7
Subtracting natural numbers
Textbook: Part 1, lesson 7, pp. 28–31
GoalSubtract natural numbers; check subtraction by addition; find the distance between points on the number ray.
New words
minuend · kamayuvchisubtrahend · ayiriluvchidifference · ayirmadistance · masofa
Explanation
Finding the second addend from the sum and one addend is called subtraction. In subtraction the subtrahend is taken from the minuend and the difference is obtained. For natural numbers the minuend cannot be smaller than the subtrahend. The difference tells how much the first number exceeds the second. To check subtraction, add the subtrahend to the difference; you must get the minuend. On the number ray, the distance between two points is the larger coordinate minus the smaller.
Worked examples
6 502 − 1 874 = 4 628. Check: 4 628 + 1 874 = 6 502, correct.
The distance between A(5) and B(19) is AB = 19 − 5 = 14 unit segments. Estimate check: 803 − 396 ≈ 800 − 400 = 400.
Class activity
“Reverse check”: pairs give each other a 4-digit subtraction; one solves it and the other checks it by adding difference and subtrahend.
Practice
1
Compute 9 000 − 3 475.
5525
2
Find the distance between C(12) and D(47) on the number ray.
35
3
A book has 384 pages. Dilnoza read 157 of them. How many pages are left unread?
227
4
Why can 15 − 20 not be done with natural numbers?
The minuend (15) is smaller than the subtrahend (20); such a difference does not exist among natural numbers.