Math Problems Fractions and Mixed Numbers

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Questions and Answers

What is the result of $ rac{2}{1}$ - $ rac{1}{1}$ - $ rac{1}{3}$ - 3$ rac{1}{1}$?

  • $-5$ (correct)
  • $-4$
  • $-3$
  • $-1$

Calculate the result of $ rac{5}{6}$ + (-$ rac{7}{12}$).

  • $ rac{11}{12}$
  • $ rac{5}{12}$
  • $ rac{1}{2}$
  • $ rac{1}{12}$ (correct)

What is the result of -1$ rac{4}{15}$ + $ rac{3}{5}$?

  • $- rac{11}{15}$ (correct)
  • $ rac{1}{15}$
  • $- rac{7}{15}$
  • $- rac{1}{3}$

What is the result of -5 + (-$ rac{3}{7}$)?

<p>$-5 rac{3}{7}$ (C)</p> Signup and view all the answers

Calculate -2$ rac{7}{11}$ + 1$ rac{5}{22}$.

<p>$-1 rac{9}{22}$ (C)</p> Signup and view all the answers

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Study Notes

Basic Arithmetic Operations with Fractions

  • Evaluating $\frac{2}{1}$ - $\frac{1}{1}$ - $\frac{1}{3}$ - 3$\frac{1}{1}$ combines whole numbers and improper fractions for a final result.
  • The expression simplifies to a whole number and a fraction, demonstrating subtraction with both types of numbers.

Adding and Subtracting Fractions

  • Adding fractions involving negative numbers, such as $\frac{5}{6}$ + (-$\frac{7}{12}$), requires a common denominator for accurate calculations.
  • Calculate the common denominator for $\frac{5}{6}$ and -$\frac{7}{12}$, finding the resulting value after simplification.

Mixed Numbers and Improper Fractions

  • Mixed numbers like -1$\frac{4}{15}$ are converted to improper fractions when adding to $\frac{3}{5}$ for easier computation.
  • Maintaining signs is crucial to determine the final result when dealing with negative mixed numbers.

Combining Negative Whole Numbers and Fractions

  • The operation -5 + (-$\frac{3}{7}$) highlights how to add negative whole numbers to fractions, resulting in a larger negative value.

Operations with Mixed Numbers

  • The problem -2$\frac{7}{11}$ + 1$\frac{5}{22}$ combines mixed numbers and requires converting both into improper fractions or improper and proper for addition.
  • A common denominator is identified to perform addition of fractions and mixed numbers effectively.

Addition of Mixed Numbers with Negatives

  • The problem -5$\frac{1}{14}$ + (-2$\frac{4}{21}$) illustrates adding two mixed negative numbers to yield a more significant negative result.
  • Conversion to improper fractions before addition simplifies the process and avoids error.

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