37
Rational numbers and the properties of operations on them
Textbook, pp. 172–176
GoalUnderstand rational numbers; perform operations with them and use the properties of operations.
New words
rational number · ratsional soncommutative property · o‘rin almashtirish xossasiassociative property · guruhlash xossasidistributive property · taqsimot xossasi
Explanation
A number that can be written as m/n with an integer numerator m and a natural denominator n is a rational number. Integers (7 = 7/1), common fractions, negative fractions (−3/4), decimals (0.25 = 1/4) and mixed numbers are all rational. Addition, subtraction, multiplication and division (except by zero) of rational numbers follow the sign rules for integers and the rules for fractions. The commutative, associative and distributive properties also hold for rational numbers: a + b = b + a, (a + b) + c = a + (b + c), a · (b + c) = a · b + a · c.
Worked examples
(−3/4) + 1/2 = −3/4 + 2/4 = −1/4.
(−2/3) · (9/10): the sign is negative, 2/3 · 9/10 = 18/30 = 3/5, so the answer is −3/5.
Class activity
“Rational family”: cards show numbers such as −5, 3/7, 0, −0.6, 2 1/2. Pupils write each as m/n to show that it is rational.
Practice
1
Which of −5, 3/7, 0, −0.6 are rational?
All of them
2
Compute (−3/4) + 1/2.
−1/4
3
Compute (−2/3) · (9/10).
−3/5
4
Why is every integer a rational number?
Every integer n can be written as n/1, which has the form m/n.