Everyday mix
Time, rates, and short money stories: pick the operation yourself.
Best in your head · no pen, no calculator why?
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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.
more of the idea
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
- Minutes to hours: divide by 60.
- Know the quarters: 15 minutes is 0.25 hours, 30 is 0.5 and 45 is 0.75.
- Hours to minutes: multiply by 60.
How many hours is 105 minutes? Answer as a decimal.
- 105 minutes is 60 minutes plus 45 minutes.
- 60 minutes is 1 hour, and 45 minutes is 0.75 of an hour.
- In hours: 1 + 0.75 = 1.75.
Answer: 1.75
Rate times hours
- Change the time into hours first.
- Multiply the rate by the hours.
- Half an hour earns half the rate, and a quarter hour earns a quarter of it.
At $30 per hour, how much do you earn in 45 minutes?
- 45 minutes is 0.75 hours.
- $30 × 0.75 = $22.50.
Answer: $22.50
Two facts, one question
- Say what you are finding, and its unit.
- Orders times the price each is the revenue. Take away the costs for the profit.
- A bill shared equally: divide by the number of people.
- 4 weeks of a weekly amount: multiply by 4, or double it twice.
9 orders at $35 each. The costs total $180. What is the profit?
- Revenue: 9 × $35 = $315.
- Profit: $315 − $180 = $135.
Answer: $135
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.
practice
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Minutes to hours
worked example
How many hours is 45 minutes? Answer as a decimal.
- Minutes are sixtieths of an hour: 45 ÷ 60 = 0.75 hours.
Answer: 0.75
Rate × time
worked example
At $85 per hour, how much do you earn in 45 minutes?
- 45 minutes is 0.75 hours, and $85 × 0.75 = $63.75.
Answer: $63.75
Short money stories
worked example
A $381.50 bill is split equally among 7 people. How much does each person pay?
- $381.50 ÷ 7 = $54.50.
- Check: 7 × $54.50 = $381.50.
Answer: $54.50