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-1 3/10 + 2 1/5

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To add the two mixed numbers \(-1 \frac{3}{10}\) and \(2 \frac{1}{5}\), we can follow these steps:

  1. Convert the mixed numbers to improper fractions.
  2. Find a common denominator.
  3. Add the fractions.
  4. Convert back to a mixed number if necessary.

Step 1: Convert to Improper Fractions

\(-1 \frac{3}{10}\):

  • The improper fraction can be calculated as: \[ -1 \frac{3}{10} = -\left(1 \times 10 + 3\right)/10 = -\frac{13}{10} \]

\(2 \frac{1}{5}\):

  • The improper fraction can be calculated as: \[ 2 \frac{1}{5} = 2 \times 5 + 1/5 = \frac{11}{5} \]

Step 2: Find a Common Denominator

The denominators are \(10\) and \(5\). The least common denominator (LCD) is \(10\).

Convert \(\frac{11}{5}\) to a fraction with a denominator of \(10\): \[ \frac{11}{5} = \frac{11 \times 2}{5 \times 2} = \frac{22}{10} \]

Step 3: Add the Fractions

Now we can add the fractions: \[ -\frac{13}{10} + \frac{22}{10} = \frac{-13 + 22}{10} = \frac{9}{10} \]

Step 4: Convert Back to a Mixed Number

\(\frac{9}{10}\) is already a proper fraction and can be expressed as: \[ \frac{9}{10} = 0 \frac{9}{10} \] This is just \(0.9\) in decimal form.

Thus, the final result of \(-1 \frac{3}{10} + 2 \frac{1}{5}\) is: \[ \frac{9}{10} \] or equivalently in decimal format, \(0.9\).

?

Apologies if my previous explanation wasn't clear or if you were looking for something specific. Let's walk through the calculation of \(-1 \frac{3}{10} + 2 \frac{1}{5}\) again clearly step by step.

Step 1: Convert Mixed Numbers to Improper Fractions

  1. Convert \(-1 \frac{3}{10}\):

    • To convert \(-1 \frac{3}{10}\) to an improper fraction: \[ -1 \frac{3}{10} = -\left(1 \times 10 + 3\right)/10 = -\frac{13}{10} \]

  2. Convert \(2 \frac{1}{5}\):

    • To convert \(2 \frac{1}{5}\) to an improper fraction: \[ 2 \frac{1}{5} = \left(2 \times 5 + 1\right)/5 = \frac{11}{5} \]

Step 2: Find a Common Denominator

The denominators of the two fractions are \(10\) and \(5\). The least common denominator (LCD) is \(10\).

Convert \(\frac{11}{5}\) to have a denominator of \(10\): \[ \frac{11}{5} = \frac{11 \times 2}{5 \times 2} = \frac{22}{10} \]

Step 3: Add the Fractions

Now we can add the fractions: \[ -\frac{13}{10} + \frac{22}{10} = \frac{-13 + 22}{10} = \frac{9}{10} \]

Step 4: Result

The result of \(-1 \frac{3}{10} + 2 \frac{1}{5}\) is: \[ \frac{9}{10} \]

This improper fraction can also be represented as \(0.9\) in decimal form.

If you require further clarification or help with a different aspect of the problem, please let me know!

so it would be in fraction, 9/10? or -9/10?

The result of the calculation \(-1 \frac{3}{10} + 2 \frac{1}{5}\) is:

\[ \frac{9}{10} \]

This means the result is positive, not negative.

To summarize:

  • When you add \(-1 \frac{3}{10}\) (which is \(-\frac{13}{10}\)) and \(2 \frac{1}{5}\) (which is \(\frac{22}{10}\)), the total is:

\[ -\frac{13}{10} + \frac{22}{10} = \frac{9}{10} \]

So, the answer is \(\frac{9}{10}\).