16
Review problems
Textbook: Part 1, lesson 16, pp. 64–65
GoalReview multiplication, division, division with remainder, the distributive law and simplifying expressions.
New words
product · ko‘paytmaquotient · bo‘linmaremainder · qoldiqsimplifying · soddalashtirish
Explanation
Multiplication has the properties a · b = b · a and a · (b · c) = (a · b) · c. Division is the inverse of multiplication, and we check a result by multiplying. Division by zero is impossible. In division with remainder, dividend = divisor × incomplete quotient + remainder, and the remainder is smaller than the divisor. The distributive law lets us open brackets and take out a common factor. Simplifying an expression before solving an equation makes the work easier.
Worked examples
There were 9 rows with 35 trees each, and 5 more were planted in each row. In total 9 × (35 + 5) = 9 × 40 = 360 trees.
4x + 6x − 9 = 51 → 10x − 9 = 51 → 10x = 60 → x = 6.
Class activity
“Find the mistake”: the teacher writes 4 deliberately wrong solutions (for example 4(x + 3) = 4x + 3). Pupils find and fix the errors.
Practice
1
Find the value of 12a + 5b for a = 4, b = 6.
78
2
Compute 4 536 : 18.
252
3
A number divided by 21 gives incomplete quotient 14 and remainder 11. Find the number.
305
4
How do we check by division that 36 × 14 = 504 is correct?
504 : 14 must give 36 (or 504 : 36 must give 14).