Everyday mix
Time, rates, and short money stories: pick the operation yourself.
Best in your head · no pen, no calculator why?
Opens at level 14. You're level 1. You can read and practice here now.
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
- 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.
worked example
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.
worked example
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.
worked example
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
Minutes to hours
worked example
How many hours is 45 minutes? Answer as a decimal.
Answer: 0.75
- Minutes are sixtieths of an hour: 45 ÷ 60 = 0.75 hours.
Rate × time
worked example
At $85 per hour, how much do you earn in 45 minutes?
Answer: $63.75
- 45 minutes is 0.75 hours, and $85 × 0.75 = $63.75.
Short money stories
worked example
A $381.50 bill is split equally among 7 people. How much does each person pay?
Answer: $54.50
- $381.50 ÷ 7 = $54.50.
- Check: 7 × $54.50 = $381.50.