To solve the expression \( \frac{3}{12} - \frac{2}{10} + \frac{6}{25} - \frac{3}{4} + \frac{2}{5} \), let's first simplify each fraction and then perform the arithmetic operations:

1. Simplify the fractions:
   - \( \frac{3}{12} = \frac{1}{4} \)
   - \( \frac{2}{10} = \frac{1}{5} \)
   - \( \frac{6}{25} \) remains as is
   - \( \frac{3}{4} \) remains as is
   - \( \frac{2}{5} \) remains as is

Now, the expression becomes:
\[
\frac{1}{4} - \frac{1}{5} + \frac{6}{25} - \frac{3}{4} + \frac{2}{5}
\]

2. Combine like terms:
   - \( \frac{1}{4} - \frac{3}{4} = -\frac{2}{4} = -\frac{1}{2} \)
   - \( -\frac{1}{5} + \frac{2}{5} = \frac{1}{5} \)

So the expression now is:
\[
-\frac{1}{2} + \frac{1}{5} + \frac{6}{25}
\]

3. Find a common denominator (in this case, 50):
   - \( -\frac{1}{2} = -\frac{25}{50} \)
   - \( \frac{1}{5} = \frac{10}{50} \)
   - \( \frac{6}{25} = \frac{12}{50} \)

4. Add the fractions:
\[
-\frac{25}{50} + \frac{10}{50} + \frac{12}{50} = \frac{-25 + 10 + 12}{50} = \frac{-3}{50}
\]

So, the result is \( -\frac{3}{50} \).

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How do you find a common denominator for adding fractions?
2. Can you simplify the expression \( \frac{3}{12} - \frac{3}{4} \) further?
3. What is the decimal equivalent of \( -\frac{3}{50} \)?
4. How would the expression change if we had \( \frac{3}{4} + \frac{2}{5} \) instead of subtracting?
5. How do you subtract mixed numbers with different denominators?

**Tip:** Always simplify fractions where possible before performing arithmetic operations; it makes calculations easier and often prevents errors.

Learn how to simplify and solve the fraction expression 3/12 - 2/10 + 6/25 - 3/4 + 2/5. This problem covers key concepts in fraction arithmetic, including simplification and finding a common denominator. Suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation