☰ Contents · Algebra

Numerical expressions

Lessons 2 · 1 lessons · Sh.A. Alimov, O.R. Xolmuhamedov, M.A. Mirzaahmedov. Algebra, Grade 7, revised and expanded 5th edition. O‘qituvchi NMIU, Tashkent, 2017
2

Numerical expressions

Textbook: pp. 6–9
GoalFind the value of a numerical expression by following the order of operations.
New words
numerical expression · sonli ifodavalue of an expression · sonli ifodaning qiymatitrue equality · to‘g‘ri tenglikstage (level) of operations · amallar bosqichi
Explanation

Numbers, operation signs and brackets written together form a numerical expression, and the number we get after doing the operations is its value. Addition and subtraction are first-stage operations, multiplication and division are second-stage, and raising to a power is third-stage. Without brackets, the third stage is done first, then the second, and the first stage last; operations of the same stage go from left to right. With brackets, the inside is computed first, and with nested brackets we start from the innermost pair. In a fraction-like expression we find the value of the numerator and of the denominator first and then divide. Two expressions joined by “=” form a true equality when their values are equal.

Worked examples
4 + 3 · 2² - 10 : 5 = 4 + 3 · 4 - 2 = 4 + 12 - 2 = 14. First the power, then multiplication and division, last addition and subtraction.
20 - (3 + 2 · 4) · 2 = 20 - (3 + 8) · 2 = 20 - 11 · 2 = 20 - 22 = -2. Brackets first, then multiplication.
Class activity

“Operation traffic light”: a long expression is written on the board. Three pupils take turns: “red” does the brackets, “yellow” does powers and multiplication, “green” does addition and subtraction. A team that finishes without mistakes scores a point.

Practice
1
Name the stages of arithmetic operations.
2
Compute 5 + 2 · 3³ - 12 : 4.
3
Compute (2 · 4² - 7) : (3 · 2 - 1).
4
Why do 6 + 12 · 3 and (6 + 12) · 3 have different values?