How much per one?
Keep quantity names and units while making the reference one.
Begin with the activity ↓How much per one?
If 3 notebooks cost 6,000 won, each costs 2,000 won. Divide total cost by notebook count to make the reference one notebook. A per-one rate lets us compare differently sized bundles.
If 3 notebooks cost 6,000 won, each costs 2,000 won. Divide total cost by notebook count to make the reference one notebook. A per-one rate lets us compare differently sized bundles.
Write units too: 6,000 won ÷ 3 notebooks = 2,000 won per notebook. Unlike a multiplier between lengths in matching units, dividing cost by count leaves a rate unit. The unit tells you what was divided by what.
A second bundle of 4 notebooks for 7,200 won costs 1,800 won per notebook. The first bundle has a smaller total price but a higher per-notebook price. Assuming equal size and quality, the second has the lower unit price.
Dividing count by price gives notebooks per won, answering a different question. The requested rate determines the division. Do not replace this decision with a rule to divide the larger number by the smaller one.
Total price divided by count is the bundle’s average price per notebook. It does not promise that a single notebook is sold at that price. Discounts or fixed delivery fees can change the rate as quantity changes.
Change counts and total prices for the two bundles below. Compare unit prices after making both references one notebook. Next we use a reference of one hundred for percentages.
Listen one paragraph at a time
Hold on to this distinction
Comparing total prices can mislead when counts differ. Read 6,000 ÷ 3 and 7,200 ÷ 4 as won per notebook.
Change it and check
Change both bundles’ counts and prices. Check whether the lower total and lower unit price always belong to the same bundle.
Bundle A
Total cost: 6000 won
6000 ÷ 3 = 2000 won/notebook
Bundle B
Total cost: 7200 won
7200 ÷ 4 = 1800 won/notebook
B: lower average unit price.
Counts range from 1 to 6 and prices use multiples of 600 won. Compare notebooks of equal size and quality, excluding extra fees. The display calculates each bundle’s average unit price.
Try with paper and objects
Draw three notebooks sharing 6,000 won equally. Do the same for four notebooks and 7,200 won, then compare the per-notebook prices.
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1800 · won/notebook
9,000 ÷ 5 = 1,800 won per notebook. Omit commas in the input.
Does your explanation include these ideas?
Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.
Continue, or pause here
Read percentages as ratios to a whole and examine changing reference wholes.