9
The basic property of a fraction
Textbook, pp. 31–33
GoalKnow the basic property of a fraction; replace a fraction by an equal one.
New words
numerator · suratdenominator · maxrajbasic property of a fraction · kasrning asosiy xossasiequal fractions · teng kasrlar
Explanation
If we multiply or divide both the numerator and the denominator of a fraction by the same natural number, the value of the fraction does not change. This is the basic property of a fraction: a/b = (a · n)/(b · n) = (a : n)/(b : n). For example 2/3 = 8/12, because the numerator and denominator were multiplied by 4. It lets us write the same quantity in different ways: half a pizza is 1/2 and also 4/8. Adding or subtracting the same number to the numerator and denominator changes the fraction, so that is not allowed.
Worked examples
Write 2/3 with denominator 12: 12 : 3 = 4, so multiply numerator and denominator by 4, giving 2/3 = 8/12.
18/24: divide numerator and denominator by 6, so 18/24 = 3/4.
Class activity
“Fraction pizzas”: several equal circles are drawn on the board and split into 2, 4, 6 and 8 equal parts. Pupils write the same shaded part as different fractions: 1/2 = 2/4 = 3/6 = 4/8.
Practice
1
3/5 = ?/20. Find the numerator.
12/20
2
15/45 = ?/3. Find the numerator.
1/3
3
Write 5/7 as a fraction with denominator 35.
25/35
4
Why can't we add 1 to the numerator and denominator of 2/3 and call it 3/4?
2/3 = 8/12 but 3/4 = 9/12. They are different numbers: adding changes the value.