![Screenshot 2025-05-06 205312.png](https://res.cloudinary.com/aptidude/image/upload/v1746545689/aptidude_questions/yvpwqzify12gqvcmr98p.png)

Question

Accepted Answer

What you're solving for 
Simplify the given expression. 
What's given in the problem

• The expression to simplify: $4\frac{4}{5} 	imes \frac{3}{8} + (3\frac{1}{2} + \frac{2}{3}) 	imes \frac{4}{5}$

Helpful information

• Mixed fractions can be converted to improper fractions using the formula: $a\frac{b}{c} = \frac{a 	imes c + b}{c}$

How to solve 
Simplify the expression using the order of operations (PEMDAS/BODMAS).

1. Step 1 Convert mixed fractions to improper fractions 
	• $4\frac{4}{5} = \frac{4 	imes 5 + 4}{5} = \frac{24}{5}$ 
	• $3\frac{1}{2} = \frac{3 	imes 2 + 1}{2} = \frac{7}{2}$

2. Step 2 Substitute the improper fractions into the expression 
	• $\frac{24}{5} 	imes \frac{3}{8} + (\frac{7}{2} + \frac{2}{3}) 	imes \frac{4}{5}$

3. Step 3 Simplify the terms inside the parentheses 
	• Find a common denominator for $\frac{7}{2}$ and $\frac{2}{3}$, which is $6$. 
	• $\frac{7}{2} = \frac{7 	imes 3}{2 	imes 3} = \frac{21}{6}$ 
	• $\frac{2}{3} = \frac{2 	imes 2}{3 	imes 2} = \frac{4}{6}$ 
	• $\frac{21}{6} + \frac{4}{6} = \frac{21+4}{6} = \frac{25}{6}$

4. Step 4 Substitute the simplified term back into the expression 
	• $\frac{24}{5} 	imes \frac{3}{8} + \frac{25}{6} 	imes \frac{4}{5}$

5. Step 5 Perform the multiplications 
	• $\frac{24}{5} 	imes \frac{3}{8} = \frac{24 	imes 3}{5 	imes 8} = \frac{72}{40} = \frac{9}{5}$ 
	• $\frac{25}{6} 	imes \frac{4}{5} = \frac{25 	imes 4}{6 	imes 5} = \frac{100}{30} = \frac{10}{3}$

6. Step 6 Substitute the results back into the expression 
	• $\frac{9}{5} + \frac{10}{3}$

7. Step 7 Add the fractions 
	• Find a common denominator for $\frac{9}{5}$ and $\frac{10}{3}$, which is $15$. 
	• $\frac{9}{5} = \frac{9 	imes 3}{5 	imes 3} = \frac{27}{15}$ 
	• $\frac{10}{3} = \frac{10 	imes 5}{3 	imes 5} = \frac{50}{15}$ 
	• $\frac{27}{15} + \frac{50}{15} = \frac{27+50}{15} = \frac{77}{15}$

Solution 
The simplified expression is $\frac{77}{15}$.

Answer

Answer

Answer