23 divided by the sum of \( \frac{2}{3} \) and \( \frac{3}{10} \) \( \left(\frac{2}{3}+\frac{3}{10}\right) \times 23 \) \( \left.\frac{2}{3}+\frac{3}{10}\right) \div 23 \div\left(\frac{2}{3}-\frac{3}{10}\right) \) \( \frac{23}{3}+\frac{3}{10} \)

To solve \( 23 \div \left(\frac{2}{3} + \frac{3}{10}\right) \), we first need to find the sum of \( \frac{2}{3} \) and \( \frac{3}{10} \). The least common multiple of the denominators 3 and 10 is 30. Converting \( \frac{2}{3} \) to a fraction with a denominator of 30 gives us \( \frac{20}{30} \), and \( \frac{3}{10} \) becomes \( \frac{9}{30} \). Adding these two fractions results in \( \frac{20}{30} + \frac{9}{30} = \frac{29}{30} \). Now, compute \( 23 \div \frac{29}{30} \), which is the same as multiplying by the reciprocal: \( 23 \times \frac{30}{29} = \frac{690}{29} \), or approximately 23.79. To explore real-world applications, think about how fractions and division are used in cooking. If a recipe calls for certain amounts but yields more servings than intended, you may need to adjust the ingredients proportionally. Understanding how to manipulate fractions helps in avoiding culinary disasters! Whether you’re making double chocolate chip cookies for a crowd or scaling down a family-size casserole, mastering these calculations keeps your kitchen running smoothly!