Then \( b = 2.5 - (-\frac{1}{4}) = 2.5 + 0.25 = 2.75 = \frac{11}{4} \)

["Understanding the Calculation: ( b = 2.5 - \left(-\frac{1}{4}\right) = 2.5 + 0.25 = 2.75 = \frac{11}{4} )", "Solving equations step by step is essential for mastering algebra and building confidence in mathematical computations. One such straightforward calculation involves working with decimals and fractions to simplify expressions into a clean fractional form. Let’s break down the expression:", "[\nb = 2.5 - \left(-\frac{1}{4}\right)\n]", "### Step 1: Simplify the Subtraction of a Negative Fraction\nSubtracting a negative number is the same as adding its positive counterpart:\n[\n2.5 - (-\frac{1}{4}) = 2.5 + \frac{1}{4}\n]", "### Step 2: Convert Decimals to Fractions\nTo perform accurate addition, convert ( 2.5 ) into a fraction:\n[\n2.5 = \frac{5}{2}\n]\nNow the expression becomes:\n[\n\frac{5}{2} + \frac{1}{4}\n]", "### Step 3: Find a Common Denominator\nThe denominators are 2 and 4. The least common denominator is 4:\n[\n\frac{5}{2} = \frac{5 \ imes 2}{2 \ imes 2} = \frac{10}{4}\n]\nSo,\n[\n\frac{10}{4} + \frac{1}{4} = \frac{11}{4}\n]", "### Final Result\nThus,\n[\nb = \frac{11}{4}\n]\nThis fractional value can also be expressed as a decimal:\n[\nb = 2.75\n]", "### Why This Matters in Algebra\nThis simplification demonstrates how decimals and fractions seamlessly convert and relate, enhancing computational fluency. Expressing ( b ) as ( \frac{11}{4} ) offers insights into rational numbers and simplifies further algebraic manipulation, especially when solving equations or working with proportions.", "### Conclusion\nUnderstanding step-by-step transformation—from decimals to fractions and back—strengthens problem-solving skills. Whether simplifying expressions or checking answers, recognizing equivalent forms ensures clarity and correctness.\nSo remember: ( 2.5 - (-\frac{1}{4}) = 2.75 = \frac{11}{4} ) — a clear bridge between decimal and fractional representations.", "---", "Keywords: algebraic simplification, converting decimals to fractions, adding fractions with different denominators, solving for ( b ), fraction equivalence, math calculation steps, rational numbers, decimal-to-fraction conversion.\nMeta Description: Learn step-by-step how to simplify ( b = 2.5 - (-\frac{1}{4}) ) into ( \frac{11}{4} ), combining decimals and fractions for clearer algebraic understanding."]