Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
The Currency System: Indian money is counted in Rupees () and Paise (). The fundamental conversion rule is . Visually, you can imagine a grid of small squares representing paise; when all squares are filled, they combine to form one large square representing .
Decimal Representation: Money is written using a decimal point to separate Rupees from Paise. For example, in , the digits to the left of the dot () are Rupees, and the two digits to the right () are Paise. Visually, the decimal point acts as a separator or a 'fence' between the two units.
Conversion Rules: To convert Rupees into Paise, we multiply by (or simply remove the decimal point). To convert Paise into Rupees, we divide by or count two places from the right and insert a decimal point. For example, becomes .
Addition of Money: When adding money, we arrange the numbers in columns so that the decimal points are perfectly aligned vertically. We add from right to left, starting with Paise. If the Paise total is or more, we carry over the hundreds digit to the Rupees column, just like a standard addition carry-over.
Subtraction of Money: To find the difference between two amounts or calculate change, align the decimals vertically and subtract. If the Paise in the top number is less than the Paise in the bottom number, we borrow Rupee from the Rupees column, which is equal to Paise.
Multiplication of Money: To find the cost of multiple items, multiply the amount by the number of items. We perform the multiplication as if they are whole numbers and then place the decimal point in the product so that there are exactly two digits to its right. For example, .
Division of Money: To find the 'Unit Price' (the cost of one item), we divide the total amount by the number of items. In the long division method, the decimal point in the quotient (the answer) is placed directly above the decimal point in the dividend (the total amount).
📐Formulae
💡Examples
Problem 1:
Riya bought a school bag for and a lunch box for . What is the total amount she spent?
Solution:
Step 1: Align the amounts vertically by their decimal points. \begin{array}{r@{\quad}l} ₹ 245.50 \\ + ₹ 128.75 \\ \hline ₹ 374.25 \end{array} Step 2: Add the Paise: Paise. Write in the Paise column and carry over to the Rupees column. Step 3: Add the Rupees: . Total amount = .
Explanation:
To find the total, we use addition. By lining up the decimals, we ensure Rupees are added to Rupees and Paise to Paise, carrying over correctly when Paise exceed .
Problem 2:
If the total cost of identical toy cars is , what is the cost of toy car?
Solution:
Step 1: Set up the division: . Step 2: Divide the Rupees: . Step 3: Divide the Paise: . Step 4: Combine the results with the decimal point in the correct place. Cost of toy car = .
Explanation:
To find the price of a single item when the total for many is known, we use division. The decimal point in the answer stays in the same relative position as the original amount.