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Fraction Classroom · 2.5.0 · Teacher answers & responses

Compare a fractional discount with a fixed reduction

Calculate the amount removed and the amount paid for two offers on the same starting price, then check when a different starting price changes the result.

Both offers share the same starting price. Removed amount plus final price equals $12 in each row.OfferStarting priceRemovedFinal priceA: 1/4 off$12$3$9B: $2 off$12$2$10
Both offers share the same starting price. Removed amount plus final price equals $12 in each row.

Build the idea

model. An item has the same $12 starting price in two offers. Offer A removes 1/4 of the price. Offer B removes $2. Which final price is lower, and by how much?

  1. Confirm a common reference: both offers apply to an identical item starting at $12 under the stated assumptions. A comparison of different starting prices would need separate calculations.
  2. For Offer A, find the reduction first: one quarter of twelve dollars is three dollars. Subtract it from twelve to obtain a nine-dollar final price.
  3. For Offer B, subtract the fixed two-dollar reduction to obtain ten dollars. Compare nine and ten using the same dollar unit.
  4. Check each offer by adding reduction and final price to recover twelve dollars. Then state the lower final price and the one-dollar difference; naming only the larger reduction leaves the payment unstated.

Worked example: Offer A costs $9 and Offer B costs $10, so A is $1 lower. The quarter-price reduction is $3; it is not the amount paid.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. Support: the price is $16 and 1/4 is removed. Enter the dollar reduction, then state the final price on paper.

Answer: 4

Teacher response: One quarter of $16 is $4, leaving $12 to pay.

p2. Core: the price is $18 and 1/3 is removed. Enter the final price in dollars.

Answer: 12

Teacher response: The reduction is $6; $18 − $6 leaves $12.

p3. Challenge: a $6 item has either 1/4 off or $2 off. Enter the lower final price in dollars and name the offer.

Answer: 4

Teacher response: The fixed reduction gives $4, while a quarter off gives $4.50. The offer that won at $12 need not win at $6.

e1. Independent check: a $20 item has either 1/4 off or $3 off. How many dollars lower is the quarter-off final price? Record both final prices.

Answer: 2

Look for:

  • Calculates the reduction and payment separately.
  • Compares offers from the same reference price and checks the result by recombining payment and reduction.

Teacher response: The quarter-off price is $15 and the fixed-reduction price is $17; the difference is $2.

Transfer the idea

transfer. At what shared starting price do a quarter-off offer and a $2 reduction give the same final price? Explain using the reductions.

Answer: At $8. One quarter of eight is two, so both offers remove $2 and leave $6. The equality concerns the same starting price and the stated assumptions.

Run the 15-minute workshop

teach-1. 3 minutes: Ask learners to label saving and payment as different quantities in a quarter-off offer.

teach-2. 4 minutes: Complete both rows of the worked comparison and reverse each subtraction to verify the starting price.

teach-3. 5 minutes: Solve support and core items before using the challenge to test whether the same offer always wins.

teach-4. 3 minutes: Complete the independent two-offer record, naming both final prices and their difference.

Respond to the learner

misconception. A quarter-price discount means the final price is one quarter of the original price.

Teacher response: Distinguish a quarter off from paying a quarter. A quarter off removes one part and leaves three equal quarter-parts to pay.

support. Partition a drawn price bar into four equal parts, cross out the removed part and label the three remaining parts.

extend. At a $10 starting price, compare one fifth off with $2 off: both final prices are $8. Explain why a fractional reduction depends on the starting amount.

Teaching notes