18
Calculation algorithms for the four operations
Textbook: Part 1, lesson 18, pp. 70–73
GoalKnow the rules for the order of operations (the algorithm) and evaluate expressions correctly.
New words
stage of operations · amallar bosqichialgorithm · algoritmbracket · qavsvalue of an expression · ifodaning qiymati
Explanation
Addition and subtraction are stage I; multiplication and division are stage II. Rule 1: in an expression without brackets that has operations of one stage, they are done from left to right. Rule 2: if both stages occur without brackets, do stage II first, then stage I. Rule 3: if there are brackets, do the operations inside them first. A fixed order for doing a task is called an algorithm. If the properties of operations make the work easier, we may leave the order: 37 · 8 + 13 · 8 = (37 + 13) · 8 = 400.
Worked examples
120 − 36 : 4 + 5 × 7 = 120 − 9 + 35 = 111 + 35 = 146 (first : and ×, then − and +).
(96 + 4 × 6) : 5 − 48 : 12 = (96 + 24) : 5 − 4 = 120 : 5 − 4 = 24 − 4 = 20.
Class activity
“Order numbers”: the teacher writes an expression; pupils number each operation in the order it is done, calculate and check with a partner.
Practice
1
Find the value of 250 − 12 × 5 + 45 : 9.
195
2
Compute (84 − 24) : 6 + 7 × 3.
31
3
Compute 45 × 8 + 55 × 8 in a convenient way.
800
4
Why is 8 + 2 × 5 equal to 18 and not 50?
Multiplication is a stage II operation and goes first: 2 × 5 = 10, then 8 + 10 = 18.