Making Change

Changing the math of money is an important concept. It involves understanding how to return the right amount of money when someone pays more for something than it is worth. Let us understand this concept in depth.

Understanding money

Before we start making the conversion, it is important to understand what currencies we use every day. Generally, money is divided into coins and notes. Each has its own value.

• coins:
  • Pennies - 1 cent
  • Nickel - 5 cents
  • Dimes - 10 cents
  • Quarter - 25 cents
• Bill:
  • 1 dollar - 100 cents
  • 5 dollars - 500 cents
  • 10 dollars - 1000 cents
  • 20 dollars - 2000 cents

The basic method of bringing about change

Whenever you buy something and pay more than the price of the item, you should get the difference back. This difference is called "change." Let's learn how it is calculated.

Start with the amount paid:
    Amount paid = $10
Subtract the cost of the item:
    Price of item = $6
Calculate the change:
    Change = Amount Paid – Item Cost
    Change = $10 - $6 = $4

An example

Imagine you buy a toy car that costs $3. You give the cashier $5. How much money should you get?

Start with the amount paid:
    Amount paid = $5
Subtract the cost of the item:
    Price of item = $3
Calculate the change:
    Change = Amount Paid – Item Cost
    Change = $5 - $3 = $2

You should get $2 back in return.

Visual depictions

Visual depictions can help us understand how to bring about change. Let's visualise this scenario using symbols.

Amount paid:

item cost:

Changes made:

Step-by-step approach

Let us understand the process of bringing about change using a step-by-step approach.

1. Identify the amount of money owed by the customer.
2. Determine the cost of the item.
3. Subtract the cost of the item from the money given.
4. The result is that the customer gets some amount back in return.
5. Provide this change using the minimum number of notes and coins possible.

Example in steps

Suppose you buy a book for $7 and pay with a $10 note. How do you get the change?

1. Amount paid: $10
2. Item Price: $7
3. Calculate the change: $10 - $7 = $3
4. Change: $3
5. Give change: Use a $1 dollar note three times, or use $1 dollar note and $2 coin if available.

Use of coins and notes

To transact change efficiently, try to use the maximum amount of change. This makes the transaction easier and faster.

Example:

Change required: $1.65
Optimal Changes:
    $1 bill = 1 x $1
    50 cents = 1 x 50 cents
    10 cents = 1 x 10 cents
    5 cents = 1 x 5 cents
Last change: $1 + 50 cents + 10 cents + 5 cents

Practice problems

Here are some practice problems that will help you get a better understanding of making transformations.

Problem 1

You buy a sandwich for $4 and pay with $10 bill. How much change should you get?

Amount paid: $10
Item Price: $4
Change = Amount Paid – Item Cost
Change = $10 - $4 = $6

Change: $6

Problem 2

You buy a chocolate bar for $0.75 and pay with $5 bill. What's your revenge?

Amount paid: $5
Item Price: $0.75
Change = Amount Paid – Item Cost
Change = $5 - $0.75 = $4.25

Change: $4.25

Problem 3

A toy costs $8.50 and you pay with $20 bill. How much change do you get?

Amount paid: $20
Item Price: $8.50
Change = Amount Paid – Item Cost
Change = $20 - $8.50 = $11.50

Change: $11.50

Tips for making a change

• Start with the highest value notes and coins to simplify the change process.
• Double-check your math to make sure the correct change is given.
• Practice over and over again to get more comfortable with the process.

Summary

Handling money is a fundamental skill. By understanding how to cut costs from payments and in turn distribute money efficiently, you gain confidence in handling everyday transactions.

Final thoughts

Remember, practice is the key. The more you practice making change, the easier and faster it will be. As you get better, try challenging yourself with more complex transactions involving different coins and bills. Happy learning!

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