Simplify:- (36% of 630) ÷ 1.4 =?

Options

A. a. 156
B. b. 160
C. c. 164
D. d. 162

Answer

To simplify the expression \( (36\% \text{ of } 630) \div 1.4 \), we will follow these steps:

### Step 1: Convert the percentage to a fraction
We know that \( 36\% \) can be expressed as a fraction:
\[ 36\% = \frac{36}{100} \]

### Step 2: Calculate \( 36\% \text{ of } 630 \)
Now, we can calculate \( 36\% \text{ of } 630 \):
\[ 36\% \text{ of } 630 = \frac{36}{100} \times 630 \]

### Step 3: Simplify the multiplication
To simplify \( \frac{36}{100} \times 630 \):
\[ = \frac{36 \times 630}{100} \]

### Step 4: Perform the multiplication
Calculating \( 36 \times 630 \):
\[ 36 \times 630 = 22680 \]
So,
\[ \frac{22680}{100} = 226.8 \]

### Step 5: Divide by 1.4
Now we need to divide \( 226.8 \) by \( 1.4 \):
\[ \frac{226.8}{1.4} \]

### Step 6: Convert the division into multiplication
To make the division easier, we can convert \( 1.4 \) into a fraction:
\[ 1.4 = \frac{14}{10} = \frac{7}{5} \]
Thus,
\[ \frac{226.8}{1.4} = 226.8 \times \frac{5}{7} \]

### Step 7: Calculate \( 226.8 \times \frac{5}{7} \)
First, we can simplify \( 226.8 \) by converting it to a fraction:
\[ 226.8 = \frac{2268}{10} \]
Now we can multiply:
\[ \frac{2268}{10} \times \frac{5}{7} = \frac{2268 \times 5}{10 \times 7} = \frac{11340}{70} \]

### Step 8: Simplify the fraction
Now we simplify \( \frac{11340}{70} \):
\[ \frac{11340 \div 10}{70 \div 10} = \frac{1134}{7} \]

### Step 9: Perform the division
Now we divide \( 1134 \) by \( 7 \):
\[ 1134 \div 7 = 162 \]

### Final Answer
Thus, the simplified value of \( (36\% \text{ of } 630) \div 1.4 \) is:
\[ \boxed{162} \]