The Coupon Decimals
At two stores, the same notebook costs different amounts. Store A sells it for $4.50. Store B sells it for $4.05. Store A has a coupon for $0.75 off one notebook. Store B has a coupon for $0.50 off one notebook. A student, Tessa, says Store B is cheaper before coupons because $4.05 is less than $4.50, but after coupons she is not sure. She also says $4.50 and $4.05 are “the same except for a zero,” so the coupons should make them equal. The class is buying 6 notebooks for a project. Each coupon applies to one notebook only; the store will let them use up to 6 coupons, one per notebook. They need to decide which store is cheaper for 6 notebooks and by how much. The teacher asks for a clear comparison using place value and a table.
1. Find the total cost of 6 notebooks at each store with coupons. Show the price per notebook after the coupon and the multiplication.
Read the worked answer
Store A: $4.50 − $0.75 = $3.75 per notebook. Then 6 × $3.75 = $22.50.
Store B: $4.05 − $0.50 = $3.55 per notebook. Then 6 × $3.55 = $21.30.
Store B is cheaper by $22.50 − $21.30 = $1.20.
2. Explain why $4.50 and $4.05 are not the same, using place value.
Read the worked answer
In $4.50, the 5 is in the tenths place (5 tenths = 50 cents) and the 0 is in the hundredths place. In $4.05, the 0 is in the tenths place and the 5 is in the hundredths place (5 cents). So $4.50 = 4 dollars and 50 cents, while $4.05 = 4 dollars and 5 cents. The difference is 45 cents, not zero. Writing 4.50 as 4.5 is valid because the trailing zero in the hundredths place does not change the value, but the zero in 4.05 is in a different place and does matter.
3. Tessa says the zero does not matter, so the coupons should make the prices equal. Identify the flaw and write a corrected statement.
Read the worked answer
Tessa’s flaw is treating the zero in 4.50 and the zero in 4.05 as if they were in the same place. In 4.50 the zero is a trailing hundredths zero; in 4.05 it is a tenths zero. Corrected statement: “4.50 equals 4.5, but 4.05 is 45 cents less than 4.50. After the coupons, Store A is $3.75 per notebook and Store B is $3.55, so Store B is still cheaper by $0.20 per notebook, or $1.20 for six.”