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

Verified step by step guidance

1. Convert each fraction to have a common denominator. The least common denominator (LCD) of 3 and 4 is 12.
2. Rewrite $-\frac{7}{3}$ as $-\frac{28}{12}$ by multiplying both the numerator and the denominator by 4.
3. Rewrite $\frac{3}{4}$ as $\frac{9}{12}$ by multiplying both the numerator and the denominator by 3.
4. Add the two fractions: $-\frac{28}{12}+\frac{9}{12}$.
5. Combine the numerators over the common denominator: $\frac{-28+9}{12}$.

Key Concepts

Adding Fractions

To add fractions, they must have a common denominator. This involves finding the least common multiple (LCM) of the denominators, converting each fraction to an equivalent fraction with this common denominator, and then adding the numerators while keeping the denominator the same.

Negative Numbers in Fractions

When dealing with negative fractions, it is important to understand how to handle the negative sign. A negative fraction can be represented as the negative of the numerator or the denominator, and this affects the overall value when performing operations like addition.

Simplifying Fractions

After performing operations on fractions, the result may need to be simplified. This involves dividing the numerator and the denominator by their greatest common divisor (GCD) to express the fraction in its simplest form, making it easier to understand and use.