63
Dividing a decimal fraction by a natural number
Textbook: Part 2, lesson 63, pp. 104–109
GoalDivide a decimal by a natural number and by 10, 100, 1000.
New words
quotient · bo‘linmalong division · burchak usulidivisor · bo‘luvchidividend · bo‘linuvchi
Explanation
To divide a decimal by a natural number, divide ignoring the point, put the point in the quotient as soon as the whole part has been divided, and carry on dividing. If the whole part is smaller than the divisor, the whole part of the quotient is 0: 2.56 : 8 = 0.32. If a remainder is left, we can write a zero on the right of the decimal and continue, since a zero does not change it. We check by multiplying. To divide a decimal by 10, 100 or 1000, move the point 1, 2 or 3 places to the left, writing zeros on the left if needed: 36.8 : 1000 = 0.0368.
Worked examples
25.2 : 6 = 4.2 (25 : 6 = 4, remainder 1, point, 12 : 6 = 2). Check: 4.2 · 6 = 25.2. 3.6 : 8 = 0.45; 7.5 : 4 = 1.875.
42.8 : 100 = 0.428 (point 2 places left); 5.3 : 1000 = 0.0053 (zeros written on the left).
Class activity
“Equal pieces”: a 7.5 m ribbon is cut into 5 equal parts. With a ruler, fold a 75 cm paper strip into 5 and compare the piece length with 7.5 : 5.
Practice
1
Calculate 18.9 : 7.
2.7
2
Calculate 0.54 : 9.
0.06
3
Calculate 53.2 : 100.
0.532
4
Why can a zero be written on the right when dividing 7.5 : 4?
7.5 = 7.50 = 7.500; a zero does not change the value.