☰ Contents · Mathematics

Problems with proportions. Direct and inverse proportionality

Lessons 23–24 · 2 lessons · M.A. Mirzaahmedov, A.A. Rahimqoriyev, Sh.N. Ismailov, M.A. To‘xtaxodjayeva. Mathematics Grade 6, 2nd edition. O‘qituvchi NMIU, Tashkent, 2017
23

Uses of the basic property of a proportion

Textbook, pp. 98–100
GoalUse the basic property of a proportion to solve problems.
New words
setting up a proportion · proporsiya tuzishunknown · noma’lumcorresponding quantities · mos kattaliklarprice · narx
Explanation

If two quantities in a problem depend on each other, we set up a proportion from their corresponding values. Quantities in the same unit must stand in the same places: kilograms over kilograms, soms over soms. For example if 8 notebooks cost 24,000 soms, 5 notebooks cost x soms: 8 : 5 = 24,000 : x. We find the unknown with the basic property: x = 5 · 24,000 : 8 = 15,000. Then check the answer makes sense: fewer notebooks should cost less.

Worked examples
From x : 12 = 5 : 6 we get x = 12 · 5 : 6 = 10.
4 kg of apples cost 28,000 soms. For 6 kg: 4 : 6 = 28,000 : x, so x = 6 · 28,000 : 4 = 42,000 soms.
Class activity

“Market proportions”: each group makes a price list (for example 3 pencils cost 9,000 soms) and asks another group: “How much do 7 pencils cost?” The answer is found with a proportion.

Practice
1
In 3 : x = 12 : 20, find x.
2
In 9 : 4 = x : 8, find x.
3
4 kg of apples cost 28,000 soms. How many soms do 6 kg cost?
4
In 4 : 6 = 28,000 : x, why do we put kilograms over kilograms and soms over soms?