L.11 Least number of coins

Least number of coins

key points :

Least number of coins means using the smallest number of coins to make a certain amount.
Always try to use bigger value coins first
👉 Example: ₹10, ₹5, ₹2, ₹1
This helps to reduce the total number of coins.

Look at the amount (Example: ₹12)

Choose the biggest coin possible

Use smaller coins for the remaining amount

Count total coins used

👉 ₹12 = ₹10 + ₹2 → 2 coins (least number)

Do not use many small coins if a bigger coin is available
❌ ₹5 = ₹1 + ₹1 + ₹1 + ₹1 + ₹1 (5 coins)
✔️ ₹5 = ₹5 (1 coin)
Always check if a bigger coin can replace smaller coins

Students will be able to:

Learn with an example

📘 How do you make 5 rupees and 50 paise using the fewest coins?

Start with 5-rupee coins and count by ₹5.00. When you’ve gone past ₹5.50, you’ve gone too far. 1 5-rupee coin makes ₹5.00. 2 5-rupee coins make ₹10.00—too much. You can have 1 5-rupee coin. 1 5-rupee coin is worth ₹5.00.
Now count up by ₹2.00 from ₹5.00 to find out how many 2-rupee coins you can have. 1 2-rupee coin makes ₹7.00—too much. You can have 0 2-rupee coins. So far, you have 1 5-rupee coin and 0 2-rupee coins, which are worth ₹5.00.
Now count up by ₹1.00 from ₹5.00 to find out how many 1-rupee coins you can have. 1 1-rupee coin makes ₹6.00—too much. You can have 0 1-rupee coins. So far, you have 1 5-rupee coin, 0 2-rupee coins, and 0 1-rupee coins, which are worth ₹5.00.
Finally, count up by 50p from ₹5.00 to find out how many 50-paise coins you can have. 1 50-paise coin makes ₹5.50. That’s the total you want.
To make 5 rupees and 50 paise with the fewest coins, you’ll use 1 5-rupee coin, 0 2-rupee coins, 0 1-rupee coins, and 1 50-paise coin.

📘 How do you make 8 rupees and 50 paise using the fewest coins?

Start with 5-rupee coins and count by ₹5.00. When you’ve gone past ₹8.50, you’ve gone too far. 1 5-rupee coin makes ₹5.00. 2 5-rupee coins make ₹10.00—too much. You can have 1 5-rupee coin. 1 5-rupee coin is worth ₹5.00.
Now count up by ₹2.00 from ₹5.00 to find out how many 2-rupee coins you can have. 1 2-rupee coin makes ₹7.00. 2 2-rupee coins make ₹9.00—too much. You can have 1 2-rupee coin. So far, you have 1 5-rupee coin and 1 2-rupee coin, which are worth ₹7.00.
Now count up by ₹1.00 from ₹7.00 to find out how many 1-rupee coins you can have. 1 1-rupee coin makes ₹8.00. 2 1-rupee coins make ₹9.00—too much. You can have 1 1-rupee coin. So far, you have 1 5-rupee coin, 1 2-rupee coin, and 1 1-rupee coin, which are worth ₹8.00.
Finally, count up by 50p from ₹8.00 to find out how many 50-paise coins you can have. 1 50-paise coin makes ₹8.50. That’s the total you want.
To make 8 rupees and 50 paise with the fewest coins, you’ll use 1 5-rupee coin, 1 2-rupee coin, 1 1-rupee coin, and 1 50-paise coin.

📘 How do you make 3 rupees and 50 paise using the fewest coins?

Start with 5-rupee coins and count by ₹5.00. When you’ve gone past ₹3.50, you’ve gone too far. 1 5-rupee coin makes ₹5.00—too much. You can have 0 5-rupee coins. 0 5-rupee coins are worth 0p.
Now count up by ₹2.00 from 0p to find out how many 2-rupee coins you can have. 1 2-rupee coin makes ₹2.00. 2 2-rupee coins make ₹4.00—too much. You can have 1 2-rupee coin. So far, you have 0 5-rupee coins and 1 2-rupee coin, which are worth ₹2.00.
Now count up by ₹1.00 from ₹2.00 to find out how many 1-rupee coins you can have. 1 1-rupee coin makes ₹3.00. 2 1-rupee coins make ₹4.00—too much. You can have 1 1-rupee coin. So far, you have 0 5-rupee coins, 1 2-rupee coin, and 1 1-rupee coin, which are worth ₹3.00.
Finally, count up by 50p from ₹3.00 to find out how many 50-paise coins you can have. 1 50-paise coin makes ₹3.50. That’s the total you want.
To make 3 rupees and 50 paise with the fewest coins, you’ll use 0 5-rupee coins, 1 2-rupee coin, 1 1-rupee coin, and 1 50-paise coin.

Let’s practice!🖊️