doing math

courses › Mental Arithmetic

Everyday mix

level 14 course

Time, rates, and short money stories: pick the operation yourself.

Best in your head · no pen, no calculator why?

Learn first (about 3 minutes)

Opens at level 14.

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Builds on: Bigger multiplication (not open yet) · Money & prices (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

Everyday problems hand you a short story instead of a sum, so the first job is picking the operation. Say what you are finding, and in what unit.

Time is the classic trap. An hour has 60 minutes, not 100, so 1 hour 30 minutes is 1.5 hours, not 1.3. Change minutes into hours before you multiply by a rate per hour.

In money stories, revenue is the money taken in from sales, and profit is revenue minus costs. Sharing a total equally is a division. Last, ask whether the answer fits the story.

Techniques

Minutes are sixtieths of an hour

Changing minutes to hours, or hours to minutes.

  1. Minutes to hours: divide by 60.
  2. Know the quarters: 15 minutes is 0.25 hours, 30 is 0.5 and 45 is 0.75.
  3. Hours to minutes: multiply by 60.
worked example

Example: How many hours is 105 minutes? Answer as a decimal.

  1. 105 minutes is 60 minutes plus 45 minutes.
  2. 60 minutes is 1 hour, and 45 minutes is 0.75 of an hour.
  3. In hours: 1 + 0.75 = 1.75.

Answer: 1.75

Rate times hours

Earnings or costs at a rate per hour.

  1. Change the time into hours first.
  2. Multiply the rate by the hours.
  3. Half an hour earns half the rate, and a quarter hour earns a quarter of it.
worked example

Example: At $30 per hour, how much do you earn in 45 minutes?

  1. 45 minutes is 0.75 hours.
  2. $30 × 0.75 = $22.50.

Answer: $22.50

Two facts, one question

A short money story.

  1. Say what you are finding, and its unit.
  2. Orders times the price each is the revenue. Take away the costs for the profit.
  3. A bill shared equally: divide by the number of people.
  4. 4 weeks of a weekly amount: multiply by 4, or double it twice.
worked example

Example: 9 orders at $35 each. The costs total $180. What is the profit?

  1. Revenue: 9 × $35 = $315.
  2. Profit: $315 − $180 = $135.

Answer: $135

Tips by skill

  • TipMinutes to hours: An hour is 60 minutes. Divide minutes by 60 to get hours; multiply hours by 60 to get minutes.
  • TipRate × time: Change the time to hours first, then multiply by the rate. 30 minutes is half an hour.
  • TipShort money stories: Name what you are finding. Profit is revenue minus costs, an equal split is a division, and 4 weeks is 4 times the weekly amount.

Watch out for

  • Reading 1 hour 30 minutes as 1.30 hours. Minutes are sixtieths of an hour, so 30 minutes is 0.5 hours.
  • Giving the revenue as the profit. Profit is what is left after the costs.
  • Adding costs the story doesn't mention. Use only the numbers it gives.

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

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