possible. Since \(\frac{-19}{12}\) is already in simplest form, this is the final expression for the sum.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Adding and Subtracting Fractions

To add or subtract fractions, they must have a common denominator. This involves finding the least common denominator (LCD), converting each fraction to an equivalent fraction with the LCD, and then performing the addition or subtraction on the numerators.

Finding the Least Common Denominator (LCD)

The LCD is the smallest number that both denominators divide into evenly. It is essential for combining fractions with different denominators, ensuring the fractions are expressed with a common base for accurate addition or subtraction.

Simplifying Fractions

After adding or subtracting fractions, the result should be simplified by dividing the numerator and denominator by their greatest common divisor (GCD). Simplifying makes the fraction easier to understand and use in further calculations.

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