what should be subtracted from $$ \left(1+\frac{3}{10}\right) $$to get $$ \frac56 $$?

Let's denote the number that should be subtracted by $ x $. We need to solve the following equation:

\[
\left(1 + \frac{3}{10}\right) - x = \frac{5}{6}
\]

### Step 1: Simplify the expression on the left side

The expression $ 1 + \frac{3}{10} $ can be rewritten as:

\[
1 + \frac{3}{10} = \frac{10}{10} + \frac{3}{10} = \frac{13}{10}
\]

Now the equation becomes:

\[
\frac{13}{10} - x = \frac{5}{6}
\]

### Step 2: Solve for $ x $

To find $ x $, subtract $ \frac{5}{6} $ from $ \frac{13}{10} $:

\[
x = \frac{13}{10} - \frac{5}{6}
\]

### Step 3: Find a common denominator

The least common denominator (LCD) for 10 and 6 is 30. Convert each fraction:

\[
\frac{13}{10} = \frac{13 \times 3}{10 \times 3} = \frac{39}{30}
\]
\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\]

### Step 4: Subtract the fractions

Now subtract:

\[
x = \frac{39}{30} - \frac{25}{30} = \frac{39 - 25}{30} = \frac{14}{30}
\]

Simplify $ \frac{14}{30} $:

\[
\frac{14}{30} = \frac{7}{15}
\]

### Final Answer:
The number that should be subtracted is $ \frac{7}{15} $.

Would you like any further details or have any questions? 

Here are some related questions:
1. How do you subtract fractions with different denominators?
2. What is the least common denominator and how do you find it?
3. How do you simplify fractions after subtraction?
4. What is the process to add and subtract mixed numbers?
5. How can we convert mixed numbers to improper fractions?
6. Why is it important to simplify fractions?
7. How do you check the result of a subtraction involving fractions?
8. Can you subtract fractions directly without finding a common denominator?

**Tip:** When subtracting fractions, always ensure you find the least common denominator to simplify your calculations.

Learn how to subtract fractions step-by-step with the problem: What should be subtracted from $ \left(1 + \frac{3}{10}\right) $ to get $ \frac{5}{6} $? Follow a detailed solution including finding common denominators and simplifying fractions. Suitable for students in Grades 6-8.

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