Math Problem Statement

a) 3/4 + -6/7 + 9/-14

Solution

Let's solve this expression step by step:

34+(67)+914\frac{3}{4} + \left(-\frac{6}{7}\right) + \frac{9}{-14}

  1. First, simplify the fractions: 914=914\frac{9}{-14} = -\frac{9}{14}

    So the expression becomes: 3467914\frac{3}{4} - \frac{6}{7} - \frac{9}{14}

  2. To add and subtract fractions, we need to find a common denominator. The denominators here are 4, 7, and 14. The least common denominator (LCD) of 4, 7, and 14 is 28.

  3. Now, convert each fraction to have a denominator of 28:

    • 34=3×74×7=2128\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}
    • 67=6×47×4=2428-\frac{6}{7} = \frac{-6 \times 4}{7 \times 4} = \frac{-24}{28}
    • 914=9×214×2=1828-\frac{9}{14} = \frac{-9 \times 2}{14 \times 2} = \frac{-18}{28}
  4. Now, add the fractions: 212824281828\frac{21}{28} - \frac{24}{28} - \frac{18}{28}

  5. Combine the numerators: 212418=2121 - 24 - 18 = -21

  6. So, the result is: 2128\frac{-21}{28}

  7. Simplify the fraction: 2128=34\frac{-21}{28} = \frac{-3}{4}

Thus, the answer is: 34\boxed{-\frac{3}{4}}

Would you like more details or clarification?

Here are 5 related questions you can explore:

  1. How do you find the least common denominator (LCD) of fractions?
  2. What is the process for adding and subtracting negative fractions?
  3. How do you simplify a fraction after combining like terms?
  4. What happens when you add a negative fraction to a positive fraction?
  5. How do you convert improper fractions into mixed numbers?

Tip: When adding and subtracting fractions, always ensure the denominators match by finding the least common denominator.

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Math Problem Analysis

Mathematical Concepts

Fractions
Addition and Subtraction of Fractions
Simplifying Fractions

Formulas

LCD (Least Common Denominator)
Fraction Simplification

Theorems

Adding/Subtracting Fractions with Different Denominators

Suitable Grade Level

Grades 6-8