43
Proper and improper fractions
Textbook: Part 2, lesson 43, pp. 28–30
GoalTell proper from improper fractions; compare a fraction with 1.
New words
proper fraction · to‘g‘ri kasrimproper fraction · noto‘g‘ri kasrwhole (1) · butun (1)numerator and denominator · surat va maxraj
Explanation
A fraction whose numerator is smaller than its denominator is a proper fraction, for example 3/8. A fraction whose numerator is larger than or equal to its denominator is an improper fraction, for example 8/8 and 11/8. A fraction with equal numerator and denominator equals one whole: 8/8 = 1, because eight eighths make the whole thing. A proper fraction is always less than 1, an improper fraction is greater than or equal to 1. So every improper fraction is larger than any proper fraction. On the number ray, proper fractions lie between 0 and 1.
Worked examples
Sort 5/9, 2/2, 9/5, 1/12, 13/13: proper — 5/9 and 1/12; improper — 2/2, 9/5, 13/13. Of these, 2/2 and 13/13 each equal 1.
With denominator 6: the smallest fraction greater than 1 is 7/6; the fraction equal to 1 is 6/6; the largest fraction less than 1 is 5/6.
Class activity
“Chocolate bar”: draw a rectangle of 12 squares. Colour 7 of them (7/12), then draw another bar to show 15/12. Why did the second one need two bars?
Practice
1
Which fractions are improper: 4/9, 9/4, 9/9, 3/10?
9/4 and 9/9
2
Write 3 proper fractions with denominator 13.
For example: 1/13, 6/13, 12/13
3
What part of an hour is 45 minutes?
45/60
4
Why can an improper fraction not be less than 1?
Its numerator is not smaller than the denominator, so the shares taken are at least all the shares of the whole.