65
Dividing a decimal fraction by a decimal fraction
Textbook: Part 2, lesson 65, pp. 116–120
GoalDivide a decimal by a decimal; divide by 0.1, 0.01, 0.001.
New words
dividend · bo‘linuvchidivisor · bo‘luvchimoving the point · vergulni surishquotient · bo‘linma
Explanation
To divide by a decimal, move the point to the right in both the dividend and the divisor by as many places as there are digits after the point in the divisor. The divisor becomes a natural number and we divide as a decimal by a natural number. The quotient does not change, because both numbers were multiplied by the same number. For example, 7.28 : 1.3 = 72.8 : 13 = 5.6. If the dividend has too few digits, write zeros on the right: 6 : 0.4 = 60 : 4 = 15. Dividing by 0.1, 0.01 or 0.001 is the same as multiplying by 10, 100 or 1000: 5.7 : 0.01 = 570.
Worked examples
2.4 : 0.15: move the points 2 places to the right: 240 : 15 = 16. Check: 16 · 0.15 = 2.4.
A rectangle has area 7.2 cm² and one side 2.4 cm. The other side: 7.2 : 2.4 = 72 : 24 = 3 cm.
Class activity
“Cards”: write 5 division problems (for example, 3.6 : 0.9) on cards. On the back write the version with the points moved (36 : 9) and the answer, and check in pairs.
Practice
1
Calculate 9.6 : 0.8.
12
2
Calculate 0.36 : 0.12.
3
3
Calculate 4.5 : 0.25.
18
4
Why does moving the point the same number of places in both numbers not change the quotient?
Both numbers become the same number of times larger (10, 100, ... times), so the dividend is still the same number of times larger than the divisor.