Work out the following :
`2""1/4-1""7/10`

Answer

To solve the problem \( 2 \frac{1}{4} - 1 \frac{7}{10} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 2 \frac{1}{4} \):
- Multiply the whole number (2) by the denominator (4): \( 2 \times 4 = 8 \)
- Add the numerator (1): \( 8 + 1 = 9 \)
- The improper fraction is \( \frac{9}{4} \).

For \( 1 \frac{7}{10} \):
- Multiply the whole number (1) by the denominator (10): \( 1 \times 10 = 10 \)
- Add the numerator (7): \( 10 + 7 = 17 \)
- The improper fraction is \( \frac{17}{10} \).

So, we have:
\[ 2 \frac{1}{4} = \frac{9}{4} \quad \text{and} \quad 1 \frac{7}{10} = \frac{17}{10} \]

### Step 2: Find a Common Denominator
Next, we need to find a common denominator for the fractions \( \frac{9}{4} \) and \( \frac{17}{10} \).

The denominators are 4 and 10. The least common multiple (LCM) of 4 and 10 is 20.

### Step 3: Convert Fractions to Have the Same Denominator
Now, we convert both fractions to have the common denominator of 20.

For \( \frac{9}{4} \):
- Multiply the numerator and denominator by 5:
\[ \frac{9 \times 5}{4 \times 5} = \frac{45}{20} \]

For \( \frac{17}{10} \):
- Multiply the numerator and denominator by 2:
\[ \frac{17 \times 2}{10 \times 2} = \frac{34}{20} \]

### Step 4: Subtract the Fractions
Now we can subtract the two fractions:
\[ \frac{45}{20} - \frac{34}{20} = \frac{45 - 34}{20} = \frac{11}{20} \]

### Step 5: Final Answer
The final answer is:
\[ \frac{11}{20} \]

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