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Measurement - Calculating with Money

Grade 3IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Understanding Currency Units and Symbols: Money is measured in dollars ($\$ ) and cents (c). Visually, the dollar sign is an 'SS' with one or two vertical lines through it and is placed before the amount, like $10\$10. The cent sign is a small 'cc' with a slash through it and is placed after the number, like 25c25c. Remember the key relationship: 100100 cents is exactly equal to $1\$1.

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The Decimal Point as a Separator: In money notation, a decimal point separates the whole dollars from the cents. For example, in $4.50\$4.50, the 44 represents dollars and the 5050 represents cents. Visually, there are always exactly two digits after the decimal point to show the cents, even if the amount is a whole number like $7.00\$7.00.

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Comparing Money Values: To find which amount is larger, first compare the dollars. If the dollars are equal, compare the cents. Visually, if you compare $3.20\$3.20 and $3.80\$3.80, you can see that 8080 cents is a larger part of a dollar than 2020 cents, making $3.80\$3.80 the greater value.

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Adding Money with Column Alignment: When adding two or more prices, it is vital to line up the decimal points in a straight vertical column. This ensures that you are adding cents to cents and dollars to dollars. Imagine a vertical 'spine' that every decimal point must sit on to keep the math tidy and accurate.

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Calculating Change using Subtraction: Change is the 'leftover' money you receive when you pay with an amount larger than the cost. The formula is Change=Amount Paid−Total Cost\text{Change} = \text{Amount Paid} - \text{Total Cost}. Visually, this is like taking the cost away from your total pile of money and seeing what remains on the table.

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Rounding to the Nearest Dollar: To estimate totals, we often round to the nearest dollar. If the cent part is 5050 or more, round up to the next dollar; if it is 4949 or less, round down. Visually, think of $2.50\$2.50 as being at the peak of a hill; since it has reached the halfway point, it rolls forward to $3.00\$3.00.

📐Formulae

100 cents=$1.00100\text{ cents} = \$1.00

Total Cost=Price A+Price B\text{Total Cost} = \text{Price A} + \text{Price B}

Change=Amount Paid−Total Cost\text{Change} = \text{Amount Paid} - \text{Total Cost}

Rounding: $X.50→Round Up to $(X+1)\text{Rounding: } \$X.50 \rightarrow \text{Round Up to } \$(X+1)

💡Examples

Problem 1:

Oliver buys a sandwich for $4.65\$4.65 and a bottle of water for $1.20\$1.20. How much does he spend in total?

Solution:

Step 1: Set up the addition by lining up the decimal points: $4.65+$1.20\$4.65 + \$1.20. Step 2: Add the cents column: 65+20=8565 + 20 = 85 cents. Step 3: Add the dollars column: 4+1=54 + 1 = 5 dollars. Total Spent = $5.85\$5.85.

Explanation:

To find the total, we add the two amounts. Aligning the decimals ensures we add the cents together and the dollars together correctly.

Problem 2:

Sophia buys a notebook for $6.30\$6.30 and pays with a $10.00\$10.00 bill. How much change should she receive?

Solution:

Step 1: Set up the subtraction: $10.00−$6.30\$10.00 - \$6.30. Step 2: Subtract the cents. Since we cannot take 3030 from 0000, borrow 11 dollar from the $10\$10, leaving $9\$9 and giving us 100100 cents. Step 3: 100 cents−30 cents=70 cents100\text{ cents} - 30\text{ cents} = 70\text{ cents}. Step 4: 9 dollars−6 dollars=3 dollars9\text{ dollars} - 6\text{ dollars} = 3\text{ dollars}. Total Change = $3.70\$3.70.

Explanation:

Change is found by subtracting the price from the payment. We use regrouping (borrowing) because the price has more cents than the zero cents in the $10.00\$10.00 payment.