Pregunta
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12. \( \frac{7}{16}+\frac{3}{8} \)

Ask by Harmon Herrera. in the United States
Feb 04,2025

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\[ \frac{7}{16} + \frac{3}{8} = \frac{13}{16} \]

Solución

To add the fractions \( \frac{7}{16} \) and \( \frac{3}{8} \), follow these steps: 1. **Find a Common Denominator:** The denominators are 16 and 8. The least common denominator (LCD) is 16 because 16 is a multiple of 8. 2. **Convert Fractions to Have the Same Denominator:** - The first fraction already has the denominator 16: \[ \frac{7}{16} \] - Convert the second fraction to have the denominator 16: \[ \frac{3}{8} = \frac{3 \times 2}{8 \times 2} = \frac{6}{16} \] 3. **Add the Fractions:** Now that both fractions have the same denominator, add the numerators: \[ \frac{7}{16} + \frac{6}{16} = \frac{7 + 6}{16} = \frac{13}{16} \] **Final Answer:** \[ \frac{7}{16} + \frac{3}{8} = \frac{13}{16} \]

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The Deep Dive

To combine the fractions \( \frac{7}{16} \) and \( \frac{3}{8} \), we need a common denominator. The number 16 is already a multiple of 8, so we can convert \( \frac{3}{8} \) to its equivalent with a denominator of 16: \[ \frac{3}{8} = \frac{3 \times 2}{8 \times 2} = \frac{6}{16} \] Now, we can add the fractions: \[ \frac{7}{16} + \frac{6}{16} = \frac{13}{16} \] Thus, the answer is \( \frac{13}{16} \). To spice things up, did you know that fractions date back thousands of years? The ancient Egyptians used a unique system for representing fractions, often breaking them down into sums of unit fractions, where the numerator was always 1! Next time you tackle fractions, channel your inner Egyptian mathematician—it’s a fun way to see numbers! If you're doing your math homework, always double-check that you've converted all fractions to the same denominator before adding or subtracting! It's a common pitfall to overlook, leading to mistakes. Plus, practicing with different types of denominators can help solidify your understanding. Happy calculating!

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