doing math

courses › Fractions, Decimals & Percents

Money & prices

level 13 course

Totals, change, discounts, and changes on top of changes.

In your head, jot if needed · no calculator why?

Learn first (about 3 minutes)

Opens at level 13.

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Builds on: Decimals (not open yet) · Percents (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

Money is decimals with two places: cents are hundredths of a dollar. Keep dollars and cents apart, and remember that every 100 cents carry over as one dollar.

With percents, keep two questions apart: how much comes off or goes on (the change) and what you pay (the final price). A price after one change is the new starting point for the next. That is why a 10% rise and a 10% cut don't cancel: 100 goes up to 110, then down to 99.

Techniques

Dollars first, then cents

Adding two or three prices.

  1. Add the whole dollars.
  2. Add the cents. Every 100 cents make one more dollar.
  3. Put the two together.
worked example

Example: $8.60 + $14.75

  1. Dollars: $8 + $14 = $22.
  2. Cents: 60¢ and 75¢ make 135¢, which is $1.35.
  3. $22 + $1.35 = $23.35.

Answer: $23.35

Count up to make change

Working out change from a payment.

  1. Count up from the price to the next whole dollar.
  2. Count on from there to the amount paid.
  3. Add the two jumps.
worked example

Example: You pay $50 for a $31.40 item. How much change do you get?

  1. $31.40 up to $32 is 60¢.
  2. $32 up to $50 is $18.
  3. Change: $18.60.

Answer: $18.60

One change at a time

A price after a percent off or on, or after two changes in a row.

  1. Find the change: the percent of the current amount.
  2. Take it off for a discount, or add it for an increase. That gives the final price.
  3. For a second change, start from the new amount, not the original.
  4. Or multiply: 20% off is × 0.8, and 10% up is × 1.1.
worked example

Example: Increase 200 by 10%, then decrease the result by 20%. What is the final amount?

  1. Up 10%: 200 × 1.1 = 220.
  2. Down 20% of the new amount: 220 × 0.8 = 176.

Answer: 176

Tips by skill

  • TipMoney totals: Add the dollars, then the cents. Every 100 cents makes one more dollar.
  • TipMaking change: Count up from the price to the next dollar, then on to the amount paid. Add the two jumps.
  • TipFinal price: Find the percent of the price, then take it off or add it on. Give the new price, not the change.
  • TipChange after change: Apply the first change, then take the second percent of the new amount. Equal ups and downs don't cancel.

Watch out for

  • Forgetting to carry a dollar. 50¢ and 75¢ make $1.25, so $12.50 + $7.75 is $20.25, not $19.25.
  • Taking away only the dollars for change. Paying $20 for $13.75, the 75¢ uses up one of the dollars: $6.25, not $7.25.
  • Giving the discount instead of the final price. 15% off $80 takes $12 off, so you pay $68.
  • Assuming equal changes cancel. Up 10% and then down 10% ends below where you started.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

your rounds

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