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Which sum is less than 1 ? A. \( \frac{3}{3}+\frac{2}{5}=\frac{6}{19} \) B. \( \frac{3}{5}+\frac{1}{2}=\frac{4}{7} \) C. \( \frac{2}{3}+\frac{3}{4}=\frac{7}{7} \) D. \( \frac{5}{8}+\frac{2}{3}=\frac{7}{1} \)

Ask by Bradley Ross. in the United States
Feb 04,2025

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Tutor-Verified Answer

Answer

None of the sums is less than 1.

Solution

Let's evaluate each of the given sums to determine which one is less than 1. ### Option A: \[ \frac{3}{3} + \frac{2}{5} = 1 + 0.4 = 1.4 \] **Result:** \(1.4 > 1\) ### Option B: \[ \frac{3}{5} + \frac{1}{2} = 0.6 + 0.5 = 1.1 \] **Result:** \(1.1 > 1\) ### Option C: \[ \frac{2}{3} + \frac{3}{4} \approx 0.666 + 0.75 = 1.416 \] **Result:** \(1.416 > 1\) ### Option D: \[ \frac{5}{8} + \frac{2}{3} \approx 0.625 + 0.666 = 1.291 \] **Result:** \(1.291 > 1\) **Conclusion:** All the sums provided in options A, B, C, and D are **greater than 1**. Therefore, **none of the sums is less than 1**. **Final Answer:** None of the provided sums is less than 1.

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The Deep Dive

Let’s dive into the world of fractions! To determine which of these sums is less than 1, we need to evaluate each equation, comparing the left and right sides. For instance, in option A, \( \frac{3}{3}+\frac{2}{5} \) simplifies to \( 1+\frac{2}{5} \), which equals \( \frac{7}{5} \) – definitely greater than 1! Similarly, check the others: options C and D clearly exceed 1 when simplified (C equals 2 and D also equals 7). When you're dealing with fractions, remember that adding two fractions with high numerators and denominators like in options B, C, and D often tips the scale over 1. It’s all about that careful balancing act! In this case, B is close but if you carry out the operations, you'll find it's actually greater than \( \frac{4}{7} \). So, keep an eye out for those sneaky fractions next time!

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