Subjects arithmetic

Fraction Simplification 57Cd38

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1. **State the problem:** Simplify the expression $\frac{23}{12} + 1 \frac{11}{12} - 1 \frac{3}{4}$. 2. **Convert mixed numbers to improper fractions:** $1 \frac{11}{12} = \frac{12 \times 1 + 11}{12} = \frac{23}{12}$ $1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$ 3. **Rewrite the expression with improper fractions:** $\frac{23}{12} + \frac{23}{12} - \frac{7}{4}$ 4. **Find a common denominator:** The denominators are 12 and 4. The least common denominator (LCD) is 12. 5. **Convert $\frac{7}{4}$ to denominator 12:** $\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}$ 6. **Add and subtract fractions:** $\frac{23}{12} + \frac{23}{12} - \frac{21}{12} = \frac{23 + 23 - 21}{12} = \frac{25}{12}$ 7. **Convert improper fraction to mixed number:** $\frac{25}{12} = 2 \frac{1}{12}$ **Final answer:** $2 \frac{1}{12}$