Let's break this down step by step.

The expression is:

\[
\frac{5}{20} + \frac{6}{8} - \frac{8}{4} : \frac{12}{9}
\]

### Step 1: Simplify the fractions
- \(\frac{5}{20} = \frac{1}{4}\)
- \(\frac{6}{8} = \frac{3}{4}\)
- \(\frac{8}{4} = 2\)
- \(\frac{12}{9} = \frac{4}{3}\)

Now, the expression becomes:

\[
\frac{1}{4} + \frac{3}{4} - 2 : \frac{4}{3}
\]

### Step 2: Perform the division
Division by a fraction is equivalent to multiplying by its reciprocal, so:
\[
2 : \frac{4}{3} = 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2}
\]

Now, the expression is:

\[
\frac{1}{4} + \frac{3}{4} - \frac{3}{2}
\]

### Step 3: Find a common denominator
The common denominator for \( \frac{1}{4}, \frac{3}{4}, \) and \( \frac{3}{2} \) is 4. Let's rewrite \(\frac{3}{2}\) as \( \frac{6}{4} \):

\[
\frac{1}{4} + \frac{3}{4} - \frac{6}{4}
\]

### Step 4: Perform the operations
Now, combine the terms:

\[
\frac{1 + 3 - 6}{4} = \frac{-2}{4} = -\frac{1}{2}
\]

### Final Answer:
The value of the expression is:

\[
-\frac{1}{2}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you divide fractions?
2. How can you simplify fractions more efficiently?
3. Why is finding a common denominator important in addition and subtraction of fractions?
4. How does multiplying by the reciprocal work in division?
5. Can negative results appear frequently when working with fractions?

### Tip:
When dividing by a fraction, always multiply by its reciprocal for a quicker solution.

Learn how to simplify the fraction expression 5/20 + 6/8 - 8/4 ÷ 12/9 with a step-by-step breakdown. This problem covers fraction simplification, division by a fraction, and finding common denominators. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation