79
Proper and improper fractions
Textbook: Part 3, lesson 79, pp. 25–27
GoalProper and improper fractions: comparing numerator and denominator; a fraction as division; writing 1 as a fraction.
New words
proper fraction · to‘g‘ri kasrimproper fraction · noto‘g‘ri kasrwhole · butunnumerator and denominator · surat va maxraj
Explanation
A fraction whose numerator is smaller than its denominator is a proper fraction; it is less than 1: 3/5. A fraction whose numerator is equal to or larger than its denominator is an improper fraction; it is equal to or greater than 1: 7/5, 5/5. A fraction with equal numerator and denominator equals 1: 6/6 = 1. The fraction bar also means division: 12/3 = 12 : 3 = 4.
Worked examples
3/5 is proper (3 < 5); 7/5 is improper (7 > 5); 5/5 = 1 is also improper.
A pizza is cut into 4 slices. 4/4 is a whole pizza; 6 slices are 6/4, which is more than 1.
Class activity
“Proper or improper”: fractions are written on cards. Children sort proper fractions to one side and improper ones to the other and explain why.
Practice
1
Write the improper fractions among 3/8, 8/3, 5/5, 2/9.
8/3, 5/5
2
Write 63/9 as a natural number.
7
3
Write 1 as a fraction with denominator 7.
7/7
4
Pizzas are cut into 6 equal slices. There are 9 slices on the table. Write this as a fraction with denominator 6.
9/6
5
Write the fraction with denominator 5 whose numerator is 3 more than the denominator.
8/5