7
Chapter I review exercises
Textbook: pp. 30–34
GoalReview Chapter I (expressions, formulas, laws, brackets) and solve mixed exercises.
New words
simplification · soddalashtirishnumerical value · son qiymatiwriting a formula · formula tuzishlike terms · o‘xshash hadlar
Explanation
To simplify an algebraic expression we first open the brackets and then combine like terms. For the numerical value it is convenient to substitute the values of the letters into the simplified expression. In a word problem we denote the unknown or given quantities by letters and build an expression or a formula. When calculating by a formula we make sure the units agree. Remembering the order of operations and the laws at every step prevents mistakes. It is useful to check the result with at least one substituted value.
Worked examples
3(2a - b) - 2(a - 4b) = 6a - 3b - 2a + 8b = 4a + 5b. For a = 1, b = -2: 4 - 10 = -6.
Aziz went shopping with a soums and bought 3 pencils (p soums each) and one notebook (q soums). The money left is a - 3p - q. For a = 10 000, p = 1200, q = 3000: 10 000 - 3600 - 3000 = 3400 soums.
Class activity
“Expression staircase”: a five-step staircase is drawn on the board, each step carrying one task (open, combine, evaluate...). A group moves up a step only after a correct answer.
Practice
1
Find the value of 3(a - b) + 2ab at a = 4, b = -1.
7
2
Simplify 5(x + 2) - (3x - 4).
2x + 14
3
A rectangle has perimeter p and base a. Express its height h by a formula.
h = p : 2 - a
4
Why is it convenient to simplify an expression before substituting numbers?
The simplified expression has fewer operations, so the calculation is faster and mistakes are less likely.