121
How division and multiplication are linked
Textbook: Part 3, lesson 114, pp. 90–91
GoalThe link between division and multiplication; finding an unknown part.
New words
inverse operations · teskari amallarunknown factor · noma’lum ko‘paytuvchiunknown dividend · noma’lum bo‘linuvchiunknown divisor · noma’lum bo‘luvchi
Explanation
Multiplication and division are inverse operations. From 7 × 8 = 56 we get 56 : 8 = 7 and 56 : 7 = 8. Unknown factor = product : known factor. Unknown dividend = quotient × divisor. Unknown divisor = dividend : quotient.
Worked examples
If x : 9 = 8 then x = 8 × 9 = 72; if 72 : y = 9 then y = 72 : 9 = 8.
A rectangle has area 36 dm² and length 9 dm: its width is 36 : 9 = 4 dm.
Class activity
“Find the inverse”: children start with “7 × 8 = 56”, write the two division equalities, then make an equation with an unknown for a partner to solve.
Practice
1
Solve: x : 9 = 8. x = ?
72
2
Solve: f × 4 = 28. f = ?
7
3
Solve: 72 : y = 9. y = ?
8
4
The first factor is 6 and the product is 54. What is the second factor?
9
5
A rectangle has area 36 dm² and length 9 dm. How many dm is its width?
4
6
After dividing by 8 the quotient is 7. What is the dividend?
56