49
Fraction problems
Textbook: Part 2, lesson 49, pp. 50–51
GoalSolve word problems with fractions: a part of a number, the whole from its part, one number as a part of another.
New words
part of a number · sonning qismifinding the whole · butunni topishthe remaining part · qolgan qismproblem statement · masala sharti
Explanation
In a fraction problem, first decide what is known and what must be found, then draw a diagram. The whole equals 1 (or b/b). To find a/b of a number, divide it by b and multiply by a. If a/b of a number is known, divide the known amount by a and multiply by b to find the whole. To find what part one number is of another, write the first over the second as a fraction. For the remaining part, subtract the part taken from the whole (1 or b/b). Always check the answer against the statement.
Worked examples
A book has 120 pages and 3/8 was read. Read: 120 : 8 · 3 = 45 pages; remaining: 120 − 45 = 75 pages.
If 2/7 of a field is 18 ar, the whole field is 18 : 2 · 7 = 63 ar. The remaining 5/7 is 63 − 18 = 45 ar.
Class activity
“Solve with a diagram”: draw a strip, divide it into equal shares, mark the known and unknown parts, and solve the problem from the picture.
Practice
1
A book has 84 pages and 5/12 of it was read. How many pages were read?
35
2
In a class of 24 pupils, 1/3 go to sports and 1/4 to chess. How many pupils are left?
10
3
3/10 of a number is 21. Find the number.
70
4
Why do we find one share first in a «find the part» problem?
Because the whole is divided into equal shares; once we know one share, we multiply to get the required number of shares.