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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.Thecentsignisasmall′. The cent sign is a small 'c′withaslashthroughitandisplacedafterthenumber,like' with a slash through it and is placed after the number, like 25c.Rememberthekeyrelationship:. Remember the key relationship: 100centsisexactlyequaltocents is exactly equal to\11.

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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,the, the 4representsdollarsandtherepresents dollars and the50representscents.Visually,therearealwaysexactlytwodigitsafterthedecimalpointtoshowthecents,eveniftheamountisawholenumberlikerepresents 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\7.007.00.

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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 \\3.20andand\3.803.80, you can see that 8080 cents is a larger part of a dollar than 2020 cents, making \\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 textChange=textAmountPaid−textTotalCost\\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 \\2.50asbeingatthepeakofahill;sinceithasreachedthehalfwaypoint,itrollsforwardtoas being at the peak of a hill; since it has reached the halfway point, it rolls forward to\3.003.00.

📐Formulae

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

textTotalCost=textPriceA+textPriceB\\text{Total Cost} = \\text{Price A} + \\text{Price B}

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

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

💡Examples

Problem 1:

Oliver buys a sandwich for \\4.65andabottleofwaterforand a bottle of water for\1.201.20. How much does he spend in total?

Solution:

Step 1: Set up the addition by lining up the decimal points: \\4.65 + \1.201.20. 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$.

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 \\6.30andpayswithaand pays with a\10.0010.00 bill. How much change should she receive?

Solution:

Step 1: Set up the subtraction: \\10.00 - \6.306.30. Step 2: Subtract the cents. Since we cannot take 3030 from 0000, borrow 11 dollar from the \\10,leaving, leaving \99 and giving us 100100 cents. Step 3: 100textcents−30textcents=70textcents100\\text{ cents} - 30\\text{ cents} = 70\\text{ cents}. Step 4: 9textdollars−6textdollars=3textdollars9\\text{ dollars} - 6\\text{ dollars} = 3\\text{ dollars}. Total Change = \\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$ payment.