86
Problem solving
Textbook: Part 3, lesson 86, pp. 46–48
GoalSolving fraction problems with a diagram: part of a number, the remainder, adding several parts.
New words
diagram · sxemaremainder · qolgan qismtotal · jamipart of the way · yo‘l qismi
Explanation
If a problem has a whole and its parts, draw a diagram: a segment split into as many equal parts as the denominator. Find one share (divide the whole by the denominator), then take the number of shares you need. With several parts, you can add the numerators for parts with the same denominator, or work out each part separately and add the results. Subtract from the whole to find what is left.
Worked examples
A garden of 600 m²: 2/5 is apple trees and 1/5 is pear trees. One share is 600 : 5 = 120 m²; 120 × 3 = 360 m² has fruit trees.
A 36 km route, the cyclist rode 5/12 of it: 36 : 12 = 3, 3 × 5 = 15 km; left 36 − 15 = 21 km.
Class activity
“Draw the diagram”: each pair draws a segment for a problem, marks the parts, and another pair solves the problem from the diagram.
Practice
1
A garden has area 600 m². 2/5 has apple trees and 1/5 pear trees. How many m² have fruit trees?
360
2
A library has 480 books: 1/4 are poems, 3/8 are stories and the rest are science books. How many science books are there?
180
3
The route is 36 km. A cyclist rode 5/12 of it. How many kilometres are left?
21
4
From 90 m of thread, 1/5 was used for a shirt and 1/3 for a curtain. How many metres are left?
42
5
The Tashkent–Samarkand road is about 300 km. A bus covered 3/5 of it at 60 km/h. How many hours did it drive?
3