Subtracting and estimating
After driving for a few hours, the question always pops up , "How much further?" To answer this we subtract. And when we don't need an exact answer, we estimate.
What is this?
If the full trip is 720 km and we have covered 285 km, the distance left is 720 − 285 = 435 km. Subtraction is like asking, "What must I add to 285 to reach 720?"
Like addition, we line up the digits in columns and subtract starting from the ones place. If the top digit is smaller than the bottom one, we borrow ten from the next column to the left. This is the rule from earlier classes , it works the same with bigger numbers.
Estimation is a faster shortcut. Suppose two cities are 487 km apart. We round 487 to the nearest hundred , that gives 500. Now we can say "about 500 km". This is enough when we are just planning. We round 487 up to 500 because 487 is closer to 500 than to 400. The rule: look at the tens digit. If it is 5 or more, round up; if less than 5, round down.
Estimation is what every traveller does first. "About 6 hours by car." "Around 1,500 km in all." It is fast, it is friendly, and it stops us from carrying a calculator everywhere.
Worked examples
Example 1. Total trip: 850 km. Covered: 365 km. How much is left?
8 5 0
- 3 6 5
-------
4 8 5
485 km still to go.
Example 2. Estimate 487 + 312 to the nearest hundred.
- 487 rounds to 500.
- 312 rounds to 300.
- Estimate: 500 + 300 = 800.
The exact answer is 799, so our estimate is very close.
Example 3. A car has a 50-litre tank. It has used 28 litres. How many litres are left?
- 50 − 28 = 22 litres left.
Try it
- 600 − 274.
- 1,250 − 875.
- A trip is 1,800 km. We have done 1,265 km. How much is left?
- Round these to the nearest hundred: 348, 562, 1,275, 4,950.
- Estimate 689 − 412 by rounding both numbers to the nearest hundred.
Hands-on
Halfway question. Pick any route between two cities (say 600 km). Ask: "If we have done 250 km, how far is left?" Now invent two more starting distances and answer the same question.
Bill estimation. Next time someone shops, look at the three biggest items. Round each to the nearest ten or hundred and add them up in your head. Then compare with the real bill. How close were you?