Let's break down and solve the expression step by step:

Expression:  
\[
2 \frac{1}{4} \times \frac{4}{5} \div \left( \frac{3}{4} - \frac{1}{2} \right)
\]

### Step 1: Convert mixed number to improper fraction.
\[
2 \frac{1}{4} = \frac{9}{4}
\]
So, the expression becomes:
\[
\frac{9}{4} \times \frac{4}{5} \div \left( \frac{3}{4} - \frac{1}{2} \right)
\]

### Step 2: Subtract the fractions inside the parentheses.
To subtract \(\frac{1}{2}\) from \(\frac{3}{4}\), first find a common denominator:
\[
\frac{1}{2} = \frac{2}{4}
\]
\[
\frac{3}{4} - \frac{2}{4} = \frac{1}{4}
\]
Now, the expression is:
\[
\frac{9}{4} \times \frac{4}{5} \div \frac{1}{4}
\]

### Step 3: Simplify the division.
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{9}{4} \times \frac{4}{5} \times \frac{4}{1}
\]

### Step 4: Multiply the fractions.
First, simplify:
\[
\frac{9}{4} \times \frac{4}{5} = \frac{36}{20}
\]
Next, multiply:
\[
\frac{36}{20} \times \frac{4}{1} = \frac{144}{20}
\]

### Step 5: Simplify the result.
Simplify \(\frac{144}{20}\) by dividing both the numerator and the denominator by 4:
\[
\frac{144 \div 4}{20 \div 4} = \frac{36}{5}
\]

So, the final result is:
\[
\frac{36}{5} = 7 \frac{1}{5}
\]

### Final Answer:  
\[
7 \frac{1}{5}
\]

Would you like further details on any of the steps?

Here are 5 related questions:
1. How do you convert mixed numbers to improper fractions?
2. What is the rule for dividing by a fraction?
3. Can you simplify \(\frac{9}{4} \times \frac{4}{5}\) directly without multiplying first?
4. How do you find a common denominator for subtracting fractions?
5. How can we simplify large fractions more efficiently?

**Tip:** When multiplying or dividing fractions, always simplify where possible before carrying out operations to make calculations easier.

Learn how to solve the mixed fraction expression 2 1/4 * 4/5 divided by (3/4 - 1/2) step-by-step. This detailed guide covers converting mixed numbers, multiplying and dividing fractions, and simplifying results. Perfect 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