100
Problem solving
Textbook: Part 3, lesson 100, pp. 90–92
GoalSolving multi-step problems with fractions: finding parts step by step, speed and time.
New words
multi-step problem · murakkab masalastep · bosqichcombined part · umumiy qismspeed · tezlik
Explanation
A multi-step problem needs several operations to answer the question. At each step note what we are finding. In fraction problems, drawing a diagram, finding the parts separately or adding their numerators helps. In motion problems we use S = v × t.
Worked examples
In a 40-page notebook 3/8 is written on and 1/8 has drawings: 40 : 8 × (3 + 1) = 20 pages used, 20 pages empty.
Walking at 5 km/h for 3/5 of an hour: S = 5 × 3/5 = 15/5 = 3 km.
Class activity
“Problem workshop”: groups break a fraction problem into steps, write each step on a separate card and draw a diagram, then hand it to another group to solve.
Practice
1
3/8 of a 40-page notebook is filled with writing and 1/8 with drawings. How many pages are empty?
20
2
From 12 kg of rice 1/4 was used on the first day and 1/3 on the second. How many kilograms are left?
5
3
One pipe fills 2/9 of a pool in an hour and another fills 4/9. If both work together, what part of the pool is still empty after one hour?
3/9
4
3/10 of a road is 15 km. How many kilometres is the whole road?
50
5
A walker went at 5 km/h for 3/5 of an hour. How many kilometres did he cover?
3