Dollars with dollars, cents with cents
Every amount of money has two parts: the dollars before the decimal point and the cents after it. $2.45 is 2 dollars and 45 cents. $1.30 is 1 dollar and 30 cents.
To add them, add the dollars to the dollars and the cents to the cents. The dollars: 2 + 1 = 3. The cents: 45 + 30 = 75. So $2.45 + $1.30 = $3.75.
$2.45 is two $1 bills and 45 cents in coins.
$1.30 is one $1 bill and 30 cents in coins.
Put them together: 3 bills are 3 dollars, and the coins are 75 cents. $2.45 + $1.30 = $3.75.
When the cents pass 100
Now add $2.45 + $1.80. The dollars are 2 + 1 = 3. The cents are 45 + 80 = 125, and that is more than 100.
A hundred cents is a dollar, so trade 100 of the cents for one more dollar: 125 cents is 1 dollar and 25 cents. That dollar joins the other dollars, 3 + 1 = 4, and 25 cents are left. So $2.45 + $1.80 = $4.25.
The cents from both prices, 45 and 80, counted together: they reach 100 at the fourth coin and 125 at the last.
The first 100 cents are traded for a fourth $1 bill, and 25 cents are left: $4.25.
Two slips when adding
Writing the 125 cents straight after the dollars, as $3.125, is the first slip. The cents take only two places after the decimal point, so the 100 must be traded for a dollar first.
The second slip is to trade the cents and then forget the dollar they made. The 125 cents became 1 dollar and 25 cents. Writing $3.25 keeps the 25 cents but loses that dollar.
Subtracting: break a dollar
Now take $1.80 away from $4.25. Start with the cents: 80 cents are to be taken from 25 cents, and 25 cents is not enough.
$4.25: four $1 bills and 25 cents. The 25 cents are not enough to take 80 cents from.
So break one of the dollars into 100 cents. $4.25 becomes 3 dollars and 125 cents. It is still the same amount of money, made of different pieces.
One $1 bill traded for four 25¢ coins, which are 100 cents: now 3 dollars and 125 cents, still $4.25.
Now there are enough cents. The cents: 125 − 80 = 45. The dollars: 3 − 1 = 2. So $4.25 − $1.80 = $2.45.
Check by adding back: $2.45 + $1.80 = $4.25, which is the adding you have just done.
Two slips when subtracting
Turning the cents round, 80 − 25 = 55, gives $3.55. That takes 25 cents away from 80 cents, but it is the 80 cents that are being taken away, from 25 cents that are too few.
Breaking a dollar and then not taking it off the dollars gives $3.45. When a dollar is broken into cents, there is one dollar fewer: 4 dollars become 3.
Worked example: Enough Money for Two Things or Not
Question Ravi has a $5 note. A toy car costs $3.20 and a ball costs $2.50. (a) How much do the toy car and the ball cost altogether? (b) Does Ravi have enough money to buy both? If not, how much more money does he need?
1.Add the dollars with the dollars: $3 + $2 = $5.
Add the dollars with the dollars: $3 + $2 = $5. 2.Add the cents with the cents: 20 + 50 = 70 cents.
Add the cents with the cents: 20 + 50 = 70 cents. 3.(a) The two things cost $5 and 70 cents, which is $5.70 altogether.
(a) The toy car and the ball cost $5.70 altogether. 4.(b) Compare $5.70 with the $5 that Ravi has. The cost is more, so he does not have enough. He needs 70 cents more.
(b) $5.70 is more than $5. Ravi needs 70 cents more.
Answer: (a) $5.70; (b) No. Ravi needs 70 cents more.
Common mistakes
- Looking only at the dollars. $3 + $2 = $5 looks like enough, but the cents still have to be paid, and they are 20 + 50 = 70 cents more.
- Comparing the $5 note with each price on its own. $5 is enough for the toy car alone and for the ball alone, but the question asks about both together.
Worked example: Two Prices Whose Cents Make More Than a Dollar
Question A bun costs 85 cents and a packet of milk costs 60 cents. (a) Ali buys one bun and one packet of milk. How much does he pay? (b) Mei buys two buns and one packet of milk. How much does she pay?
1.Add the cents: 85 + 60 = 145 cents.
Add the cents: 85 + 60 = 145 cents. 2.145 cents is more than 100 cents. Change 100 cents for $1: 145 = 100 + 45.
Change 100 cents for $1. There are 45 cents left. 3.(a) Ali pays $1 and 45 cents, which is $1.45.
(a) Ali pays $1.45. 4.Mei pays for one more bun: 145 + 85 = 230 cents. Change 200 cents for $2: 230 = 200 + 30.
Mei pays for one more bun: 145 + 85 = 230 cents, which is $2 and 30 cents. 5.(b) Mei pays $2.30.
(b) Mei pays $2.30.
Answer: (a) $1.45; (b) $2.30
Common mistakes
- Writing 145 cents as $145. One dollar is 100 cents, so 145 cents is 1 dollar and 45 cents, which is $1.45.
- Adding only one bun for Mei. She buys two buns, so 85 cents is added twice: 85 + 85 + 60 = 230 cents.