Add and subtract money in decimal notation

What you will learn

• Add and subtract money in decimal notation

Models used: number sentences, stories, bar models.

Before you start

• Count amounts in dollars and cents

Keep dollars with dollars and cents with cents

A drink costs $1.75 and a sandwich costs $2.50. What is the total cost?

1. Our two prices. Read each value with the heading above its column.

   Read each amount as dollars and cents. The two digits after the decimal point count cents.

   $1.75 + $2.50

   Different coins can have different values. One dollar and one hundred cents are two names for the same amount.

   Our two prices

   Item	Dollars	Cents
   Drink	1	75
   Sandwich	2	50

2. An exchange keeps the value the same. Read each value with the heading above its column.

   Add the cents: 75 + 50 = 125 cents. Exchange 100 of them for one extra dollar; 25 cents remain.

   125 cents = $1.25

   An exchange keeps the value the same

   Cents altogether	Exchange	Cents left
   125 cents	100 cents = $1	25 cents

3. The combined cost. Read each value with the heading above its column.

   Add the dollars, including that extra dollar. One plus two plus one is four dollars, with 25 cents left.

   $1.75 + $2.50 = $4.25

   The combined cost

   Dollars	Cents	Total
   4	25	$4.25

4. The bar is measured in cents. It shows the same prices without a decimal point.

   Check by taking the sandwich price back out. The money left must equal the drink price.

   $4.25 − $2.50 = $1.75

   425

   175drink: 175 cents250sandwich: 250 cents

Worked example: A new example, together

Calculate $6.47 − $1.89.

1. The complete bar is the whole. Each labelled section is one part of it.

   Read every value and its unit. Keep dollars and cents distinct until you rename them.

   Using one common unit makes money values comparable and calculations consistent.

   6.47

   ?dollars1.89dollars

2. The complete bar is the whole. Each labelled section is one part of it.

   Align dollars with dollars and cents with cents.

   6.47

   ?dollars1.89dollars
   Calculate $6.47 − $1.89.

   4.58 dollars

3. The complete bar is the whole. Each labelled section is one part of it.

   Align dollars with dollars and cents with cents.

   6.47

   ?dollars1.89dollars

4. The complete bar is the whole. Each labelled section is one part of it.

   647 − 189 = 458 cents.

   6.47

   ?dollars1.89dollars

5. The complete bar is the whole. Each labelled section is one part of it.

   Convert to dollars: $4.58.

   6.47

   ?dollars1.89dollars

6. The complete bar is the whole. Each labelled section is one part of it.

   Check the result against the question we started with.

   Convert the result back to cents to verify the calculation.

   We found 4.58 dollars. Using one common unit makes money values comparable and calculations consistent.

   6.47

   ?dollars1.89dollars

Common mistakes to discuss

• A single digit after the point. The two places after the point are cents. $5.70 is five dollars and seventy cents; $5.7 should be written $5.70.

Check your understanding

• Add and subtract money in decimal notation
• compare, combine or rename money while preserving its value
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.