24
Problems about parts
Textbook: Part 1, lesson 24, pp. 96–97
GoalSolve “how many times more/less” and parts problems with a diagram and the one-part method.
New words
part · qismtimes as many · marta ko‘ptimes fewer · marta kamone-part method · bir qism usuli
Explanation
If one quantity is 3 times another, take the smaller as 1 part and the larger as 3 parts; the total is 1 + 3 = 4 parts. Divide the total by the number of parts to find the size of one part, then multiply by the number of parts needed. In the same way, in “2 parts yellow and 3 parts blue” the total is 5 parts. If a whole is split into several equal parts, one part is taken and the rest is known, divide the rest by the number of remaining parts to find one part. A diagram of segments shows the meaning of the problem.
Worked examples
Two rolls hold 120 m of cloth, the first 5 times the second. Total 1 + 5 = 6 parts, one part is 120 : 6 = 20 m. The second roll has 20 m, the first 5 × 20 = 100 m.
Sardor split a book into 4 equal parts and read one part; 45 pages remain. The remaining 3 parts = 45 pages, 1 part is 45 : 3 = 15 pages, the book has 4 × 15 = 60 pages.
Class activity
“Drawing parts”: pupils fold a long paper strip into 5 equal parts and colour one; if the strip is 30 cm they find the length of each part.
Practice
1
Two classes have 90 pupils in total, one has twice as many as the other. How many pupils are in the larger class?
60
2
Of 35 balloons the red ones are 4 times the yellow ones. How many yellow balloons?
7
3
A mix of 3 parts flour and 4 parts sugar weighs 2 100 g. How many grams of sugar?
1200
4
Why is the total 4 parts in a “3 times as many” problem?
The smaller is 1 part and the larger is 3 parts; 1 + 3 = 4.