Find each sum or difference. See Example 1.9⁄10 - ( -4⁄3)

Verified step by step guidance

1. Identify the operation: You need to find the difference between \( \frac{9}{10} \) and \( -\frac{4}{3} \).
2. Rewrite the expression: Subtracting a negative is the same as adding a positive, so \( \frac{9}{10} - (-\frac{4}{3}) \) becomes \( \frac{9}{10} + \frac{4}{3} \).
3. Find a common denominator: The denominators are 10 and 3. The least common multiple of 10 and 3 is 30.
4. Convert each fraction to have the common denominator: \( \frac{9}{10} = \frac{27}{30} \) and \( \frac{4}{3} = \frac{40}{30} \).
5. Add the fractions: \( \frac{27}{30} + \frac{40}{30} = \frac{67}{30} \).

Key Concepts

Fractions

Fractions represent a part of a whole and are expressed as a ratio of two integers, where the numerator is the top number and the denominator is the bottom number. Understanding how to manipulate fractions, including addition, subtraction, and finding a common denominator, is essential for solving problems involving them.

Negative Numbers

Negative numbers are values less than zero and are crucial in arithmetic operations. When subtracting a negative number, it is equivalent to adding its positive counterpart. This concept is vital for correctly interpreting and solving expressions that involve negative values.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order, which is essential for accurately solving expressions involving multiple operations.