Math Problem Statement

-1 1/2 + -1/-2 - -3/5

Solution

Let's break down the expression step by step:

112+12(35)-1 \frac{1}{2} + \frac{-1}{-2} - \left( \frac{-3}{5} \right)

Step 1: Convert mixed number to an improper fraction

Convert 112-1 \frac{1}{2} to an improper fraction: 112=32-1 \frac{1}{2} = -\frac{3}{2}

Step 2: Simplify the second term

12\frac{-1}{-2} simplifies to: 12\frac{1}{2}

Step 3: Remove the negative sign in the third term

(35)-\left(\frac{-3}{5}\right) becomes: 35\frac{3}{5}

Step 4: Add all the fractions

Now the expression becomes: 32+12+35-\frac{3}{2} + \frac{1}{2} + \frac{3}{5}

Step 5: Combine 32-\frac{3}{2} and 12\frac{1}{2}

32+12=22=1-\frac{3}{2} + \frac{1}{2} = -\frac{2}{2} = -1

Step 6: Add 1-1 and 35\frac{3}{5}

1+35-1 + \frac{3}{5} To combine these, convert 1-1 to a fraction with a denominator of 5: 1=55-1 = -\frac{5}{5}

Now, add the fractions: 55+35=5+35=25-\frac{5}{5} + \frac{3}{5} = \frac{-5 + 3}{5} = \frac{-2}{5}

Final Answer:

112+12(35)=25-1 \frac{1}{2} + \frac{-1}{-2} - \left( \frac{-3}{5} \right) = -\frac{2}{5}

Would you like more details on any of these steps?

Here are 5 related questions for further practice:

  1. What is the result of 214+36(47)-2 \frac{1}{4} + \frac{-3}{6} - \left(\frac{-4}{7}\right)?
  2. How do you convert a mixed number to an improper fraction?
  3. What happens when both numerator and denominator are negative in a fraction?
  4. How do you add fractions with different denominators?
  5. How would you solve 2341562 \frac{3}{4} - 1 \frac{5}{6}?

Tip: Always simplify negative signs before performing arithmetic with fractions to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Addition and Subtraction of Fractions
Simplifying Fractions

Formulas

Mixed Number to Improper Fraction Conversion: a b/c = (a*c + b)/c
Adding/Subtracting Fractions: a/b + c/d = (a*d + b*c)/(b*d)

Theorems

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Suitable Grade Level

Grades 6-8