To change a decimal numeral to a fraction, express the decimal as a fraction with denominator 10,100 , 1000 and then reduce it to its lowest term.
Amit bought a comic book for `Rs 45.60` and a magazine for Rs 70.00. What is the total amount ( in Rs ) spent by Amit ( Express in lowest fractional form ) ?

Options

A. `( 102)/( 5)`
B. `( 156)/( 2)`
C. `( 578)/( 5)`
D. `( 1156)/( 5)`

Answer

To solve the problem step by step, we will first find the total amount spent by Amit and then convert the decimal amount into a fraction and reduce it to its lowest terms.

### Step 1: Calculate the total amount spent by Amit
Amit bought a comic book for Rs 45.60 and a magazine for Rs 70.00. To find the total amount spent, we will add these two amounts together.

\[ \text{Total Amount} = 45.60 + 70.00 \]

### Step 2: Perform the addition
Now, let's perform the addition:

\[ 45.60 + 70.00 = 115.60 \]

### Step 3: Convert the decimal to a fraction
To convert the decimal 115.60 into a fraction, we can express it as follows:

\[ 115.60 = \frac{11560}{100} \]

Here, we multiply 115.60 by 100 to eliminate the decimal point, which gives us 11560 as the numerator and 100 as the denominator.

### Step 4: Simplify the fraction
Now, we need to simplify the fraction \(\frac{11560}{100}\) to its lowest terms. We can do this by finding the greatest common divisor (GCD) of 11560 and 100.

1. **Finding GCD**: The GCD of 11560 and 100 is 20.
2. **Dividing both numerator and denominator by GCD**:

\[ \frac{11560 \div 20}{100 \div 20} = \frac{578}{5} \]

### Final Answer
Thus, the total amount spent by Amit expressed in the lowest fractional form is:

\[ \text{Total Amount} = \frac{578}{5} \text{ Rs} \]