22
Chapter II review problems
Textbook: Part 1, lesson 22, pp. 88–91
GoalReview Chapter II: multiplication and division, order of operations, powers, equations, diagrams.
New words
order of operations · amallar tartibipower · darajaequation · tenglamadiagram · diagramma
Explanation
Multiplication and division are inverse operations; we check one with the other. In division with remainder the remainder is smaller than the divisor. The distributive law lets us open brackets and take out a common factor. When calculating, do the inside of brackets first, then powers, then stage II and finally stage I operations. We solve a word problem with a diagram and an equation, then check the answer. Tables and diagrams show data clearly.
Worked examples
358 × 27 − 258 × 27 = (358 − 258) × 27 = 100 × 27 = 2 700.
A yard has hens and rabbits with 20 heads and 56 legs. Suppose all have 2 legs: 20 × 2 = 40; the missing 56 − 40 = 16 legs belong to rabbits (2 extra each): 16 : 2 = 8 rabbits and 20 − 8 = 12 hens.
Class activity
“Chapter championship”: teams complete one task at each of 6 stations (order of operations, powers, equations, word problem, diagram, division with remainder) and score a point for each correct answer.
Practice
1
Find the value of (12 + 8)² : 4 − 3³.
73
2
Solve 5x + 7x − 24 = 96.
10
3
Two cans hold 300 l of milk; the second holds 4 times as much as the first. How many litres are in the first can?
60
4
How do we check that 36 × 14 = 504 is correct?
By division: 504 : 14 must give 36, or 504 : 36 must give 14.