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Fraction Classroom · 2.5.0 · Student pages

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.

Anonymous group code: __________   Date: __________

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.

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

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

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.

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.