Find the difference:
`4/(7)-3/(10)`

Answer

To find the difference between the fractions \( \frac{4}{7} \) and \( \frac{3}{10} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the Denominators
The denominators of the fractions are 7 and 10. We need to find the LCM of these two numbers.

- The factors of 7 are just 7 (since it is a prime number).
- The factors of 10 are 2 and 5.

Since there are no common factors between 7 and 10, the LCM is calculated by multiplying these numbers together:
\[ \text{LCM} = 7 \times 10 = 70 \]

### Step 2: Rewrite Each Fraction with the LCM as the Denominator
Now that we have the LCM, we will rewrite each fraction so that they both have a denominator of 70.

- For \( \frac{4}{7} \):
\[ \frac{4}{7} = \frac{4 \times 10}{7 \times 10} = \frac{40}{70} \]

- For \( \frac{3}{10} \):
\[ \frac{3}{10} = \frac{3 \times 7}{10 \times 7} = \frac{21}{70} \]

### Step 3: Subtract the Two Fractions
Now we can subtract the two fractions:
\[ \frac{40}{70} - \frac{21}{70} = \frac{40 - 21}{70} = \frac{19}{70} \]

### Final Answer
The difference between \( \frac{4}{7} \) and \( \frac{3}{10} \) is:
\[ \frac{19}{70} \]

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