☰ Contents · Algebra

Review of Grades 5–6 topics

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

Review of Grades 5–6 topics

Textbook: pp. 3–5
GoalRecall percentages, rational numbers, equations, proportions and the arithmetic mean from Grades 5–6 to prepare for the algebra course.
New words
percent · foizproportion · proporsiyaarithmetic mean · o‘rta arifmetikrational number · ratsional son
Explanation

One percent is one hundredth of a number: 1% = 1/100. To find p percent of a number, multiply it by p/100; to find the whole when its percent is known, divide the part by p and multiply by 100. A proportion is an equality a : b = c : d; its basic property says that the product of the middle terms equals the product of the extreme terms: b · c = a · d. The arithmetic mean of several numbers is their sum divided by how many numbers there are. When multiplying rational numbers, equal signs give a positive result and different signs give a negative one. In a simple equation we find the unknown term by using the inverse operation.

Worked examples
15% of 240 is 240 · 15 : 100 = 36. Conversely, if 15% of a number is 36, the number is 36 : 15 · 100 = 240.
In the proportion x : 6 = 10 : 4 we get x = 6 · 10 : 4 = 15. Check: 15 : 6 = 2.5 and 10 : 4 = 2.5.
Class activity

“Discount shop”: the teacher writes the prices of 5 goods on the board. Each group draws a card with a discount (10%, 20%, 25%, 50%) and computes the new price. The fastest correct group scores a point.

Practice
1
Find 35% of 80.
2
Compute 6 · (-7) + 20 : (-4).
3
Solve the equation 3x + 12 = 4 · 6.
4
Why is the product of two negative numbers positive?