Find each sum or difference. 9/10 - (-4/3)

Verified step by step guidance

1. Identify the problem as a subtraction of two fractions: \(\frac{9}{10} - \left(-\frac{4}{3}\right)\).
2. Recognize that subtracting a negative fraction is equivalent to adding its positive counterpart, so rewrite the expression as \(\frac{9}{10} + \frac{4}{3}\).
3. Find the least common denominator (LCD) of the two fractions. The denominators are 10 and 3, so the LCD is the least common multiple of 10 and 3.
4. Convert each fraction to an equivalent fraction with the LCD as the denominator by multiplying numerator and denominator appropriately.
5. Add the numerators of the equivalent fractions and write the sum over the common denominator: \(\frac{\text{new numerator}}{\text{LCD}}\).

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. If denominators differ, find the least common denominator (LCD) first.

Subtracting Negative Numbers

Subtracting a negative number is equivalent to adding its positive counterpart. For example, a - (-b) becomes a + b. This rule simplifies expressions and helps avoid sign errors.

Finding the Least Common Denominator (LCD)

The LCD is the smallest number that both denominators divide into evenly. It is used to rewrite fractions with different denominators into equivalent fractions with the same denominator, enabling addition or subtraction.