Simplify:- 3.5 * (80 ÷ 2.5) = ?

Options

A. a. 122
B. b. 111
C. c. 222
D. d. none of these

Answer

To simplify the expression \( 3.5 \times (80 \div 2.5) \), we can follow these steps:

### Step 1: Simplify the division inside the parentheses
First, we need to calculate \( 80 \div 2.5 \).

\[ 80 \div 2.5 = \frac{80}{2.5} \]

To make the division easier, we can convert \( 2.5 \) to a fraction. Since \( 2.5 = \frac{25}{10} \), we can rewrite the division as:

\[ \frac{80}{\frac{25}{10}} = 80 \times \frac{10}{25} \]

### Step 2: Simplify the fraction
Now, we simplify \( \frac{10}{25} \):

\[ \frac{10}{25} = \frac{2}{5} \]

So now we have:

\[ 80 \times \frac{2}{5} \]

### Step 3: Perform the multiplication
Next, we multiply \( 80 \) by \( \frac{2}{5} \):

\[ 80 \times \frac{2}{5} = \frac{80 \times 2}{5} = \frac{160}{5} \]

Now, we can simplify \( \frac{160}{5} \):

\[ \frac{160}{5} = 32 \]

### Step 4: Multiply by 3.5
Now we substitute back into the original expression:

\[ 3.5 \times 32 \]

We can convert \( 3.5 \) to a fraction as well:

\[ 3.5 = \frac{35}{10} \]

So we have:

\[ \frac{35}{10} \times 32 = \frac{35 \times 32}{10} \]

### Step 5: Calculate \( 35 \times 32 \)
Now we calculate \( 35 \times 32 \):

\[ 35 \times 32 = 1120 \]

### Step 6: Divide by 10
Now we divide by \( 10 \):

\[ \frac{1120}{10} = 112 \]

### Final Answer
Thus, the simplified value of \( 3.5 \times (80 \div 2.5) \) is:

\[ \boxed{112} \]

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