20
Finding a number from its part
Textbook, pp. 82–86
GoalFind a whole number from its given part.
New words
finding the whole · butunni topishits part · qismipercent · foizequation · tenglama
Explanation
If a/b of a number is M, the number itself is found by dividing M by a/b: N = M : a/b = M · b/a. For example, if 3/5 of a number is 18, the number is 18 : 3/5 = 18 · 5/3 = 30. Percentages work the same way: if 15% of a number is 12, the number is 12 : 15 · 100 = 80. Finding a part is done by multiplying; finding the whole is done by dividing. To avoid mixing them up, ask yourself “into how many parts was the whole divided?”.
Worked examples
If 2/7 of a number is 14, then 14 : 2/7 = 14 · 7/2 = 49. Check: 2/7 of 49 is 7 · 2 = 14.
3/8 of a road is 45 km. The whole road is 45 : 3/8 = 45 · 8/3 = 120 km.
Class activity
“The missing whole”: each group gets a task like “2/5 of a number is 16”. They draw a bar, find the size of one part and then determine the whole.
Practice
1
2/7 of a number is 14. Find the number.
49
2
3/8 of a road is 45 km. How many km is the whole road?
120
3
15% of a number is 12. Find the number.
80
4
Why do we divide the part by the fraction, rather than multiply, when finding the whole?
The part is smaller than the whole. If a/b of N is M, then M = N · a/b, so N = M : a/b.