Mathematics often presents us with fascinating puzzles that require careful attention and a structured approach. Today, we’ll explore a math equation that combines fractions with basic operations such as addition, subtraction, and division. Whether you’re a student, educator, or simply a math enthusiast, this problem is a perfect brain teaser.

The Equation

Let’s take a closer look at the equation:

113−(−58+32)÷3=?\frac{11}{3} – \left( \frac{-5}{8} + \frac{3}{2} \right) \div 3 = ?311​−(8−5​+23​)÷3=?

This equation may seem complex at first glance, but by breaking it down step by step, you’ll see that it’s quite manageable.

Step 1: Solve Inside the Parentheses

First, we need to address the expression within the parentheses:

−58+32\frac{-5}{8} + \frac{3}{2}8−5​+23​

To add these fractions, they must have a common denominator. The denominators are 8 and 2, so the least common denominator is 8. We rewrite the fractions:

−58+128=−5+128=78\frac{-5}{8} + \frac{12}{8} = \frac{-5 + 12}{8} = \frac{7}{8}8−5​+812​=8−5+12​=87​

Step 2: Division by 3

Next, we divide the result by 3:

78÷3=78×13=724\frac{7}{8} \div 3 = \frac{7}{8} \times \frac{1}{3} = \frac{7}{24}87​÷3=87​×31​=247​

Step 3: Subtract from the First Fraction

Now, subtract this from the first fraction in the original equation:

113−724\frac{11}{3} – \frac{7}{24}311​−247​

To subtract these fractions, they again need a common denominator. The least common denominator for 3 and 24 is 24. Rewriting the fractions:

8824−724=88−724=8124\frac{88}{24} – \frac{7}{24} = \frac{88 – 7}{24} = \frac{81}{24}2488​−247​=2488−7​=2481​

Step 4: Simplification

Finally, simplify the fraction:

8124=278\frac{81}{24} = \frac{27}{8}2481​=827​

Thus, the answer to the equation is:

278 or 338\frac{27}{8} \text{ or } 3 \frac{3}{8}827​ or 383​

Conclusion

Mathematical problems like this one offer a rewarding challenge, allowing us to apply fundamental operations and concepts to arrive at the solution. Whether you’re practicing for an exam or simply enjoying the beauty of math, working through equations like this can sharpen your skills and boost your confidence. Next time you encounter a math puzzle, remember to break it down into smaller steps—it’s the key to solving even the most complicated problems!